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<journal-meta>
<journal-id journal-id-type="publisher-id">INFORMATICA</journal-id>
<journal-title-group><journal-title>Informatica</journal-title></journal-title-group>
<issn pub-type="epub">1822-8844</issn><issn pub-type="ppub">0868-4952</issn><issn-l>0868-4952</issn-l>
<publisher>
<publisher-name>Vilnius University</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">INFOR604</article-id>
<article-id pub-id-type="doi">10.15388/25-INFOR604</article-id>
<article-categories><subj-group subj-group-type="heading">
<subject>Research Article</subject></subj-group></article-categories>
<title-group>
<article-title>A Synthetic Decision-Support System Based on Multi-Facet Fuzzy Sets with Dynamic Parameter Settings for Next-Gen Battery Technology Investments</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Zavadskas</surname><given-names>Edmundas Kazimieras</given-names></name><email xlink:href="edmundas.zavadskas@vilniustech.lt">edmundas.zavadskas@vilniustech.lt</email><xref ref-type="aff" rid="j_infor604_aff_001">1</xref><bio>
<p><bold>E.K. Zavadskas</bold> received the PhD degree in building structures from the Vilnius Institute of Civil Engineering, Lithuania, in 1973, the DSc degree in building technology and management from the Moscow Institute of Civil Engineering, Soviet Union, in 1987. He is currently the prof. chief researcher at the Institute of Sustainable Construction, Faculty of Civil Engineering, Vilnius Gediminas Technical University, Vilnius, Lithuania. He is the founder of Vilnius Gediminas Technical University in 1990. He is the author and coauthor of more than 600 papers and a number of monographs in Lithuanian, English, German, and Russian. His research interests include multicriteria decision-making, civil engineering, sustainable development, and fuzzy multicriteria decision making. Dr. K. Zavadskas is a member of the Lithuanian Academy of Science; a member of several foreign Academies of Sciences; the Honorary doctor from Poznan, Saint-Petersburg, and Kyiv universities, a member of international organizations; a member of steering and programme committees at many international conferences; the Chairman of EURO Working Group ORSDCE; an associate editor, guest editor, or editorial board member for 40 international journals including <italic>Computers-Aided Civil and Infrastructure Engineering</italic>, <italic>Automation in Construction</italic>, <italic>Informatica</italic>, <italic>International Journal of Information Technology and Decision Making</italic>, <italic>Archives of Civil and Mechanical Engineering</italic>, <italic>International Journal of Fuzzy Systems</italic>, <italic>Symmetry</italic>, <italic>Sustainability</italic>, <italic>Applied Intelligence</italic>, <italic>Energy</italic>, <italic>Entropy</italic>, and others; the founding editor of <italic>Technological and Economic Development of Economy</italic>, <italic>Journal of Civil Engineering and Management</italic>, <italic>International Journal of Strategic Property Management</italic>. He has been a highly cited researcher in 2014, 2018, 2019, and 2020.</p></bio>
</contrib>
<contrib contrib-type="author">
<name><surname>Dinçer</surname><given-names>Hasan</given-names></name><email xlink:href="hdincer@medipol.edu.tr">hdincer@medipol.edu.tr</email><xref ref-type="aff" rid="j_infor604_aff_002">2</xref><xref ref-type="aff" rid="j_infor604_aff_003">3</xref><xref ref-type="aff" rid="j_infor604_aff_004">4</xref><xref ref-type="corresp" rid="cor1">∗</xref><bio>
<p><bold>H. Dinçer</bold> is professor of finance at Istanbul Medipol University, Faculty of Economics and Administrative Sciences, Istanbul-Turkey. Dr. Dincer has BAs in financial markets and investment management from Marmara University. He received his PhD in finance and banking with his thesis entitled ‘The Effect of Changes on the Competitive Strategies of New Service Development in the Banking Sector”. He has work experience in the finance industry as a portfolio specialist and his major academic studies focusing on financial instruments, performance evaluation, and economics. He is the executive editor of the <italic>International Journal of Finance and Banking Studies</italic> (<italic>IJFBS</italic>) and the founder member of the Society for the Study of Business and Finance (SSBF). He has about 500 scientific articles and some of them are indexed in SSCI, SCI-Expended and Scopus. In addition to them, he is also an editor of many different books published by Springer and IGI Global.</p></bio>
</contrib>
<contrib contrib-type="author">
<name><surname>Yüksel</surname><given-names>Serhat</given-names></name><email xlink:href="serhatyuksel@medipol.edu.tr">serhatyuksel@medipol.edu.tr</email><xref ref-type="aff" rid="j_infor604_aff_002">2</xref><xref ref-type="aff" rid="j_infor604_aff_003">3</xref><xref ref-type="aff" rid="j_infor604_aff_004">4</xref><bio>
<p><bold>S. Yüksel</bold> is a professor of finance in İstanbul Medipol University. Before this position, he worked as a senior internal auditor for seven years in Finansbank, Istanbul-Turkey and 1 year in Konya Food and Agriculture University as an assistant professor. Dr. Yüksel has a BS in business administration (in English) from Yeditepe University (2006) with full scholarship. He got his master degree from the economics in Boğaziçi University (2008). He also has a PhD in banking from Marmara University (2015). His research interests lie in energy economics, banking, finance and financial crisis. He has more than 500 scientific articles and some of them are indexed in SSCI, SCI, Scopus and Econlit. Also, he is the editor of some books that will be published by Springer and IGI Global.</p></bio>
</contrib>
<aff id="j_infor604_aff_001"><label>1</label>Institute of Sustainable Construction, <institution>Vilnius Gediminas Technical University</institution>, Vilnius, <country>Lithuania</country></aff>
<aff id="j_infor604_aff_002"><label>2</label>School of Business, <institution>Istanbul Medipol University</institution>, Istanbul, <country>Turkey</country></aff>
<aff id="j_infor604_aff_003"><label>3</label>Department of Economics and Management, <institution>Khazar University</institution>, Baku, <country>Azerbaijan</country></aff>
<aff id="j_infor604_aff_004"><label>4</label>Clinic of Economics, <institution>Azerbaijan State University of Economics (UNEC)</institution>, Baku, <country>Azerbaijan</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>∗</label>Corresponding author.</corresp>
</author-notes>
<pub-date pub-type="ppub"><year>2026</year></pub-date><pub-date pub-type="epub"><day>19</day><month>9</month><year>2025</year></pub-date><volume>37</volume><issue>1</issue><fpage>193</fpage><lpage>227</lpage><history><date date-type="received"><month>5</month><year>2025</year></date><date date-type="accepted"><month>9</month><year>2025</year></date></history>
<permissions><copyright-statement>© 2026 Vilnius University</copyright-statement><copyright-year>2026</copyright-year>
<license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0/">
<license-p>Open access article under the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">CC BY</ext-link> license.</license-p></license></permissions>
<abstract>
<p>New generation battery technology investments play a key role in the transition process from fossil fuels to renewable energy. The main problem related to the subject is that decision makers experience uncertainty about which of these numerous criteria affecting investment performance are prioritized. The lack of comprehensive models in the literature for systematically prioritizing these criteria creates a significant gap. The aim of this study is to determine the priority strategies to increase the performance of new generation battery technology investments. In this context, an innovative decision-making model is developed by integrating multi-facet fuzzy sets, logarithmic least-squares and WASPAS techniques. This study makes a significant contribution to the literature by prioritizing the performance indicators of new generation battery technology investments via an innovative decision-making model. The development of multi-facet fuzzy sets in this study provides an important contribution to the literature. Moreover, dynamic decision-making opportunity is provided by redefining membership degrees with different parameter sets for each scenario. This provides the opportunity to make clearer decisions based on scenarios and dynamic evaluations in complex decision-making processes. The main findings of the study indicate that circularity and compatibility with existing manufacturing infrastructure are priorities in improving the performance of these projects.</p>
</abstract>
<kwd-group>
<label>Key words</label>
<kwd>multi-facet fuzzy sets</kwd>
<kwd>dynamic parameter settings</kwd>
<kwd>synthetic evaluations</kwd>
<kwd>new generation battery technology</kwd>
<kwd>energy economics</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="j_infor604_s_001">
<label>1</label>
<title>Introduction</title>
<p>Next-generation battery technology investments refer to strategic research and development projects carried out to increase energy storage capacity and ensure environmental sustainability. These investments are of great importance, especially in the transition from fossil fuels to renewable energy (Maher and Boumaiza, <xref ref-type="bibr" rid="j_infor604_ref_016">2024</xref>). In this process, alternative technologies such as solid-state batteries, lithium-sulfur, sodium-ion and flow battery systems come to the fore. New-generation battery technologies are also very effective in achieving sustainable development goals. Battery recycling processes and circular economy applications are being developed in an integrated manner with these investments. However, new-generation battery investments also bring some challenges. In this context, there are some technical and economic obstacles such as high research costs and security risks (Plante, <xref ref-type="bibr" rid="j_infor604_ref_022">2025</xref>). In addition, dependence on critical raw materials is among the risks that need to be managed carefully. In this context, next-generation battery technology investments are considered one of the fundamental building blocks of the energy transformation. Due to this situation, these projects are considered a strategic priority by both the public and private sectors. In summary, to ensure the performance improvement of these projects, several measures must be implemented to manage these risks correctly.</p>
<p>Some criteria need to be improved systematically to increase the performance of next-generation battery technology investments. These criteria should be addressed at both technical and economic levels. Energy density is an issue that needs to be provided to achieve this goal. Increasing the amount of energy per battery is the most critical technical criterion. Cycle life and stability are also another important factors in this process. The number of charge-discharge cycles a battery can perform is directly related to the return on investment. Like this situation, charging time is also of critical importance in this process. Batteries that can be fully charged in a short time are of great importance in terms of user acceptance, especially in electric vehicles. This is necessary so that the batteries do not overheat and do not lose performance. Easy access to raw materials also increases the performance of these projects. In this context, battery production should be carried out with more sustainable and abundant materials instead of environmentally problematic metals. On the other hand, production and maintenance costs should be reduced for new technologies to be competitive. This situation contributes significantly to increasing the financial profitability of the projects. Furthermore, security risks such as fire and explosion should be minimized in new battery systems. The high security of investment projects allows more investors to focus on these projects.</p>
<p>It is necessary to determine the most important criteria in new generation battery technology investments. The fact that businesses do not have an unlimited budget when making investments forces them to make strategic decisions. Budget constraints make it impossible to improve all criteria at the same time at the highest level. Therefore, it is necessary to determine which criteria contribute more to investment performance. This helps to direct resources to the right areas (Moyo <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_018">2023</xref>). On the other hand, highlighting critical criteria allows businesses to develop priority strategies. This also plays an important role in preventing loss of time and waste of resources. Moreover, determining the most important variables reduces uncertainties and enables more effective decisions to be made. Businesses design their strategic plans more soundly according to the determined priority criteria. In addition, the risk-benefit balance can be established more accurately. With the help of this issue, issues regarding which areas are riskier or more beneficial to invest in can be clarified. The fact that there are few studies in the literature that systematically determine the most effective criteria in new generation battery technology investments is considered a research gap. This deficiency leads to various problems and uncertainties at both academic and practical levels. Businesses lack models based on measurable and prioritized criteria that can guide their investment decisions. This deficiency increases the risk of errors in strategic planning.</p>
<p>To satisfy this deficiency, this study aims to determine the priority strategies to increase the performance of next-generation battery technology investments. In this process, a new decision-making model is developed to achieve this goal. In the first stage, the evaluations for the criteria and alternatives are constructed by the synthetic assessments. The second stage is related to the weighting the criteria with case and parameter-based multi-facet fuzzy logarithmic least-squares. Finally, the alternatives are ranked by considering fuzzy weighted aggregated sum product assessment (WASPAS). New generation battery technologies are of critical importance in many areas such as electric vehicles, renewable energy systems and portable devices. However, to increase the investment performance of these technologies, some technical and economic criteria need to be systematically improved. Many criteria have an impact on increasing the performance of these investments. However, there is a lack of systematic analysis in the literature on which of these criteria are more critical. This leads to decision uncertainty for investors. On the other hand, a new decision-making model is needed to solve this problem. Existing classical methods may be insufficient to solve these complex problems. The elimination of these deficiencies can be considered as the most important motivation of the study. In this context, this study aims to determine the answers to the following questions by establishing a new decision-making model.</p>
<list>
<list-item id="j_infor604_li_001">
<label>(1)</label>
<p>What are the technical and economic criteria that most affect performance in new generation battery technology investments?</p>
</list-item>
<list-item id="j_infor604_li_002">
<label>(2)</label>
<p>What strategies should be implemented as a priority in line with existing criteria and alternatives?</p>
</list-item>
<list-item id="j_infor604_li_003">
<label>(3)</label>
<p>How does the newly developed decision-making model contribute to strategic planning in investment decisions?</p>
</list-item>
</list>
<p>This study makes a significant contribution to the literature by systematically determining the technical and economic criteria affecting performance in new generation battery technology investments and presenting an innovative decision-making model that enables the development of priority strategies. The superiorities of the proposed model are demonstrated below. (1) The development of multi-facet fuzzy sets in this study provides an important contribution to the literature. These sets are introduced as a new type of fuzzy numbers that provide dynamic decision making. The dynamic feature is the redefinition of membership degrees with different parameter sets. Moreover, each scenario or fuzzy is created differently according to its evaluations. Scenario 1 is called the negative case. The priority of this scenario penalizes uncertainty and non-membership. Scenario 2 defines the positive case that aims to provide high membership with reward engagement. On the other side, Scenario 3 proposes an unstable case with prioritized resistance and penalized low membership. Moreover, scenario 4 defines the natural case with neutral and balanced behaviour of the decision maker. (2) In addition, dynamic evaluation can be done according to the conditions in this proposed model. Therefore, dynamic parameter sets are determined with various statistical calculations. The dynamic evaluations could also be considered by computing the parameters with per-item statistics. Accordingly, four extreme conditions are defined to determine the dynamic parameters for the multi-facet fuzzy sets. Condition 1 considers the maximum variance with the largest variance. Condition 2 defines the maximum entropy with the largest entropy measurement. Condition 3 is based on the maximum resistance potential. Condition 4 is a balanced position giving the average parameter values of these three conditions. This provides an opportunity to make clearer decisions based on scenarios and dynamic evaluations in complex decision-making processes.</p>
<p>The second section of the study examines the relevant literature and reveals current approaches and research gaps. The third section presents a detailed new decision-making model developed to make investment decisions more effective. The fourth section includes analysis results for the implementation of the proposed model. The fifth section discusses the findings and provides evaluations for literature and practitioners. Finally, the sixth section summarizes the general results of the study and provides suggestions for future research.</p>
</sec>
<sec id="j_infor604_s_002">
<label>2</label>
<title>Literature Review</title>
<p>Circularity can significantly affect the performance of next-generation battery technology investments. New-generation batteries usually contain critical minerals. The circular economy approach ensures the recovery of these minerals. This contributes to the reduction of raw material dependency (Yang and Fulton, <xref ref-type="bibr" rid="j_infor604_ref_033">2023</xref>). With the help of this condition, the costs of the projects are significantly reduced. As a result of this issue, the economic sustainability of the investments can be ensured (Suhail <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_028">2024</xref>). Circular applications are important in terms of reducing waste and reducing carbon emissions. In this way, investment projects can be evaluated as environmentally friendly. Environmentally friendly projects can also access the financing resources they need much faster (Wang <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_030">2023</xref>). On the other hand, this situation is also important in terms of providing innovation in production and design processes. Kim <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_013">2024</xref>) denoted that if the battery is designed with circular economy principles, reuse can be ensured. This situation can significantly enable the cost effectiveness of the projects. According to Zhao <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_036">2024</xref>), the image of companies that prioritize circularity is developing positively in the eyes of customers. Due to this situation, these products may be preferred more by investors with high social responsibility awareness.</p>
<p>The use of alternative materials contributes to the increase in the performance of next-generation battery technology investments. Critical minerals used in battery technologies are expensive and limited resources (Şensoy, <xref ref-type="bibr" rid="j_infor604_ref_026">2023</xref>). On the other hand, alternative materials are cheaper and more abundant. This situation significantly reduces the cost of batteries. As a result of this situation, the investment payback period is significantly improved (Altiparmak <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_002">2025</xref>). The materials used in traditional batteries can be environmentally harmful. Alternative materials can have a lower carbon footprint. This situation allows the environmental pollution problem to be significantly reduced. The use of alternative materials is also necessary to reduce supply chain risk (Daniarta <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_005">2024</xref>). Most critical elements are produced in geopolitically sensitive regions. Pesaran (<xref ref-type="bibr" rid="j_infor604_ref_021">2023</xref>) identified that alternative materials allow this dependency to be reduced. This situation also contributes to the provision of supply chain security. Owing to this situation, the operational sustainability of investment projects can be increased. Furthermore, Mohseni <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_017">2023</xref>) underlined that some alternative materials can provide certain advantages such as fast charging and increased energy density. This increases the competitiveness of battery systems.</p>
<p>Compatibility with existing manufacturing infrastructure significantly affects the performance of next-generation battery technology investments. The integration of a new battery technology into existing production lines significantly reduces the need for new equipment (Shaji <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_027">2023</xref>). Owing to this situation, capital expenditures of companies are significantly reduced. In the event of incompatibility, serious infrastructure transformation costs arise. This situation negatively affects the financial performance of projects (Watabe and Leaver, <xref ref-type="bibr" rid="j_infor604_ref_031">2023</xref>). Compatible technologies can be quickly put into operation in existing production systems. As a result of this issue, the time to market of the product is shortened (Du, <xref ref-type="bibr" rid="j_infor604_ref_010">2024</xref>). Thus, companies can gain a significant competitive advantage. Moreover, Vásquez <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_029">2025</xref>) identified that this situation is also critical for ensuring operational efficiency. If existing automation systems can easily integrate with new technology, operational risks decrease and efficiency increases. Otherwise, new systems must be established to reach this objective. This situation causes significant increases in costs. Moreover, Zeng and Qu (<xref ref-type="bibr" rid="j_infor604_ref_035">2023</xref>) underlined that technologies that can be tested in existing production environments can go through processes such as error analysis at an early stage. This situation also significantly supports the reduction of uncertainties in the process.</p>
<p>The safety factor critically affects the performance of next-generation battery technology investments. It is important that new battery technologies are resistant to risks such as combustion and explosion. This situation supports the business from experiencing operational interruptions (Lyu <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_015">2023</xref>). Due to this situation, continuity of investment and operational efficiency can be ensured. Moreover, this situation also plays a critical role in reducing insurance costs (Bican <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_003">2023</xref>). Insurance premiums are lower in investments made in high-security technologies. Similarly, legal compliance can be achieved more easily, so legal costs can be reduced (Ajibade <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_001">2024</xref>). These issues also contribute significantly to strengthening financial sustainability. On the other hand, according to Dhairiyasamy <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_009">2024</xref>), safety is a fundamental parameter that needs to be developed together with innovation in battery technologies. In other words, it is very necessary to bring the safety element to the forefront in research studies. Overbeck <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_020">2023</xref>) concluded that although new technology develops, some problems occur because the safety factor is not taken into consideration. This situation also leads to an increase in financial costs.</p>
<p>The literature review results show that adopting circularity principles significantly increases the economic, environmental and operational sustainability of new generation battery technology investments. The use of alternative materials reduces costs and supports supply chain security. In addition, it is seen that technologies compatible with existing production infrastructures shorten investment payback periods and provide competitive advantage. The security factor directly affects not only operational continuity but also legal and insurance costs. However, some important deficiencies are striking in the literature. Studies on the evaluation of the interactions of these factors within a holistic model framework are limited. Moreover, there are not enough studies determining the most critical of these factors. This situation emerges as a significant deficiency in the literature on new generation battery technology investments. On the other side, while many previous studies focus on technical and economic performance indicators, they often rely on static decision-making approaches. However, these criteria are subject to high uncertainty and expert subjectivity. Therefore, a fuzzy dynamic modelling framework is essential to capture these complexities and provide more adaptable and realistic evaluations. This study addresses this gap by incorporating multi-facet fuzzy sets with dynamic membership functions.</p>
</sec>
<sec id="j_infor604_s_003">
<label>3</label>
<title>Proposed Model</title>
<p>This proposed model integrates different techniques, such as synthetic evaluations, logarithmic least-squares weighting, multi-facet fuzzy sets and WASPAS. The details of these techniques are explained in the following parts.</p>
<sec id="j_infor604_s_004">
<label>3.1</label>
<title>Synthetic Evaluations with Dynamic Multi-Facet Fuzzy Sets</title>
<p>Multi-facet fuzzy sets refer to the new concept for presenting the environmental conditions of the decision making dynamically. These new sets define five functions generated from the membership degree. Primary membership degree (<italic>μ</italic>) defines the satisfactory value as in Eq. (<xref rid="j_infor604_eq_001">1</xref>) (Rankin <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_023">2024</xref>). 
<disp-formula id="j_infor604_eq_001">
<label>(1)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo fence="true" stretchy="false">[</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" stretchy="false">]</mml:mo>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ \mu \in [0,1].\]]]></tex-math></alternatives>
</disp-formula> 
Non-membership degree identifies the level of rejection as explained in Eq. (<xref rid="j_infor604_eq_002">2</xref>): 
<disp-formula id="j_infor604_eq_002">
<label>(2)</label><alternatives><mml:math display="block">
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</mml:mtable></mml:math><tex-math><![CDATA[\[ v(\mu )=\frac{1}{1+{e^{\alpha (\mu -.5)}}}.\]]]></tex-math></alternatives>
</disp-formula> 
In this equation, <italic>α</italic> denotes control parameter. The transition steepness can be proofed by computing the first derivative in Eq. (<xref rid="j_infor604_eq_003">3</xref>): 
<disp-formula id="j_infor604_eq_003">
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<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
<mml:mo fence="true" stretchy="false">]</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ \frac{dv}{d\mu }=\frac{\alpha {e^{\alpha (\mu -.5)}}}{{[1+{e^{\alpha (\mu -.5)}}]^{2}}}.\]]]></tex-math></alternatives>
</disp-formula> 
The maximum slope can be calculated at <inline-formula id="j_infor604_ineq_001"><alternatives><mml:math>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn></mml:math><tex-math><![CDATA[$\mu =.5$]]></tex-math></alternatives></inline-formula> as by using Eqs. (<xref rid="j_infor604_eq_004">4</xref>) and (<xref rid="j_infor604_eq_005">5</xref>). <disp-formula-group id="j_infor604_dg_001">
<disp-formula id="j_infor604_eq_004">
<label>(4)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mfenced separators="" open="" close="|">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mo>−</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {\left.\frac{dv}{d\mu }\right|_{\mu =.5}}=-\frac{\alpha }{4},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_005">
<label>(5)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:munder>
<mml:mrow>
<mml:mo movablelimits="false">lim</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo stretchy="false">→</mml:mo>
<mml:mi>∞</mml:mi>
</mml:mrow>
</mml:munder>
<mml:mi mathvariant="italic">v</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mfenced separators="" open="{" close="">
<mml:mrow>
<mml:mtable columnspacing="4.0pt" equalrows="false" columnlines="none" equalcolumns="false" columnalign="left left">
<mml:mtr>
<mml:mtd class="array">
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="array">
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="array">
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal">&gt;</mml:mo>
<mml:mn>.5.</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \underset{n\to \infty }{\lim }v(\mu )=\left\{\begin{array}{l@{\hskip4.0pt}l}1,\hspace{1em}& \mu \lt .5,\\ {} .5,\hspace{1em}& \mu =.5,\\ {} 0,\hspace{1em}& \mu \gt .5.\end{array}\right.\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> In this scope, <italic>α</italic> controls the transition steepness. Equations (<xref rid="j_infor604_eq_006">6</xref>)–(<xref rid="j_infor604_eq_008">8</xref>) focus on the boundedness of non-membership degrees. <disp-formula-group id="j_infor604_dg_002">
<disp-formula id="j_infor604_eq_006">
<label>(6)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">v</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mspace width="1em"/>
<mml:mtext>at</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& v(\mu )=\frac{1}{1+{e^{\alpha (.5-.5)}}}=\frac{1}{1+{e^{0}}}=\frac{1}{2}=.5\hspace{1em}\text{at}\hspace{2.5pt}\mu =.5,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_007">
<label>(7)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">v</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mo mathvariant="normal" stretchy="false">/</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mspace width="1em"/>
<mml:mtext>as</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo stretchy="false">→</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& v(\mu )=\frac{1}{1+{e^{\alpha (1-.5)}}}=\frac{1}{1+{e^{\alpha /2}}}\in (0,1)\hspace{1em}\text{as}\hspace{2.5pt}\mu \to 1,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_008">
<label>(8)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">v</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mo mathvariant="normal" stretchy="false">/</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mspace width="1em"/>
<mml:mtext>as</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo stretchy="false">→</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& v(\mu )=\frac{1}{1+{e^{\alpha (0-.5)}}}=\frac{1}{1+{e^{-\alpha /2}}}\in (0,1)\hspace{1em}\text{as}\hspace{2.5pt}\mu \to 0.\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> The third function of multi-facet fuzzy sets <inline-formula id="j_infor604_ineq_002"><alternatives><mml:math>
<mml:mi mathvariant="italic">ϵ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$\epsilon (\mu )$]]></tex-math></alternatives></inline-formula> presents uncertainty degree as shown in Eq. (<xref rid="j_infor604_eq_009">9</xref>). 
<disp-formula id="j_infor604_eq_009">
<label>(9)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:mi mathvariant="italic">ϵ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">[</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>+</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">]</mml:mo>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ \epsilon (\mu )=-a\big[\mu \ln \mu +(1-\mu )\ln (1-\mu )\big].\]]]></tex-math></alternatives>
</disp-formula> 
In this equation, <italic>a</italic> amplifies uncertainty. The Shannon entropy <inline-formula id="j_infor604_ineq_003"><alternatives><mml:math>
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$H(\mu )$]]></tex-math></alternatives></inline-formula> satisfies the conditions in Eqs. (<xref rid="j_infor604_eq_010">10</xref>)–(<xref rid="j_infor604_eq_014">14</xref>). <disp-formula-group id="j_infor604_dg_003">
<disp-formula id="j_infor604_eq_010">
<label>(10)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& H(\mu )=-\mu \ln \mu -(1-\mu )\ln (1-\mu ),\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_011">
<label>(11)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>⩾</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="1em"/>
<mml:mtext>for</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo fence="true" stretchy="false">[</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" stretchy="false">]</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& H(\mu )\geqslant 0,\hspace{1em}\text{for}\hspace{2.5pt}\mu \in [0,1],\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_012">
<label>(12)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& H(0)=H(1)=0,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_013">
<label>(13)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo stretchy="false">≈</mml:mo>
<mml:mn>.693</mml:mn>
<mml:mspace width="1em"/>
<mml:mtext>at</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mspace width="2.5pt"/>
<mml:mtext>is maximized</mml:mtext>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& H(.5)=\ln (2)\approx .693\hspace{1em}\text{at}\hspace{2.5pt}\mu =.5,\hspace{2.5pt}H(\mu )\hspace{2.5pt}\text{is maximized},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_014">
<label>(14)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">ϵ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mspace width="1em"/>
<mml:mo stretchy="false">⇒</mml:mo>
<mml:mspace width="1em"/>
<mml:mn>0</mml:mn>
<mml:mo>⩽</mml:mo>
<mml:mi mathvariant="italic">ϵ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>⩽</mml:mo>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \epsilon (\mu )=aH(\mu )\hspace{1em}\Rightarrow \hspace{1em}0\leqslant \epsilon (\mu )\leqslant a\ln (2).\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> Equations (<xref rid="j_infor604_eq_015">15</xref>)–(<xref rid="j_infor604_eq_017">17</xref>) define the maximum uncertainty at <inline-formula id="j_infor604_ineq_004"><alternatives><mml:math>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn></mml:math><tex-math><![CDATA[$\mu =.5$]]></tex-math></alternatives></inline-formula>. <disp-formula-group id="j_infor604_dg_004">
<disp-formula id="j_infor604_eq_015">
<label>(15)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">[</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">]</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \frac{d\epsilon }{d\mu }=-a\big[\ln \mu -\ln (1-\mu )\big],\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_016">
<label>(16)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mspace width="1em"/>
<mml:mo stretchy="false">⇒</mml:mo>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \ln \mu =\ln (1-\mu )\hspace{1em}\Rightarrow \hspace{1em}\mu =.5,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_017">
<label>(17)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">(</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>+</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">)</mml:mo>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \frac{{d^{2}}\epsilon }{d{\mu ^{2}}}=-a\bigg(\frac{1}{\mu }+\frac{1}{1-\mu }\bigg)\lt 0.\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> The fourth function of multi-facet fuzzy sets <inline-formula id="j_infor604_ineq_005"><alternatives><mml:math>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$n(\mu )$]]></tex-math></alternatives></inline-formula> can be defined in Eq. (<xref rid="j_infor604_eq_018">18</xref>): 
<disp-formula id="j_infor604_eq_018">
<label>(18)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ n(\mu )={\mu ^{\delta }}.\]]]></tex-math></alternatives>
</disp-formula> 
In this process, <italic>δ</italic> is a nonlinear engagement parameter. The calculation process of this parameter is indicated in Eqs. (<xref rid="j_infor604_eq_019">19</xref>)–(<xref rid="j_infor604_eq_021">21</xref>). <disp-formula-group id="j_infor604_dg_005">
<disp-formula id="j_infor604_eq_019">
<label>(19)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mtext>For</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo fence="true" stretchy="false">[</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" stretchy="false">]</mml:mo>
<mml:mspace width="1em"/>
<mml:mtext>and</mml:mtext>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo mathvariant="normal">&gt;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="1em"/>
<mml:mtext>If</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>:</mml:mo>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \text{For}\hspace{2.5pt}\mu \in [0,1]\hspace{1em}\text{and}\hspace{1em}\delta \gt 1,\hspace{1em}\text{If}\hspace{2.5pt}\mu =0:\hspace{1em}n(\mu )={0^{\delta }}=0,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_020">
<label>(20)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mtext>If</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>:</mml:mo>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \text{If}\hspace{2.5pt}\mu =1:\hspace{1em}n(\mu )={1^{\delta }}=1,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_021">
<label>(21)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mtext>For</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mspace width="1em"/>
<mml:mtext>and</mml:mtext>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo mathvariant="normal">&gt;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="2.5pt"/>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>⩽</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo fence="true" stretchy="false">[</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" stretchy="false">]</mml:mo>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \text{For}\hspace{2.5pt}0\lt \mu \lt 1\hspace{1em}\text{and}\hspace{1em}\delta \gt 1,\hspace{2.5pt}{\mu ^{\delta }}\leqslant \mu ,\hspace{2.5pt}n(\mu )\in [0,1].\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> Equations (<xref rid="j_infor604_eq_022">22</xref>) and (<xref rid="j_infor604_eq_023">23</xref>) highlight <italic>δ</italic> parameter impact and convexity. <disp-formula-group id="j_infor604_dg_006">
<disp-formula id="j_infor604_eq_022">
<label>(22)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \frac{dn}{d\mu }=\delta {\mu ^{\delta -1}},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_023">
<label>(23)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \frac{{d^{2}}n}{d{\mu ^{2}}}=\delta (\delta -1){\mu ^{\delta -2}},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> where if <inline-formula id="j_infor604_ineq_006"><alternatives><mml:math>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo mathvariant="normal">&gt;</mml:mo>
<mml:mn>1</mml:mn></mml:math><tex-math><![CDATA[$\delta \gt 1$]]></tex-math></alternatives></inline-formula>, it means the high membership and accelerating growth with convexity. If <inline-formula id="j_infor604_ineq_007"><alternatives><mml:math>
<mml:mi mathvariant="italic">δ</mml:mi>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mn>1</mml:mn></mml:math><tex-math><![CDATA[$\delta \lt 1$]]></tex-math></alternatives></inline-formula>, membership degree has the low and decelerating growth with concave.</p>
<p>The final function of the proposed fuzzy sets shows information about the cognitive or contextual resistance. Resistance function <inline-formula id="j_infor604_ineq_008"><alternatives><mml:math>
<mml:mi mathvariant="italic">ρ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$\rho (\mu )$]]></tex-math></alternatives></inline-formula> is indicated in Eqs. (<xref rid="j_infor604_eq_024">24</xref>)–(<xref rid="j_infor604_eq_027">27</xref>). <disp-formula-group id="j_infor604_dg_007">
<disp-formula id="j_infor604_eq_024">
<label>(24)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">ρ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \rho (\mu )=1-{(1-\mu )^{\varphi }},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_025">
<label>(25)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mtext>For</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo fence="true" stretchy="false">[</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" stretchy="false">]</mml:mo>
<mml:mspace width="1em"/>
<mml:mtext>and</mml:mtext>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">φ</mml:mi>
<mml:mo mathvariant="normal">&gt;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="1em"/>
<mml:mtext>If</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>:</mml:mo>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">ρ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \text{For}\hspace{2.5pt}\mu \in [0,1]\hspace{1em}\text{and}\hspace{1em}\varphi \gt 1,\hspace{1em}\text{If}\hspace{2.5pt}\mu =0:\hspace{1em}\rho (\mu )=1-{1^{\varphi }}=0,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_026">
<label>(26)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mtext>If</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>:</mml:mo>
<mml:mspace width="1em"/>
<mml:mi mathvariant="italic">ρ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \text{If}\hspace{2.5pt}\mu =1:\hspace{1em}\rho (\mu )=1-{0^{\varphi }}=1,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_027">
<label>(27)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mtext>For</mml:mtext>
<mml:mspace width="2.5pt"/>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="2.5pt"/>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mspace width="1em"/>
<mml:mo stretchy="false">⇒</mml:mo>
<mml:mspace width="1em"/>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mi mathvariant="italic">ρ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">&lt;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="2.5pt"/>
<mml:mi mathvariant="italic">ρ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mo fence="true" stretchy="false">[</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" stretchy="false">]</mml:mo>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \text{For}\hspace{2.5pt}0\lt \mu \lt 1,\hspace{2.5pt}0\lt {(1-\mu )^{\varphi }}\lt 1\hspace{1em}\Rightarrow \hspace{1em}0\lt \rho (\mu )\lt 1,\hspace{2.5pt}\rho (\mu )\in [0,1].\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> Behaviour analysis of resistance function is given in Eqs. (<xref rid="j_infor604_eq_028">28</xref>) and (<xref rid="j_infor604_eq_029">29</xref>). <disp-formula-group id="j_infor604_dg_008">
<disp-formula id="j_infor604_eq_028">
<label>(28)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">φ</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \frac{d\rho }{d\mu }=\varphi {(1-\mu )^{\varphi -1}},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_029">
<label>(29)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>=</mml:mo>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">φ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">φ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \frac{{d^{2}}\rho }{d{\mu ^{2}}}=-\varphi (\varphi -1){(1-\mu )^{\varphi -2}}.\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group></p>
<p>Generalized presentation of the dynamic multi-facet fuzzy sets is explained in Eqs. (<xref rid="j_infor604_eq_049">A.1</xref>) and (<xref rid="j_infor604_eq_050">A.2</xref>) where <italic>A</italic> refers to the dynamic multi-facet fuzzy set (DMFFS), the functions are indicated with <inline-formula id="j_infor604_ineq_009"><alternatives><mml:math>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$\mu (x)$]]></tex-math></alternatives></inline-formula>, <inline-formula id="j_infor604_ineq_010"><alternatives><mml:math>
<mml:mi mathvariant="italic">v</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$v(\mu (x))$]]></tex-math></alternatives></inline-formula>, <inline-formula id="j_infor604_ineq_011"><alternatives><mml:math>
<mml:mi mathvariant="italic">ϵ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$\epsilon (\mu (x))$]]></tex-math></alternatives></inline-formula>, <inline-formula id="j_infor604_ineq_012"><alternatives><mml:math>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$n(\mu (x))$]]></tex-math></alternatives></inline-formula>, <inline-formula id="j_infor604_ineq_013"><alternatives><mml:math>
<mml:mi mathvariant="italic">ρ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$\rho (\mu (x))$]]></tex-math></alternatives></inline-formula>. General operation rules of DMFFS are detailed in Eqs. (<xref rid="j_infor604_eq_051">A.3</xref>)–(<xref rid="j_infor604_eq_056">A.8</xref>). In this study, 4 unique scenarios are proposed named “Negative”, “Positive”, “Unstable”, “Natural”. Scenario 1 is called as “Negative Case”. The priority of this scenario penalizes uncertainty and non-membership as defined in Eq. (<xref rid="j_infor604_eq_057">A.9</xref>). Scenario 2 defines “Positive Case”. It aims to provide high membership with reward engagement as shown in Eq. (<xref rid="j_infor604_eq_058">A.10</xref>). Scenario 3 proposes “Unstable Case” with prioritized resistance and penalized low membership as in Eq. (<xref rid="j_infor604_eq_059">A.11</xref>). Scenario 4 defines “Natural Case” with neutral and balanced behaviour of the decision maker. In this scenario, it is assumed that there are no environmental effects as indicated in Eq. (<xref rid="j_infor604_eq_060">A.12</xref>). Condition 1 considers the maximum variance with the largest variance <inline-formula id="j_infor604_ineq_014"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">σ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\sigma _{i}}$]]></tex-math></alternatives></inline-formula>. Condition 2 defines the maximum entropy <inline-formula id="j_infor604_ineq_015"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${H_{i}}$]]></tex-math></alternatives></inline-formula> with the largest entropy measurement. Condition 3 is based on the maximum resistance potential (<inline-formula id="j_infor604_ineq_016"><alternatives><mml:math>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[$1-{m_{i}}$]]></tex-math></alternatives></inline-formula>). Condition 4 is a balanced position giving the average parameter values of these 3 conditions. The computations of per-item statistics are demonstrated in Eqs. (<xref rid="j_infor604_eq_030">30</xref>)–(<xref rid="j_infor604_eq_032">32</xref>). <disp-formula-group id="j_infor604_dg_009">
<disp-formula id="j_infor604_eq_030">
<label>(30)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle><mml:mstyle displaystyle="true">
<mml:mo largeop="true" movablelimits="false">∑</mml:mo></mml:mstyle>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {m_{i}}=\frac{1}{n}\sum {m_{ij}},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_031">
<label>(31)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
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</disp-formula>
<disp-formula id="j_infor604_eq_032">
<label>(32)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
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</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {H_{i}}=-\sum \frac{{\mu _{ij}}}{\textstyle\sum \mu }\ln \bigg(\frac{{\mu _{ij}}}{\textstyle\sum \mu }\bigg).\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> The dynamic parameter settings are shown in Eqs. (<xref rid="j_infor604_eq_061">A.13</xref>)–(<xref rid="j_infor604_eq_064">A.16</xref>).</p>
</sec>
<sec id="j_infor604_s_005">
<label>3.2</label>
<title>Dynamic Multi-Facet Fuzzy Logarithmic Least-Squares Weighting</title>
<p>Logarithmic least-squares weighting method is a mathematical method used to determine the weights of the criteria, especially in multi-criteria decision-making problems. In this process, based on the discrepancies obtained from the pairwise comparison matrix, the criteria weights are calculated by logarithmic regression (De Luca <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_006">2023</xref>). The first step focuses on the calculation of dependency degrees. Relation matrix (<inline-formula id="j_infor604_ineq_017"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ς</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\varsigma _{k}}$]]></tex-math></alternatives></inline-formula>) is generated via Eq. (<xref rid="j_infor604_eq_033">33</xref>). 
<disp-formula id="j_infor604_eq_033">
<label>(33)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mrow>
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</mml:mrow>
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</mml:mrow>
</mml:msub>
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<mml:mtr>
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</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ {\varsigma _{k}}=\left[\begin{array}{c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c}0\hspace{1em}& {\varsigma _{12}}\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& {\varsigma _{1n}}\\ {} {\varsigma _{21}}\hspace{1em}& 0\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& {\varsigma _{2n}}\\ {} \vdots \hspace{1em}& \vdots \hspace{1em}& \ddots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& \cdots \\ {} \vdots \hspace{1em}& \vdots \hspace{1em}& \vdots \hspace{1em}& \hspace{1em}& \ddots \hspace{1em}& \vdots \\ {} {\varsigma _{n1}}\hspace{1em}& {\varsigma _{n2}}\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& 0\end{array}\right].\]]]></tex-math></alternatives>
</disp-formula> 
The aggregated values <italic>ς</italic> are computed in the next step by Eq. (<xref rid="j_infor604_eq_034">34</xref>). 
<disp-formula id="j_infor604_eq_034">
<label>(34)</label><alternatives><mml:math display="block">
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</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:munderover>
<mml:msub>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
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<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="2.45em" minsize="2.45em">)</mml:mo>
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<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}\varsigma & =\bigg({\bigcup \limits_{i=1}^{k}}{\varsigma _{i}}\bigg)\\ {} & =\displaystyle \Bigg\{\Bigg(x,\frac{1}{k}{\sum \limits_{i=1}^{k}}{\mu _{{\varsigma _{i}}}}(x),\frac{1}{k}{\sum \limits_{i=1}^{k}}{v_{{\varsigma _{i}}}}(x),\frac{1}{k}{\sum \limits_{i=1}^{k}}{\epsilon _{{\varsigma _{i}}}}(x),\frac{1}{k}{\sum \limits_{i=1}^{k}}{n_{{\varsigma _{i}}}}(x),\frac{1}{k}{\sum \limits_{i=1}^{k}}{\rho _{{\varsigma _{i}}}}(x)\Bigg)\hspace{0.1667em}\Big|\hspace{0.1667em}x\in X\Bigg\}.\end{aligned}\]]]></tex-math></alternatives>
</disp-formula> 
Defuzzified values (<inline-formula id="j_infor604_ineq_018"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${N_{ij}}$]]></tex-math></alternatives></inline-formula>) are generated with Eqs. (<xref rid="j_infor604_eq_036">36</xref>)–(<xref rid="j_infor604_eq_038">38</xref>). <disp-formula-group id="j_infor604_dg_010">
<disp-formula id="j_infor604_eq_035">
<label>(35)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">D</mml:mi>
<mml:mi mathvariant="italic">R</mml:mi>
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<mml:mtable columnspacing="4.0pt 4.0pt 4.0pt 4.0pt 4.0pt" equalrows="false" columnlines="none none none none none" equalcolumns="false" columnalign="center center center center center center">
<mml:mtr>
<mml:mtd class="array">
<mml:mn>0</mml:mn>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>12</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋯</mml:mo>
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<mml:msub>
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</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>21</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
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<mml:mtr>
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</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋯</mml:mo>
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</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& DR=\left[\begin{array}{c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c}0\hspace{1em}& {N_{12}}\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& {N_{1n}}\\ {} {N_{21}}\hspace{1em}& 0\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& {N_{2n}}\\ {} \vdots \hspace{1em}& \vdots \hspace{1em}& \ddots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& \cdots \\ {} \vdots \hspace{1em}& \vdots \hspace{1em}& \vdots \hspace{1em}& \hspace{1em}& \ddots \hspace{1em}& \vdots \\ {} {N_{n1}}\hspace{1em}& {N_{n2}}\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& 0\end{array}\right],\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_036">
<label>(36)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:munderover accentunder="false" accent="false">
<mml:mrow>
<mml:mstyle displaystyle="true">
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</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:munderover>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:msub>
<mml:msub>
<mml:mrow>
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<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
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<mml:msub>
<mml:mrow>
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<mml:mrow>
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<mml:msub>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:msub>
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</mml:mrow>
<mml:mrow>
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<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
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<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
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<mml:mrow>
<mml:msub>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ς</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {N_{ij}}={\sum \limits_{n=1}^{5}}{w_{1}}{\mu _{{\varsigma _{ij}}}}+{w_{2}}(1-{v_{{\varsigma _{ij}}}})+{w_{3}}(1-{\epsilon _{{\varsigma _{ij}}}})+{w_{4}}{n_{{\varsigma _{ij}}}}+{w_{5}}{\rho _{{\varsigma _{ij}}}},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_037">
<label>(37)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
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<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">β</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="2em"/>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">S</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
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<mml:mrow>
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</mml:mrow>
</mml:msub>
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<mml:mfrac>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
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<mml:msub>
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</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">S</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mspace width="2em"/>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">S</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {w_{1}}=\frac{\beta }{S},\hspace{2em}{w_{2}}=\frac{\alpha }{S},\hspace{2em}{w_{3}}=\frac{a}{S},\hspace{2em}{w_{4}}=\frac{\delta }{S},\hspace{2em}{w_{5}}=\frac{\varphi }{S},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_038">
<label>(38)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">S</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">β</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi mathvariant="italic">δ</mml:mi>
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<mml:mi mathvariant="italic">φ</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& S=\beta +\alpha +a+\delta +\varphi ,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> where <italic>β</italic> is baseline membership. In the final part, equations (<xref rid="j_infor604_eq_039">39</xref>)–(<xref rid="j_infor604_eq_042">42</xref>) are considered to compute the criteria weights. <disp-formula-group id="j_infor604_dg_011">
<disp-formula id="j_infor604_eq_039">
<label>(39)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
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<mml:mi mathvariant="italic">w</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:munderover accentunder="false" accent="false">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:mo largeop="true" movablelimits="false">∑</mml:mo></mml:mstyle>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
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</mml:mrow>
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<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
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<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& \Phi (w)={\sum \limits_{i=1}^{n}}{\sum \limits_{j=1}^{n}}{\big(\ln {a_{ij}}-(\ln {w_{i}}-\ln {w_{j}})\big)^{2}},\hspace{1em}\text{subject to}\hspace{2.5pt}\sum \limits_{i}{w_{i}}=1,\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_040">
<label>(40)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
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</mml:mrow>
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</mml:mrow>
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</mml:mrow>
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</mml:mrow>
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</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {x_{k}}=\frac{1}{n}{\sum \limits_{i=1}^{n}}{b_{ki}},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_041">
<label>(41)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
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<mml:mtd class="align-even">
<mml:msub>
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</mml:mrow>
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<mml:msub>
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</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>−</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
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</mml:mrow>
<mml:mrow>
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<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {b_{ki}}=\frac{\ln {a_{ki}}-\ln {a_{ik}}}{2},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_042">
<label>(42)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
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<mml:mrow>
<mml:msup>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
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<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mrow>
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<mml:mrow>
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</mml:mrow>
<mml:mrow>
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<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">l</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {W_{k}}=\frac{{e^{{x_{k}}}}}{{\textstyle\textstyle\sum _{l=1}^{n}}{e^{{x_{l}}}}}.\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group></p>
</sec>
<sec id="j_infor604_s_006">
<label>3.3</label>
<title>Dynamic Multi-Facet Fuzzy WASPAS</title>
<p>WASPAS is a decision-making method used to solve multi-criteria decision-making problems (Chakraborty and Zavadskas, <xref ref-type="bibr" rid="j_infor604_ref_004">2014</xref>; Kutlu Gundogdu and Kahraman, <xref ref-type="bibr" rid="j_infor604_ref_014">2019</xref>). In this process, the aim is to rank the alternatives effectively (Deb <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_007">2023</xref>). Techniques such as simple additive weighting (SAW) and weighted product model (WPM) are integrated in the analysis stages (Zavadskas <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_034">2012</xref>; Yalcin Kavus <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_032">2023</xref>). This study integrates this technique with dynamic multi-facet fuzzy sets. The evaluations are obtained from the expert team in the first stage. After that, Eq. (<xref rid="j_infor604_eq_043">43</xref>) is considered to create decision matrix. 
<disp-formula id="j_infor604_eq_043">
<label>(43)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mfenced separators="" open="[" close="]">
<mml:mrow>
<mml:mtable columnspacing="4.0pt 4.0pt 4.0pt 4.0pt 4.0pt" equalrows="false" columnlines="none none none none none" equalcolumns="false" columnalign="center center center center center center">
<mml:mtr>
<mml:mtd class="array">
<mml:mn>0</mml:mn>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>12</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋯</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
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</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋯</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>21</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mn>0</mml:mn>
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<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
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<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
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</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋯</mml:mo>
<mml:mspace width="1em"/>
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</mml:mtd>
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<mml:mtr>
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</mml:mtd>
<mml:mtd class="array">
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋱</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mo>⋮</mml:mo>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋯</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mo stretchy="false">⋯</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd class="array">
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ {X_{k}}=\left[\begin{array}{c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c@{\hskip4.0pt}c}0\hspace{1em}& {X_{12}}\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& {X_{1m}}\\ {} {X_{21}}\hspace{1em}& 0\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& {X_{2m}}\\ {} \vdots \hspace{1em}& \vdots \hspace{1em}& \ddots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& \cdots \\ {} \vdots \hspace{1em}& \vdots \hspace{1em}& \vdots \hspace{1em}& \hspace{1em}& \ddots \hspace{1em}& \vdots \\ {} {X_{n1}}\hspace{1em}& {X_{n2}}\hspace{1em}& \cdots \hspace{1em}& \hspace{1em}& \cdots \hspace{1em}& 0\end{array}\right].\]]]></tex-math></alternatives>
</disp-formula> 
The normalized values are computed via Eq. (<xref rid="j_infor604_eq_044">44</xref>): 
<disp-formula id="j_infor604_eq_044">
<label>(44)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">r</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mo movablelimits="false">max</mml:mo>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ {r_{ij}}=\frac{{X_{ij}}}{\max }({X_{ij}}).\]]]></tex-math></alternatives>
</disp-formula> 
Equation (<xref rid="j_infor604_eq_045">45</xref>) is used to generate weighted values. 
<disp-formula id="j_infor604_eq_045">
<label>(45)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>×</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">r</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ {v_{ij}}={w_{ij}}\times {r_{ij}}.\]]]></tex-math></alternatives>
</disp-formula> 
The values of SAW <inline-formula id="j_infor604_ineq_019"><alternatives><mml:math>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">SAW</mml:mtext>
</mml:mrow>
</mml:msubsup></mml:math><tex-math><![CDATA[${Q_{i}^{\textit{SAW}}}$]]></tex-math></alternatives></inline-formula> and WPM <inline-formula id="j_infor604_ineq_020"><alternatives><mml:math>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">WPM</mml:mtext>
</mml:mrow>
</mml:msubsup></mml:math><tex-math><![CDATA[${Q_{i}^{\textit{WPM}}}$]]></tex-math></alternatives></inline-formula> are computed with Eqs. (<xref rid="j_infor604_eq_046">46</xref>) and (<xref rid="j_infor604_eq_047">47</xref>). <disp-formula-group id="j_infor604_dg_012">
<disp-formula id="j_infor604_eq_046">
<label>(46)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">SAW</mml:mtext>
</mml:mrow>
</mml:msubsup>
<mml:mo>=</mml:mo>
<mml:munderover accentunder="false" accent="false">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:mo largeop="true" movablelimits="false">∑</mml:mo></mml:mstyle>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
</mml:munderover>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {Q_{i}^{\textit{SAW}}}={\sum \limits_{j=1}^{m}}{v_{ij}},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_047">
<label>(47)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">WPM</mml:mtext>
</mml:mrow>
</mml:msubsup>
<mml:mo>=</mml:mo>
<mml:munderover accentunder="false" accent="false">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:mo largeop="true" movablelimits="false">∏</mml:mo></mml:mstyle>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
</mml:munderover>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">r</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msubsup>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {Q_{i}^{\textit{WPM}}}={\prod \limits_{j=1}^{m}}{r_{ij}^{{w_{ij}}}}.\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
</disp-formula-group> Equation (<xref rid="j_infor604_eq_048">48</xref>) is taken into consideration to define the combining scores <inline-formula id="j_infor604_ineq_021"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${Q_{i}}$]]></tex-math></alternatives></inline-formula>. These values are used for alternative ranking. 
<disp-formula id="j_infor604_eq_048">
<label>(48)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">SAW</mml:mtext>
</mml:mrow>
</mml:msubsup>
<mml:mo>+</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">WPM</mml:mtext>
</mml:mrow>
</mml:msubsup>
<mml:mo>.</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[ {Q_{i}}=\gamma {Q_{i}^{\textit{SAW}}}+(1-\gamma ){Q_{i}^{\textit{WPM}}}.\]]]></tex-math></alternatives>
</disp-formula>
</p>
</sec>
</sec>
<sec id="j_infor604_s_007">
<label>4</label>
<title>Analysis Results</title>
<p>The proposed model has three different stages. The details of these stages are given in the following subsections. Briefly, to enhance readability, the intermediary computational results, including parameter-based multi-facet fuzzy numbers, per-item statistics, and normalized matrices, are presented in Appendix <xref rid="j_infor604_app_002">B</xref> (Tables <xref rid="j_infor604_tab_007">A.1</xref>– <xref rid="j_infor604_tab_031">A.25</xref>). This structure ensures that the main manuscript remains focused on key findings while preserving full transparency and reproducibility. Table <xref rid="j_infor604_tab_002">2</xref> and <xref rid="j_infor604_tab_003">3</xref> give information about the linguistic evaluations from the expert. Table <xref rid="j_infor604_tab_004">4</xref> provides a comparison of the criteria weights obtained through both case-based assessments and parameter-based assessments. The similarity between these weighting results demonstrates the internal consistency and reliability of the proposed model. It is observed that circularity (CRCLT) and compatibility with existing manufacturing infrastructure (CWEMI) have the highest weights, indicating their critical role in next-generation battery technology investments. Table <xref rid="j_infor604_tab_005">5</xref> presents the final rankings of the alternatives based on the aggregated multi-facet fuzzy WASPAS results. In this ranking process, both SAW (Simple Additive Weighting) and WASPAS components are integrated to provide a balanced evaluation of the alternatives. The aggregation is performed by combining the weighted normalized performance values obtained from the parameter-based assessments. The final ranking reflects the comprehensive performance of each alternative under dynamic conditions.</p>
<p>According to the final results, energy production in extreme weather conditions (EPEWC) is identified as the most critical investment alternative for next-generation battery technologies. This finding underscores the growing importance of resilient energy solutions in response to climate change and unpredictable environmental conditions. Early-stage biotech startups (ESBST) and electric vehicles with higher energy density (EVWHD) also emerge as significant alternatives, reflecting the technological advancements and strategic priorities within the sector.</p>
<sec id="j_infor604_s_008">
<label>4.1</label>
<title>Constructing the Evaluations for the Criteria and Alternatives by the Synthetic Assessments</title>
<p>In the first stage, the initial expert evaluations for the criteria and alternatives are collected. For this purpose, the scales in Table <xref rid="j_infor604_tab_001">1</xref> are taken into consideration.</p>
<table-wrap id="j_infor604_tab_001">
<label>Table 1</label>
<caption>
<p>Evaluation scales and multi-facet fuzzy numbers by initial and case-based expert choices.</p>
</caption>
<table>
<thead>
<tr>
<td rowspan="2" style="vertical-align: middle; text-align: left; border-top: solid thin; border-bottom: solid thin">Scales</td>
<td rowspan="2" style="vertical-align: middle; text-align: left; border-top: solid thin; border-bottom: solid thin">Linguistic evaluations</td>
<td rowspan="2" style="vertical-align: middle; text-align: left; border-top: solid thin; border-bottom: solid thin">Fuzzy membership</td>
<td colspan="4" style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">Multi-facet fuzzy numbers</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Negative</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Positive</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Unstable</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Natural (Initial)</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">Extremely Low (EL)</td>
<td style="vertical-align: top; text-align: left">.1</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_022"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.98</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.10,.98,1.00,.10,.10)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_023"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.14</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.10,.60,.14,.00,.10)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_024"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.10</mml:mn>
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<mml:mn>.37</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.65</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.10,.60,.37,.10,.65)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_025"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.14</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.10</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.10</mml:mn>
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</tr>
<tr>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">Very Low (VL)</td>
<td style="vertical-align: top; text-align: left">.2</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_026"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.95</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.20,.95,1.00,.20,.20)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_027"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.57</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.14</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.20</mml:mn>
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<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_028"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.57</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.47</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.89</mml:mn>
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<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_029"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.20</mml:mn>
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<mml:mn>.57</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.14</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.20</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.20,.57,.14,.20,.20)$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">Low (L)</td>
<td style="vertical-align: top; text-align: left">.3</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_030"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.88</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.30,.88,1.00,.30,.30)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_031"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.30</mml:mn>
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<mml:mn>.55</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.11</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.30,.55,.11,.00,.30)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_032"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.55</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.47</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.97</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.30,.55,.47,.30,.97)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_033"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.55</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.11</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.30</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
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</tr>
<tr>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">Moderately Low (ML)</td>
<td style="vertical-align: top; text-align: left">.4</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_034"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.73</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.40,.73,1.00,.40,.40)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_035"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.52</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.06</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.01</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.40,.52,.06,.01,.40)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_036"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.52</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.43</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.99</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.40,.52,.43,.40,.99)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_037"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.52</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.06</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.40,.52,.06,.40,.40)$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">Neutral (N)</td>
<td style="vertical-align: top; text-align: left">.5</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_038"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.50,.50,1.00,.50,.50)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_039"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.03</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.50,.50,.00,.03,.50)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_040"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.35</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.50,.50,.35,.50,1.00)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_041"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.50</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.50,.50,.00,.50,.50)$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">6</td>
<td style="vertical-align: top; text-align: left">Moderately High (MH)</td>
<td style="vertical-align: top; text-align: left">.6</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_042"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.27</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.60,.27,1.00,.60,.60)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_043"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.48</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.08</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.60,.48,.00,.08,.60)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_044"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.48</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.25</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.60,.48,.25,.60,1.00)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_045"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.48</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.60</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.60,.48,.00,.60,.60)$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">7</td>
<td style="vertical-align: top; text-align: left">High (H)</td>
<td style="vertical-align: top; text-align: left">.7</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_046"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.12</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.89</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.70,.12,.89,.70,.70)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_047"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.45</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.17</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.70,.45,.00,.17,.70)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_048"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.45</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.14</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.70,.45,.14,.70,1.00)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_049"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.45</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.70</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.70,.45,.00,.70,.70)$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">8</td>
<td style="vertical-align: top; text-align: left">Very High (VH)</td>
<td style="vertical-align: top; text-align: left">.8</td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_050"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.05</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.57</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.80,.05,.57,.80,.80)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_051"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.43</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.33</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.80,.43,.00,.33,.80)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_052"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.43</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.04</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.80,.43,.04,.80,1.00)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left"><inline-formula id="j_infor604_ineq_053"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.43</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.80</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.80,.43,.00,.80,.80)$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">9</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Extremely High (EH)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.9</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_054"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.02</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.24</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.90,.02,.24,.90,.90)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_055"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.59</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.90,.40,.00,.59,.90)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_056"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1.00</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.90,.40,.00,.90,1.00)$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_057"><alternatives><mml:math>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.40</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.00</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>.90</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo></mml:math><tex-math><![CDATA[$(.90,.40,.00,.90,.90)$]]></tex-math></alternatives></inline-formula></td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Table <xref rid="j_infor604_tab_001">1</xref> shows the evaluation scales and multi-way fuzzy numbers. The scales include linguistic evaluations ranging from “Extremely Low” to “Extremely High”. In this process, the fuzzy membership values and multi-way fuzzy numbers are shown for each scale. This table details the numerical values for different situations such as positive, negative, undecided and neutral. One decision maker who is an expert in the field of renewable energy and project management with 20-year experience is assigned for assessing the criteria and alternatives with linguistic evaluations. These evaluations are defined initial expert assessments and then they are converted to the multi-facet fuzzy numbers by initial and different scenarios. Criteria for assessing next-generation battery technology investments are defined as circularity (CRCLT), use of alternative materials (UAMTR), compatibility with existing manufacturing infrastructure (CWEMI), safety (SFETY), synergy with hybrid systems (SWHYS). These criteria are selected based on the literature review results. Table <xref rid="j_infor604_tab_002">2</xref> gives information about the initial expert linguistic evaluations for the criteria.</p>
<p>In this study, expert evaluations were conducted to assess both the criteria and alternatives for next-generation battery technology investments. A domain expert with over 20 years of experience in renewable energy technologies and project management provided the linguistic assessments. This expert was selected based on their extensive professional background, ensuring informed and context-specific evaluations. To address potential concerns regarding subjectivity from using a single expert, the analysis incorporates multiple scenario-based assessments (Negative, Positive, Unstable, Natural) and dynamic parameter adjustments based on statistical indicators derived from the evaluation matrices. This approach increases the robustness of the results by considering different uncertainty conditions and testing the consistency of the findings across varied scenarios. While this study focuses on methodological development and applies an exploratory, expert-driven evaluation, future research is encouraged to involve larger expert groups and apply consensus-based fuzzy decision-making techniques to enhance generalizability.</p>
<table-wrap id="j_infor604_tab_002">
<label>Table 2</label>
<caption>
<p>Initial expert linguistic evaluations for the criteria.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">MH</td>
<td style="vertical-align: top; text-align: left">EH</td>
<td style="vertical-align: top; text-align: left">VH</td>
<td style="vertical-align: top; text-align: left">N</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">ML</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">VH</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">MH</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">N</td>
<td style="vertical-align: top; text-align: left">EH</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">N</td>
<td style="vertical-align: top; text-align: left">EH</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">N</td>
<td style="vertical-align: top; text-align: left">ML</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">EH</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">EH</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">H</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">MH</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">N</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
</tr>
</tbody>
</table>
</table-wrap>
<p>Table <xref rid="j_infor604_tab_002">2</xref> gives information about the initial expert linguistic evaluations. In this process, the questions are created by comparing criteria to each other. After that, the expert makes evaluations for these questions by using 9 different scales stated in Table <xref rid="j_infor604_tab_001">1</xref>. For example, to understand the impact of use of alternative materials on circularity, the expert says moderately low. However, this expert also thinks that the use of alternative materials has a very high impact on compatibility with existing manufacturing infrastructure. In the following process, the expert also provides opinions for the alternatives. Alternative investments for new generation battery technologies are identified as electric vehicles with higher energy density (EVWHD), grid storage with long cycle life (GSWCL), low-cost energy supply for manufacturers (LCESM), energy production in extreme weather conditions (EPEWC), early-stage biotech startups (ESBST). The initial expert linguistic evaluations for the alternatives are denoted in Table <xref rid="j_infor604_tab_003">3</xref>.</p>
<table-wrap id="j_infor604_tab_003">
<label>Table 3</label>
<caption>
<p>Initial expert linguistic evaluations for the alternatives.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">EH</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">MH</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">VH</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">VH</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">MH</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">N</td>
<td style="vertical-align: top; text-align: left">EH</td>
<td style="vertical-align: top; text-align: left">VH</td>
<td style="vertical-align: top; text-align: left">MH</td>
<td style="vertical-align: top; text-align: left">N</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">H</td>
<td style="vertical-align: top; text-align: left">VH</td>
<td style="vertical-align: top; text-align: left">EH</td>
<td style="vertical-align: top; text-align: left">EH</td>
<td style="vertical-align: top; text-align: left">MH</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">VH</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">MH</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">MH</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">VH</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">EH</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Table <xref rid="j_infor604_tab_003">3</xref> indicates the evaluations of the expert for the alternatives by considering the criteria. For instance, according to the expert evaluation, grid storage with long cycle life is a very important investment alternative for new generation battery technologies by considering the criterion of circularity. Next, the multi-facet fuzzy numbers by initial and case-based assessments for the criteria are determined as in Table <xref rid="j_infor604_tab_007">A.1</xref>. The multi-facet fuzzy numbers by initial and case-based assessments for the alternatives are also identified in Table <xref rid="j_infor604_tab_008">A.2</xref>. In this process, the evaluations in Tables <xref rid="j_infor604_tab_002">2</xref> and <xref rid="j_infor604_tab_003">3</xref> are converted into the multi-facet fuzzy numbers by using the information stated in Table <xref rid="j_infor604_tab_001">1</xref>. The per-item statistics for the parameter-based multi-facet fuzzy sets of criteria and alternatives are computed in Table <xref rid="j_infor604_tab_009">A.3</xref>. These values are also calculated for the alternatives in Table <xref rid="j_infor604_tab_010">A.4</xref>. The dynamic parameters by the conditions for the criteria are determined in Table <xref rid="j_infor604_tab_011">A.5</xref>. Table <xref rid="j_infor604_tab_012">A.6</xref> gives information about these values for the alternatives. The parameter-based multi-facet fuzzy numbers by the conditions for the criteria are defined in Table <xref rid="j_infor604_tab_013">A.7</xref>. The parameter-based multi-facet fuzzy numbers by the conditions for the alternatives are defined in Table <xref rid="j_infor604_tab_014">A.8</xref>.</p>
</sec>
<sec id="j_infor604_s_009">
<label>4.2</label>
<title>Weighting the Criteria with Case and Parameter-Based Multi-Facet Fuzzy Logarithmic Least-Squares</title>
<p>The average fuzzy values for overall performance of relation matrix with case and parameter-based assessments are shown in Tables <xref rid="j_infor604_tab_015">A.9</xref> and <xref rid="j_infor604_tab_016">A.10</xref>. Defuzzified values of relation matrix by the case-based assessments are constructed in Table <xref rid="j_infor604_tab_017">A.11</xref>. The defuzzified values of relation matrix by the parameter-based assessments are created in Table <xref rid="j_infor604_tab_018">A.12</xref>. The values of <inline-formula id="j_infor604_ineq_058"><alternatives><mml:math>
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<table-wrap id="j_infor604_tab_004">
<label>Table 4</label>
<caption>
<p>Comparative weights of the criteria by the case and parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td colspan="6" style="vertical-align: top; text-align: center; border-top: solid thin; border-bottom: solid thin">Case-based assessments</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Negative</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Positive</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Unstable</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Natural</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Overall</td>
</tr>
</tbody><tbody>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<td colspan="6" style="vertical-align: top; text-align: center; border-top: solid thin; border-bottom: solid thin">Parameter-based assessments</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Maximum variance</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Maximum entropy</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Maximum resistance</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Balanced</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Overall</td>
</tr>
</tbody><tbody>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">5</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">5</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">5</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">5</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">5</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Table <xref rid="j_infor604_tab_004">4</xref> denotes that the weighting results are similar for both case and parameter-based assessments. This situation gives information about the consistency of the analysis. Overall weighting results of the criteria are computed by using the aggregated values of the assessments. It is concluded that circularity (C1) and compatibility with existing manufacturing infrastructure (C3) have the greatest weights. Circularity is very important for the performance of investments in next-generation battery technologies. Circularity includes issues such as recycling and reuse. Waste reduction and secondary material use reduce production costs. This allows for increased profitability of projects. Some actions can be taken in the battery sector to ensure circularity. In this context, batteries that are easy to disassemble can be developed. This situation allows for more effective recycling. Compatibility with existing manufacturing infrastructure) is a critical factor that directly affects the performance of investments in next-generation battery technologies. Technologies compatible with existing lines significantly reduce the initial costs of projects. Compatible technologies provide a safer environment for investors. This situation significantly supports the increase in projects.</p>
</sec>
<sec id="j_infor604_s_010">
<label>4.3</label>
<title>Ranking the Alternatives with Case and Parameter-Based Multi-Facet Fuzzy WASPAS</title>
<p>In investment evaluation processes, particularly those concerning next-generation battery technologies, uncertainty and inconsistency in expert judgments are inevitable due to market dynamics and incomplete information. To enhance the adaptability of the proposed model, dynamic parameter settings are applied to the multi-facet fuzzy numbers, as defined in equations (<xref rid="j_infor604_eq_045">45</xref>) to (<xref rid="j_infor604_eq_048">48</xref>).</p>
<p>The scaling factors in these equations are calculated using statistical measures derived from the expert evaluation matrices, including variance, entropy, and maximum range. These indicators capture uncertainty, inconsistency, and the level of disagreement among experts. When these statistical values are high, the model broadens the fuzzy membership functions to realistically reflect increased uncertainty. Conversely, when the variance and entropy are low, narrower membership functions are applied to represent higher consensus.</p>
<p>Incorporating such uncertainty-sensitive mechanisms is consistent with previous studies applying fuzzy WASPAS and advanced decision-making frameworks to problems involving incomplete or ambiguous information (Yalcin Kavus <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_032">2023</xref>; Deb <italic>et al.</italic>, <xref ref-type="bibr" rid="j_infor604_ref_007">2023</xref>). Furthermore, our methodology builds on the foundation of WASPAS-based optimization for complex multi-criteria environments, as demonstrated by Zavadskas <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_034">2012</xref>). By integrating these dynamic parameters, the model offers enhanced flexibility, robustness, and practical relevance, allowing for more realistic assessments under varying scenario conditions related to battery technology investments.</p>
<p>In the final stage, selected alternatives are ranked via multi-facet fuzzy WASPAS. The average fuzzy values for overall performance of decision matrix are computed. Table <xref rid="j_infor604_tab_021">A.15</xref> gives information about the averaged fuzzy numbers for overall performance of decision matrix with case-based assessments. On the other side, parameter-based assessments are demonstrated in Table <xref rid="j_infor604_tab_022">A.16</xref>. The defuzzified values of decision matrix by the case-based assessments are constructed in Table <xref rid="j_infor604_tab_023">A.17</xref>. The defuzzified values of decision matrix by the parameter-based assessments are created in Table <xref rid="j_infor604_tab_024">A.18</xref>. Table <xref rid="j_infor604_tab_025">A.19</xref> indicates the normalized values of the decision matrix by the case-based assessments. Normalized decision matrix by the parameter-based assessments is demonstrated in Table <xref rid="j_infor604_tab_026">A.20</xref>. Table <xref rid="j_infor604_tab_027">A.21</xref> shows the weighted decision matrix by the case-based assessments. Weighted decision matrix by the parameter-based assessments is given in Table <xref rid="j_infor604_tab_028">A.22</xref>. The values of SAW, WPN and combining scores are computed in Table <xref rid="j_infor604_tab_029">A.23</xref>. These values by the parameter-based assessments are defined in Table <xref rid="j_infor604_tab_030">A.24</xref>. In the final step, alternatives are ranked by the case and the parameter-based assessments with the different combination parameters. Table <xref rid="j_infor604_tab_031">A.25</xref> explains the comparative ranking results of the alternatives by the case-based assessments with the different combination parameters. These ranking results by the parameter-based assessments are explained in Table <xref rid="j_infor604_tab_005">5</xref>.</p>
<table-wrap id="j_infor604_tab_005">
<label>Table 5</label>
<caption>
<p>Comparative ranking results of the alternatives by the parameter-based assessments with the different combination parameters.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
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</tr>
</thead>
<tbody>
<tr>
<td colspan="11" style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td colspan="11" style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td colspan="11" style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td colspan="11" style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td colspan="11" style="vertical-align: top; text-align: left">Overall</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Table <xref rid="j_infor604_tab_005">5</xref> demonstrates that energy production in extreme weather conditions is the most critical investment alternative for new generation battery technologies. Moreover, early-stage biotech startups and electric vehicles with higher energy density are other significant alternatives for this situation. Energy production in extreme weather conditions can be considered as an important and strategic investment alternative. This situation is becoming increasingly critical especially in the context of climate change and sustainable development goals. Extreme weather events such as storms and droughts are increasing worldwide. These conditions can strain or disable traditional energy production infrastructures. Investing in energy production systems that are resistant to extreme conditions plays a key role in ensuring energy supply security.</p>
<p>However, the comparative ranking results of the extended TOPSIS are given with sensitivity analysis in Table <xref rid="j_infor604_tab_006">6</xref>. The weights of the criteria are changed consecutively and provided 5 scenarios for the sensitivity analysis. The comparative results with the sensitivity cases are illustrated as follows.</p>
<table-wrap id="j_infor604_tab_006">
<label>Table 6</label>
<caption>
<p>Comparative ranking results with sensitivity analysis.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: middle; text-align: left; border-top: solid thin"/>
<td colspan="5" style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">Extended WASPAS (<inline-formula id="j_infor604_ineq_073"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.5</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.5$]]></tex-math></alternatives></inline-formula>)</td>
<td colspan="5" style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">Extended TOPSIS</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 1</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 3</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 4</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 5</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 1</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 3</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 4</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">Case 5</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Max. var.</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Max. ent.</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Max. res.</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Overall</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In Table <xref rid="j_infor604_tab_006">6</xref>, the comparative ranking results with extended TOPSIS are almost same for each case of sensitivity analysis. It demonstrates that our proposed methodology is coherent and applicable to the other extended methodologies for further studies.</p>
</sec>
</sec>
<sec id="j_infor604_s_011">
<label>5</label>
<title>Discussion</title>
<p>Circularity is an approach that prioritizes recycling and waste reduction throughout the life cycle of a product or technology. Battery designs that comply with circular economy principles can reduce environmental impacts while reducing costs. In the literature, it is emphasized that not only technological performance, but also material sustainability and recovery strategies are important in battery investments. With the provision of circularity, domestic production and resource independence can be achieved. Etxandi-Santolaya <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_011">2023</xref>) mentioned that this situation contributes significantly to reducing the economic fragility of countries. In the literature, some studies underline the importance of energy density or cost efficiency for the performance improvements of the next-generation battery technology investments (Rizos and Urban, <xref ref-type="bibr" rid="j_infor604_ref_024">2024</xref>). Unlike these traditional investment approaches, this study highlights the significance of the environmental issues in this process, such as resource efficiency and recyclability. Schulz-Mönninghoff <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_025">2023</xref>) defined that future investment strategies should integrate circular design principles to these financial issues. Easier recovery of these batteries in a circular system also reduces external dependency on raw materials. Batteries with decomposable designs reduce recycling costs.</p>
<p>It is identified that compatibility with existing manufacturing infrastructure also plays a key role for the performance improvements of the next-generation battery technology investments. Integration with the existing manufacturing infrastructure supports the return on investment of these technologies. Fahma <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_012">2024</xref>) demonstrated that establishing a new production line is quite costly in terms of both capital investment and time. It is vital that new battery technology is easily integrated into existing production lines. This allows for the reduction of restructuring costs. Denisart <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_008">2024</xref>) identified that technologies compatible with the existing infrastructure shorten the time to production. With the help of these issues, these projects can become operational in the markets very quickly. This situation offers a significant competitive advantage to the enterprises. Moreover, according to Naseri <italic>et al.</italic> (<xref ref-type="bibr" rid="j_infor604_ref_019">2023</xref>), compatibility facilitates workforce adaptation, minimizes transition risks, and supports the integration with established supply chains. From a strategic investment perspective, infrastructure adaptability not only lowers operational risks but also enhances the attractiveness of such technologies for institutional investors and industry stakeholders.</p>
<p>In our proposed methodology, several scenarios and dynamic parameters are considered for solving the complex decision-making problems. Properly, we propose negative scenario to represent pessimistic market conditions, such as raw material shortages, regulatory restrictions, or major technological setbacks. For instance, lithium supply disruptions or unfavourable policies banning certain battery components lead to increased uncertainty and reduced stakeholder engagement. However, the positive scenario reflects highly favourable market dynamics, such as breakthrough research in solid-state battery technology, major cost reductions, or supportive government incentives like tax credits for green energy storage. Under these conditions, investor engagement is maximized, and technological optimism dominates. Unstable Case captures volatile and uncertain environments, characterized by fluctuating raw material prices, geopolitical tensions affecting supply chains, or rapid but uneven technological innovation. For example, sudden policy reversals on electric vehicle incentives or global supply chain disruptions due to pandemics are reflected by this scenario’s prioritization of resistance and penalization of low membership. The natural scenario corresponds to stable, balanced market situations where neither major disruptions nor significant breakthroughs are expected. Typical examples include gradual, predictable improvements in battery technologies or steady policy environments without abrupt regulatory shifts.</p>
<p>Similarly, the dynamic parameter adjustments provide more satisfactory outcomes to discuss the performance metrics. Maximum variance condition reflects situations with highly inconsistent expert evaluations, signaling significant uncertainty or disagreement in market expectations. This often corresponds to unpredictable investment environments, such as emerging battery technologies facing technical feasibility debates or fragmented regulatory landscapes. Maximum entropy captures high system disorder, associated with rapidly evolving technologies, regulatory ambiguity, or unclear industry standards. For instance, shifting policy frameworks for battery recycling or evolving ESG (Environmental, Social, Governance) requirements increase decision complexity, justifying entropy-driven parameter adjustments. The condition of maximum resistance models contexts where stakeholders exhibit heightened resistance to adopting new battery technologies. Such scenarios may arise due to safety concerns (e.g. battery fires), public opposition to mining activities, or institutional inertia in established energy markets. Finally, balanced conditions represent moderate, predictable investment environments with average levels of uncertainty, risk, and stakeholder resistance. It applies to markets with incremental technological progress and stable policy frameworks.</p>
<p>The primary focus of this study is on technical and strategic criteria. However, it is also acknowledged that regulatory and policy mechanisms such as carbon pricing or mandatory recycling regulations can significantly influence the weight and relevance of certain investment indicators. Within this framework, the flexibility of the proposed multi-facet fuzzy model enables dynamic recalibration of membership functions based on policy-driven scenarios. For example, in a high carbon tax scenario, environmental compatibility and circularity-related criteria may gain greater importance. This adaptability enhances the practical value of the model by allowing stakeholders to test different regulatory environments. Owing to this issue, their potential impact on investment priorities can be observed.</p>
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<sec id="j_infor604_s_012">
<label>6</label>
<title>Conclusion</title>
<p>This study tries to define the priority strategies to increase the performance of new generation battery technology investments. For this purpose, an innovative decision-making model is developed by integrating multi-facet fuzzy sets, logarithmic least-squares and WASPAS techniques. In the three-stage model proposed in the study, firstly the criteria and alternatives are defined by the synthetic evaluation method. In the second stage, the criteria weights are calculated by the multi-dimensional and situational fuzzy logarithmic least squares method. In the last stage, the alternatives are ranked by using the fuzzy WASPAS method. Circularity is found the most critical factor for the development of these projects. It is also identified that compatibility with existing manufacturing infrastructure also plays a key role for the performance improvements of the next-generation battery technology investments. It is concluded that energy production in extreme weather conditions is the most critical investment alternative for new generation battery technologies. Moreover, early-stage biotech startups and electric vehicles with higher energy density are other significant alternatives for this situation. Based on the prioritization of the circularity criterion, this study suggests several actionable strategies for investors. Adopting design-for-recycling principles in battery development can be very helpful to achieve this objective. Furthermore, using recyclable and low-impact materials can contribute significantly to improving the circular performance of battery technologies. These practices not only align with environmental goals but also help future-proof investments against tightening regulatory standards.</p>
<p>This study makes a significant contribution to the literature by prioritizing the performance indicators of new generation battery technology investments via an innovative decision-making model. This provides the opportunity to make clearer decisions based on scenarios and dynamic evaluations in complex decision-making processes. There are some important limitations of this study. The criteria and alternative evaluations used in the study are based on a limited number of expert opinions. This situation may create some limitations in terms of general validity and objectivity. In future studies, an analysis can be carried out with the participation of more experts. In this context, the generalizability of the model can be increased by obtaining the opinions of more experts working in different sectors. Weighting can be done according to the demographic and experience characteristics of the experts. Despite the use of a multiple scenario approach, all possible uncertainty situations are not fully covered. In this context, sensitivity analysis can be done according to different market conditions and technological development rates. This study relies on expert judgments that can introduce subjectivity and variability depending on the experts’ background and consistency. Moreover, while the proposed model performs well for medium-scale problems, its computational complexity may increase significantly with a higher number of criteria and alternatives. Future research may address these constraints by integrating automated expert selection systems or developing scalable optimization-based fuzzy frameworks.</p>
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<app id="j_infor604_app_001"><label>A</label>
<title>Appendix. Equations</title><disp-formula-group id="j_infor604_dg_013">
<disp-formula id="j_infor604_eq_049">
<label>(A.1)</label><alternatives><mml:math display="block">
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</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& A=\big\{\big(x,\mu (x),v\big(\mu (x)\big),\epsilon \big(\mu (x)\big),n\big(\mu (x)\big),\rho \big(\mu (x)\big)\big)\mid x\in X\big\},\end{aligned}\]]]></tex-math></alternatives>
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<disp-formula id="j_infor604_eq_050">
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</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="1.19em" minsize="1.19em">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& B=\big({\mu _{B}},{v_{B}}({\mu _{B}}),{\epsilon _{B}}({\mu _{B}}),{n_{B}}({\mu _{B}}),{\rho _{B}}({\mu _{B}})\big),\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_053">
<label>(A.5)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mo>∪</mml:mo>
<mml:mi mathvariant="italic">B</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="1.19em" minsize="1.19em">(</mml:mo>
<mml:mo movablelimits="false">max</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">min</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">min</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">max</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">max</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="1.19em" minsize="1.19em">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& A\cup B=\big(\max ({\mu _{A}},{\mu _{B}}),\min ({v_{A}},{v_{B}}),\min ({\epsilon _{A}},{\epsilon _{B}}),\max ({n_{A}},{n_{B}}),\max ({\rho _{A}},{\rho _{B}})\big),\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_054">
<label>(A.6)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mo>∩</mml:mo>
<mml:mi mathvariant="italic">B</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="1.19em" minsize="1.19em">(</mml:mo>
<mml:mo movablelimits="false">min</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">max</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">max</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">min</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo movablelimits="false">max</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="1.19em" minsize="1.19em">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& A\cap B=\big(\min ({\mu _{A}},{\mu _{B}}),\max ({v_{A}},{v_{B}}),\max ({\epsilon _{A}},{\epsilon _{B}}),\min ({n_{A}},{n_{B}}),\max ({\rho _{A}},{\rho _{B}})\big),\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_055">
<label>(A.7)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mo>⊕</mml:mo>
<mml:mi mathvariant="italic">B</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>−</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>−</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>−</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& A\oplus B=({\mu _{A}}+{\mu _{B}}-{\mu _{A}}{\mu _{B}},{v_{A}}{v_{B}},{\epsilon _{A}}+{\epsilon _{B}}-{\epsilon _{A}}{\epsilon _{B}},{n_{A}}+{n_{B}}-{n_{A}}{n_{B}},{\rho _{A}}{\rho _{B}}),\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_056">
<label>(A.8)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mo>⊗</mml:mo>
<mml:mi mathvariant="italic">B</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>−</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ϵ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>−</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">ρ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& A\otimes B=({\mu _{A}}{\mu _{B}},{v_{A}}+{v_{B}}-{v_{A}}{v_{B}},{v_{A}}{v_{B}},{\epsilon _{A}}{\epsilon _{B}},{n_{A}}{n_{B}},{\rho _{A}}+{\rho _{B}}-{\rho _{A}}{\rho _{B}}),\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_057">
<label>(A.9)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">negative</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mo>=</mml:mo>
<mml:mtable displaystyle="true" columnalign="right">
<mml:mtr>
<mml:mtd>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">{</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo>−</mml:mo>
<mml:mn>5</mml:mn>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">[</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>+</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">]</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">)</mml:mo>
<mml:mspace width="0.1667em"/>
<mml:mo maxsize="1.61em" minsize="1.61em" stretchy="true">|</mml:mo>
<mml:mspace width="0.1667em"/>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mi mathvariant="italic">X</mml:mi>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">}</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {A_{\textit{negative}}}\\ {} & =\displaystyle \bigg\{\bigg(x,\mu (x),\frac{1}{1+{e^{10(\mu -.5)}}},-5\big[\mu \ln \mu +(1-\mu )\ln (1-\mu )\big],{\mu ^{1}},1-{(1-\mu )^{1}}\bigg)\hspace{0.1667em}\Big|\hspace{0.1667em}x\in X\bigg\},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_058">
<label>(A.10)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">positive</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mo>=</mml:mo>
<mml:mtable displaystyle="true" columnalign="right">
<mml:mtr>
<mml:mtd>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">{</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo>−</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">[</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>+</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">]</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">)</mml:mo>
<mml:mspace width="0.1667em"/>
<mml:mo maxsize="1.61em" minsize="1.61em" stretchy="true">|</mml:mo>
<mml:mspace width="0.1667em"/>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mi mathvariant="italic">X</mml:mi>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">}</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {A_{\textit{positive}}}\\ {} & =\displaystyle \bigg\{\bigg(x,\mu (x),\frac{1}{1+{e^{1(\mu -.5)}}},-1\big[\mu \ln \mu +(1-\mu )\ln (1-\mu )\big],{\mu ^{5}},1-{(1-\mu )^{1}}\bigg)\hspace{0.1667em}\Big|\hspace{0.1667em}x\in X\bigg\},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_059">
<label>(A.11)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">unstable</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mo>=</mml:mo>
<mml:mtable displaystyle="true" columnalign="right">
<mml:mtr>
<mml:mtd>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">{</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo>−</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">[</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>+</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">]</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">)</mml:mo>
<mml:mspace width="0.1667em"/>
<mml:mo maxsize="1.61em" minsize="1.61em" stretchy="true">|</mml:mo>
<mml:mspace width="0.1667em"/>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mi mathvariant="italic">X</mml:mi>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">}</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {A_{\textit{unstable}}}\\ {} & =\displaystyle \bigg\{\bigg(x,\mu (x),\frac{1}{1+{e^{1(\mu -.5)}}},-2\big[\mu \ln \mu +(1-\mu )\ln (1-\mu )\big],{\mu ^{1}},1-{(1-\mu )^{10}}\bigg)\hspace{0.1667em}\Big|\hspace{0.1667em}x\in X\bigg\},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_060">
<label>(A.12)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext mathvariant="italic">natural</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:mo>=</mml:mo>
<mml:mtable displaystyle="true" columnalign="right">
<mml:mtr>
<mml:mtd>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">{</mml:mo>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo><mml:mstyle displaystyle="true">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mn>.5</mml:mn>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mstyle>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo>−</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">[</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo>+</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo movablelimits="false">ln</mml:mo>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
<mml:mo fence="true" maxsize="1.19em" minsize="1.19em">]</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo mathvariant="normal" fence="true" stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mo mathvariant="normal" fence="true" stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal" fence="true" maxsize="2.03em" minsize="2.03em">)</mml:mo>
<mml:mo stretchy="false">∣</mml:mo>
<mml:mi mathvariant="italic">x</mml:mi>
<mml:mo stretchy="false">∈</mml:mo>
<mml:mi mathvariant="italic">X</mml:mi>
<mml:mo fence="true" maxsize="2.03em" minsize="2.03em">}</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mtd>
</mml:mtr>
</mml:mtable></mml:math><tex-math><![CDATA[\[\begin{aligned}{}& {A_{\textit{natural}}}\\ {} & =\displaystyle \bigg\{\bigg(x,\mu (x),\frac{1}{1+{e^{1(\mu -.5)}}},-1\big[\mu \ln \mu +(1-\mu )\ln (1-\mu )\big],{\mu ^{1}},1-{(1-\mu )^{1}}\bigg)\mid x\in X\bigg\},\end{aligned}\]]]></tex-math></alternatives>
</disp-formula>
<disp-formula id="j_infor604_eq_061">
<label>(A.13)</label><alternatives><mml:math display="block">
<mml:mtable displaystyle="true" columnalign="right left" columnspacing="0pt">
<mml:mtr>
<mml:mtd class="align-odd"/>
<mml:mtd class="align-even">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>+</mml:mo>
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<label>(A.15)</label><alternatives><mml:math display="block">
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<label>(A.16)</label><alternatives><mml:math display="block">
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</disp-formula>
</disp-formula-group> </app>
<app id="j_infor604_app_002"><label>B</label>
<title>Appendix. Tables</title>
<table-wrap id="j_infor604_tab_007">
<label>Table A.1</label>
<caption>
<p>Multi-facet fuzzy numbers by initial and case-based assessments for the criteria.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">NEGATIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .50, .50)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .73, 1.00, .40, .40)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.40, .73, 1.00, .40, .40)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .50, .50)</td>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">POSITIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .03, .50)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .52, .06, .01, .40)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .03, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .03, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .03, .50)</td>
<td style="vertical-align: top; text-align: left">(.40, .52, .06, .01, .40)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .03, .50)</td>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UNSTABLE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .35, .50, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .52, .43, .40, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .35, .50, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, .35, .50, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .35, .50, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.40, .52, .43, .40, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .35, .50, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">NATURAL</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .50, .50)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .52, .06, .40, .40)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .60, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.40, .52, .06, .40, .40)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .40, .00, .90, .90)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .48, .00, .60, .60)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.50, .50, .00, .50, .50)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_008">
<label>Table A.2</label>
<caption>
<p>Multi-facet fuzzy numbers by initial and case-based assessments for the alternatives.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">NEGATIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .50, .50)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .90, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">POSITIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .03, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .03, .50)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .17, .70)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .08, .60)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .33, .80)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .59, .90)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UNSTABLE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .35, .50, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .35, .50, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .14, .70, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .25, .60, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .04, .80, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">NATURAL</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .80, .80)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .60, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .50, .50)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .60, .60)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .00, .50, .50)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .45, .00, .70, .70)</td>
<td style="vertical-align: top; text-align: left">(.80, .43, .00, .80, .80)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.90, .40, .00, .90, .90)</td>
<td style="vertical-align: top; text-align: left">(.60, .48, .00, .60, .60)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .43, .00, .80, .80)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .48, .00, .60, .60)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .48, .00, .60, .60)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .43, .00, .80, .80)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .40, .00, .90, .90)</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_009">
<label>Table A.3</label>
<caption>
<p>Per-item statistics for the parameter-based multi-facet fuzzy sets of criteria.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_074"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${m_{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_075"><alternatives><mml:math>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">σ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msubsup></mml:math><tex-math><![CDATA[${\sigma _{i}^{2}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_076"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${H_{i}}$]]></tex-math></alternatives></inline-formula></td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.700</td>
<td style="vertical-align: top; text-align: left">.025</td>
<td style="vertical-align: top; text-align: left">1.360</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.625</td>
<td style="vertical-align: top; text-align: left">.022</td>
<td style="vertical-align: top; text-align: left">1.357</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.700</td>
<td style="vertical-align: top; text-align: left">.040</td>
<td style="vertical-align: top; text-align: left">1.345</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.625</td>
<td style="vertical-align: top; text-align: left">.037</td>
<td style="vertical-align: top; text-align: left">1.339</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.675</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.022</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">1.363</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_010">
<label>Table A.4</label>
<caption>
<p>Per-item statistics for the parameter-based multi-facet fuzzy sets of alternatives.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_077"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${m_{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_078"><alternatives><mml:math>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="italic">σ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msubsup></mml:math><tex-math><![CDATA[${\sigma _{i}^{2}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_079"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${H_{i}}$]]></tex-math></alternatives></inline-formula></td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.740</td>
<td style="vertical-align: top; text-align: left">.010</td>
<td style="vertical-align: top; text-align: left">1.600</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.700</td>
<td style="vertical-align: top; text-align: left">.004</td>
<td style="vertical-align: top; text-align: left">1.605</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.660</td>
<td style="vertical-align: top; text-align: left">.026</td>
<td style="vertical-align: top; text-align: left">1.580</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.780</td>
<td style="vertical-align: top; text-align: left">.014</td>
<td style="vertical-align: top; text-align: left">1.598</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.740</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.014</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">1.596</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_011">
<label>Table A.5</label>
<caption>
<p>Dynamic parameters by the conditions for the criteria.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_080"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\alpha _{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_081"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${a_{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_082"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\delta _{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_083"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\varphi _{i}}$]]></tex-math></alternatives></inline-formula></td>
</tr>
</thead>
<tbody>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.99</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.20</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.98</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.95</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.20</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.93</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.70</td>
<td style="vertical-align: top; text-align: left">8.80</td>
</tr>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">6.63</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.20</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">5.92</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.20</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">9.30</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">5.92</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.70</td>
<td style="vertical-align: top; text-align: left">8.80</td>
</tr>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">6.63</td>
<td style="vertical-align: top; text-align: left">4.99</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">5.92</td>
<td style="vertical-align: top; text-align: left">4.98</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.95</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">9.30</td>
<td style="vertical-align: top; text-align: left">4.93</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">5.92</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.70</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">7.75</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.80</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">7.28</td>
<td style="vertical-align: top; text-align: left">4.99</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.97</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.80</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">9.53</td>
<td style="vertical-align: top; text-align: left">4.95</td>
<td style="vertical-align: top; text-align: left">3.50</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">7.28</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">5.00</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">3.70</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">9.20</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_012">
<label>Table A.6</label>
<caption>
<p>Dynamic parameters by the conditions for the alternatives.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_084"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">α</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\alpha _{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_085"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${a_{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_086"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">δ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\delta _{i}}$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_087"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">φ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${\varphi _{i}}$]]></tex-math></alternatives></inline-formula></td>
</tr>
</thead>
<tbody>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.99</td>
<td style="vertical-align: top; text-align: left">3.96</td>
<td style="vertical-align: top; text-align: left">7.88</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.94</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.94</td>
<td style="vertical-align: top; text-align: left">3.64</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.98</td>
<td style="vertical-align: top; text-align: left">4.12</td>
<td style="vertical-align: top; text-align: left">6.82</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.98</td>
<td style="vertical-align: top; text-align: left">3.96</td>
<td style="vertical-align: top; text-align: left">7.88</td>
</tr>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">4.55</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.96</td>
<td style="vertical-align: top; text-align: left">7.88</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">2.36</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">8.94</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.64</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">5.64</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">4.12</td>
<td style="vertical-align: top; text-align: left">6.82</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">5.91</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.96</td>
<td style="vertical-align: top; text-align: left">7.88</td>
</tr>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">4.55</td>
<td style="vertical-align: top; text-align: left">4.99</td>
<td style="vertical-align: top; text-align: left">3.96</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">2.36</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.94</td>
<td style="vertical-align: top; text-align: left">3.64</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">5.64</td>
<td style="vertical-align: top; text-align: left">4.98</td>
<td style="vertical-align: top; text-align: left">4.12</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">5.91</td>
<td style="vertical-align: top; text-align: left">4.98</td>
<td style="vertical-align: top; text-align: left">3.96</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td colspan="5" style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">6.36</td>
<td style="vertical-align: top; text-align: left">4.99</td>
<td style="vertical-align: top; text-align: left">3.96</td>
<td style="vertical-align: top; text-align: left">8.59</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4.91</td>
<td style="vertical-align: top; text-align: left">5.00</td>
<td style="vertical-align: top; text-align: left">3.80</td>
<td style="vertical-align: top; text-align: left">9.29</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">1.00</td>
<td style="vertical-align: top; text-align: left">4.96</td>
<td style="vertical-align: top; text-align: left">3.64</td>
<td style="vertical-align: top; text-align: left">1.00</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">7.09</td>
<td style="vertical-align: top; text-align: left">4.99</td>
<td style="vertical-align: top; text-align: left">4.12</td>
<td style="vertical-align: top; text-align: left">7.88</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">7.27</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">4.98</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">3.96</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">8.59</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_013">
<label>Table A.7</label>
<caption>
<p>Parameter-based multi-facet fuzzy numbers by the conditions for the criteria.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .14, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .73, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .46, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .88, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .17, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .87, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .09, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.40, .73, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .69, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .27, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .15, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .34, 1.00, .14, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .07, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .12, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .64, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .14, .57, .46, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .23, .89, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .17, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .13, .89, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .09, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.40, .72, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .69, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .23, .89, .27, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .15, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .34, 1.00, .14, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .07, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .12, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .64, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .14, .57, .46, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .23, .88, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .17, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .13, .87, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .09, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.40, .72, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .69, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .23, .89, .27, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .15, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.60, .32, 1.00, .14, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .04, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .09, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .67, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.80, .10, .57, .46, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .19, .88, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .33, 1.00, .17, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .13, .88, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .09, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.40, .72, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left"/>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .69, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .05, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.70, .19, .89, .27, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .33, 1.00, .15, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_014">
<label>Table A.8</label>
<caption>
<p>Parameter-based multi-facet fuzzy numbers by the conditions for the alternatives.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .66, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .41, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .14, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .56, .44, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .16, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .12, .88, .23, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .40, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .12, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .66, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .14, .24, .66, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .29, .89, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .39, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .29, .89, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .20, .57, .41, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .38, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .38, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .38, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .44, 1.00, .14, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .57, .44, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .16, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .24, .89, .23, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .16, .57, .40, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .12, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">(.80, .15, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .15, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .66, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .14, .24, .66, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .29, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .39, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .29, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .20, .57, .41, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .38, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .38, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .38, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .44, 1.00, .14, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .56, .44, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .16, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .24, .88, .23, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .16, .57, .40, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .12, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">(.80, .15, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .36, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .15, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .66, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .07, .24, .66, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .22, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .35, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .22, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .13, .57, .41, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .19, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .27, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .27, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .27, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .38, 1.00, .14, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .56, .44, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .16, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .19, .88, .23, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .11, .57, .40, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .06, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .06, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .33, 1.00, .12, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .10, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .33, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .33, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .10, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .05, .24, .66, 1.00)</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_015">
<label>Table A.9</label>
<caption>
<p>Averaged fuzzy numbers for overall performance of relation matrix with case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.60, .42, .31, .47, .70)</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .15, .68, .85)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .34, .38, .62)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .58, .39, .30, .55)</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .15, .68, .85)</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.60, .42, .31, .47, .70)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .34, .38, .62)</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .34, .38, .62)</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .34, .38, .62)</td>
<td style="vertical-align: top; text-align: left">(.40, .58, .39, .30, .55)</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .31, .06, .82, .92)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .42, .31, .47, .70)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.50, .50, .34, .38, .62)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.00, .00, .00, .00, .00)</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_016">
<label>Table A.10</label>
<caption>
<p>Averaged fuzzy numbers for overall performance of relation matrix with parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.60, .32, 1.00, .14, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .05, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .09, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">(.40, .67, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.80, .11, .57, .46, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .19, .88, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .33, 1.00, .17, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .07, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .67, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">(.70, .13, .88, .29, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .09, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.40, .72, 1.00, .04, .99)</td>
<td style="vertical-align: top; text-align: left">(.00, .00, .00, .00, .00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .69, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .06, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.70, .19, .89, .27, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .33, 1.00, .15, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.00, .00, .00, .00, .00)</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_017">
<label>Table A.11</label>
<caption>
<p>Defuzzified relation matrix by the case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">NEGATIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.506</td>
<td style="vertical-align: top; text-align: left">.906</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.361</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.216</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.506</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.361</td>
<td style="vertical-align: top; text-align: left">.906</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.361</td>
<td style="vertical-align: top; text-align: left">.906</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.361</td>
<td style="vertical-align: top; text-align: left">.216</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.906</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.906</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.506</td>
<td style="vertical-align: top; text-align: left">.361</td>
<td style="vertical-align: top; text-align: left">.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">POSITIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.346</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.535</td>
<td style="vertical-align: top; text-align: left">.295</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.252</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.535</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.346</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.295</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.295</td>
<td style="vertical-align: top; text-align: left">.706</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.295</td>
<td style="vertical-align: top; text-align: left">.252</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.706</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.346</td>
<td style="vertical-align: top; text-align: left">.295</td>
<td style="vertical-align: top; text-align: left">.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UNSTABLE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.882</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.940</td>
<td style="vertical-align: top; text-align: left">.853</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.824</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.940</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.882</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.853</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.853</td>
<td style="vertical-align: top; text-align: left">.960</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.853</td>
<td style="vertical-align: top; text-align: left">.824</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.960</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.882</td>
<td style="vertical-align: top; text-align: left">.853</td>
<td style="vertical-align: top; text-align: left">.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">NATURAL</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.665</td>
<td style="vertical-align: top; text-align: left">.860</td>
<td style="vertical-align: top; text-align: left">.795</td>
<td style="vertical-align: top; text-align: left">.600</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.523</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.795</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.665</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.600</td>
<td style="vertical-align: top; text-align: left">.860</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.600</td>
<td style="vertical-align: top; text-align: left">.860</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.600</td>
<td style="vertical-align: top; text-align: left">.523</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.860</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.860</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.730</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.665</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.600</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.000</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_018">
<label>Table A.12</label>
<caption>
<p>Defuzzified relation matrix by the parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.595</td>
<td style="vertical-align: top; text-align: left">.902</td>
<td style="vertical-align: top; text-align: left">.797</td>
<td style="vertical-align: top; text-align: left">.498</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.447</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.817</td>
<td style="vertical-align: top; text-align: left">.716</td>
<td style="vertical-align: top; text-align: left">.627</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.499</td>
<td style="vertical-align: top; text-align: left">.903</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.499</td>
<td style="vertical-align: top; text-align: left">.903</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.719</td>
<td style="vertical-align: top; text-align: left">.537</td>
<td style="vertical-align: top; text-align: left">.448</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.914</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.905</td>
<td style="vertical-align: top; text-align: left">.697</td>
<td style="vertical-align: top; text-align: left">.606</td>
<td style="vertical-align: top; text-align: left">.511</td>
<td style="vertical-align: top; text-align: left">.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.557</td>
<td style="vertical-align: top; text-align: left">.878</td>
<td style="vertical-align: top; text-align: left">.755</td>
<td style="vertical-align: top; text-align: left">.498</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.495</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.772</td>
<td style="vertical-align: top; text-align: left">.661</td>
<td style="vertical-align: top; text-align: left">.590</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.498</td>
<td style="vertical-align: top; text-align: left">.902</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.498</td>
<td style="vertical-align: top; text-align: left">.902</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.705</td>
<td style="vertical-align: top; text-align: left">.536</td>
<td style="vertical-align: top; text-align: left">.455</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.909</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.876</td>
<td style="vertical-align: top; text-align: left">.638</td>
<td style="vertical-align: top; text-align: left">.564</td>
<td style="vertical-align: top; text-align: left">.513</td>
<td style="vertical-align: top; text-align: left">.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.587</td>
<td style="vertical-align: top; text-align: left">.886</td>
<td style="vertical-align: top; text-align: left">.772</td>
<td style="vertical-align: top; text-align: left">.533</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.496</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.772</td>
<td style="vertical-align: top; text-align: left">.662</td>
<td style="vertical-align: top; text-align: left">.590</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.530</td>
<td style="vertical-align: top; text-align: left">.909</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.530</td>
<td style="vertical-align: top; text-align: left">.909</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.710</td>
<td style="vertical-align: top; text-align: left">.538</td>
<td style="vertical-align: top; text-align: left">.456</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.911</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.882</td>
<td style="vertical-align: top; text-align: left">.655</td>
<td style="vertical-align: top; text-align: left">.584</td>
<td style="vertical-align: top; text-align: left">.536</td>
<td style="vertical-align: top; text-align: left">.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.579</td>
<td style="vertical-align: top; text-align: left">.890</td>
<td style="vertical-align: top; text-align: left">.776</td>
<td style="vertical-align: top; text-align: left">.510</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">.480</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.788</td>
<td style="vertical-align: top; text-align: left">.679</td>
<td style="vertical-align: top; text-align: left">.601</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">.509</td>
<td style="vertical-align: top; text-align: left">.904</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.509</td>
<td style="vertical-align: top; text-align: left">.904</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">.711</td>
<td style="vertical-align: top; text-align: left">.537</td>
<td style="vertical-align: top; text-align: left">.453</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.911</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.890</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.663</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.583</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.520</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_019">
<label>Table A.13</label>
<caption>
<p>Values of <inline-formula id="j_infor604_ineq_088"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${b_{ki}}$]]></tex-math></alternatives></inline-formula>, <inline-formula id="j_infor604_ineq_089"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${x_{k}}$]]></tex-math></alternatives></inline-formula>, and the weights of the criteria for the case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin"/>
<td colspan="5" style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_090"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${b_{ki}}$]]></tex-math></alternatives></inline-formula></td>
<td rowspan="2" style="vertical-align: middle; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_091"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${x_{k}}$]]></tex-math></alternatives></inline-formula></td>
<td rowspan="2" style="vertical-align: middle; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_092"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${W_{k}}$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Negative</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.426</td>
<td style="vertical-align: top; text-align: left">.460</td>
<td style="vertical-align: top; text-align: left">.102</td>
<td style="vertical-align: top; text-align: left">−.460</td>
<td style="vertical-align: top; text-align: left">.106</td>
<td style="vertical-align: top; text-align: left">.222</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.426</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.074</td>
<td style="vertical-align: top; text-align: left">.284</td>
<td style="vertical-align: top; text-align: left">−.115</td>
<td style="vertical-align: top; text-align: left">−.066</td>
<td style="vertical-align: top; text-align: left">.187</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.460</td>
<td style="vertical-align: top; text-align: left">.074</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.257</td>
<td style="vertical-align: top; text-align: left">.291</td>
<td style="vertical-align: top; text-align: left">.032</td>
<td style="vertical-align: top; text-align: left">.206</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.102</td>
<td style="vertical-align: top; text-align: left">−.284</td>
<td style="vertical-align: top; text-align: left">−.257</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.460</td>
<td style="vertical-align: top; text-align: left">−.037</td>
<td style="vertical-align: top; text-align: left">.192</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.460</td>
<td style="vertical-align: top; text-align: left">.115</td>
<td style="vertical-align: top; text-align: left">−.291</td>
<td style="vertical-align: top; text-align: left">−.460</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.035</td>
<td style="vertical-align: top; text-align: left">.193</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Positive</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.159</td>
<td style="vertical-align: top; text-align: left">.436</td>
<td style="vertical-align: top; text-align: left">.119</td>
<td style="vertical-align: top; text-align: left">−.436</td>
<td style="vertical-align: top; text-align: left">.056</td>
<td style="vertical-align: top; text-align: left">.211</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.159</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.139</td>
<td style="vertical-align: top; text-align: left">.178</td>
<td style="vertical-align: top; text-align: left">−.098</td>
<td style="vertical-align: top; text-align: left">−.044</td>
<td style="vertical-align: top; text-align: left">.191</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.436</td>
<td style="vertical-align: top; text-align: left">.139</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.079</td>
<td style="vertical-align: top; text-align: left">.356</td>
<td style="vertical-align: top; text-align: left">.028</td>
<td style="vertical-align: top; text-align: left">.205</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.119</td>
<td style="vertical-align: top; text-align: left">−.178</td>
<td style="vertical-align: top; text-align: left">−.079</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.436</td>
<td style="vertical-align: top; text-align: left">.012</td>
<td style="vertical-align: top; text-align: left">.202</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.436</td>
<td style="vertical-align: top; text-align: left">.098</td>
<td style="vertical-align: top; text-align: left">−.356</td>
<td style="vertical-align: top; text-align: left">−.436</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.052</td>
<td style="vertical-align: top; text-align: left">.190</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Unstable</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.034</td>
<td style="vertical-align: top; text-align: left">.059</td>
<td style="vertical-align: top; text-align: left">.016</td>
<td style="vertical-align: top; text-align: left">−.059</td>
<td style="vertical-align: top; text-align: left">.010</td>
<td style="vertical-align: top; text-align: left">.202</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.034</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.010</td>
<td style="vertical-align: top; text-align: left">.033</td>
<td style="vertical-align: top; text-align: left">−.016</td>
<td style="vertical-align: top; text-align: left">−.006</td>
<td style="vertical-align: top; text-align: left">.199</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.059</td>
<td style="vertical-align: top; text-align: left">.010</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.017</td>
<td style="vertical-align: top; text-align: left">.042</td>
<td style="vertical-align: top; text-align: left">.002</td>
<td style="vertical-align: top; text-align: left">.200</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.016</td>
<td style="vertical-align: top; text-align: left">−.033</td>
<td style="vertical-align: top; text-align: left">−.017</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.059</td>
<td style="vertical-align: top; text-align: left">−.001</td>
<td style="vertical-align: top; text-align: left">.200</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.059</td>
<td style="vertical-align: top; text-align: left">.016</td>
<td style="vertical-align: top; text-align: left">−.042</td>
<td style="vertical-align: top; text-align: left">−.059</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.005</td>
<td style="vertical-align: top; text-align: left">.199</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Natural</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.120</td>
<td style="vertical-align: top; text-align: left">.180</td>
<td style="vertical-align: top; text-align: left">.043</td>
<td style="vertical-align: top; text-align: left">−.180</td>
<td style="vertical-align: top; text-align: left">.033</td>
<td style="vertical-align: top; text-align: left">.207</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.120</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.039</td>
<td style="vertical-align: top; text-align: left">.098</td>
<td style="vertical-align: top; text-align: left">−.047</td>
<td style="vertical-align: top; text-align: left">−.022</td>
<td style="vertical-align: top; text-align: left">.196</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.180</td>
<td style="vertical-align: top; text-align: left">.039</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.069</td>
<td style="vertical-align: top; text-align: left">.128</td>
<td style="vertical-align: top; text-align: left">.011</td>
<td style="vertical-align: top; text-align: left">.202</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.043</td>
<td style="vertical-align: top; text-align: left">−.098</td>
<td style="vertical-align: top; text-align: left">−.069</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.180</td>
<td style="vertical-align: top; text-align: left">−.006</td>
<td style="vertical-align: top; text-align: left">.199</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.180</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.047</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">−.128</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">−.180</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.000</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">−.016</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.197</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_020">
<label>Table A.14</label>
<caption>
<p>Values of <inline-formula id="j_infor604_ineq_093"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${b_{ki}}$]]></tex-math></alternatives></inline-formula>, <inline-formula id="j_infor604_ineq_094"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${x_{k}}$]]></tex-math></alternatives></inline-formula>, and the weights of the criteria for the parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin"/>
<td colspan="5" style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_095"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${b_{ki}}$]]></tex-math></alternatives></inline-formula></td>
<td rowspan="2" style="vertical-align: middle; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_096"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${x_{k}}$]]></tex-math></alternatives></inline-formula></td>
<td rowspan="2" style="vertical-align: middle; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_097"><alternatives><mml:math>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="italic">W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub></mml:math><tex-math><![CDATA[${W_{k}}$]]></tex-math></alternatives></inline-formula></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.143</td>
<td style="vertical-align: top; text-align: left">.296</td>
<td style="vertical-align: top; text-align: left">.052</td>
<td style="vertical-align: top; text-align: left">−.299</td>
<td style="vertical-align: top; text-align: left">.038</td>
<td style="vertical-align: top; text-align: left">.208</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.143</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.050</td>
<td style="vertical-align: top; text-align: left">.144</td>
<td style="vertical-align: top; text-align: left">−.053</td>
<td style="vertical-align: top; text-align: left">−.020</td>
<td style="vertical-align: top; text-align: left">.196</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.296</td>
<td style="vertical-align: top; text-align: left">.050</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.054</td>
<td style="vertical-align: top; text-align: left">.199</td>
<td style="vertical-align: top; text-align: left">.002</td>
<td style="vertical-align: top; text-align: left">.200</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.052</td>
<td style="vertical-align: top; text-align: left">−.144</td>
<td style="vertical-align: top; text-align: left">−.054</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.291</td>
<td style="vertical-align: top; text-align: left">.008</td>
<td style="vertical-align: top; text-align: left">.202</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.299</td>
<td style="vertical-align: top; text-align: left">.053</td>
<td style="vertical-align: top; text-align: left">−.199</td>
<td style="vertical-align: top; text-align: left">−.291</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.028</td>
<td style="vertical-align: top; text-align: left">.194</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.059</td>
<td style="vertical-align: top; text-align: left">.283</td>
<td style="vertical-align: top; text-align: left">.034</td>
<td style="vertical-align: top; text-align: left">−.283</td>
<td style="vertical-align: top; text-align: left">.019</td>
<td style="vertical-align: top; text-align: left">.204</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.059</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.078</td>
<td style="vertical-align: top; text-align: left">.104</td>
<td style="vertical-align: top; text-align: left">−.039</td>
<td style="vertical-align: top; text-align: left">−.014</td>
<td style="vertical-align: top; text-align: left">.197</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.283</td>
<td style="vertical-align: top; text-align: left">.078</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.045</td>
<td style="vertical-align: top; text-align: left">.235</td>
<td style="vertical-align: top; text-align: left">.015</td>
<td style="vertical-align: top; text-align: left">.203</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.034</td>
<td style="vertical-align: top; text-align: left">−.104</td>
<td style="vertical-align: top; text-align: left">−.045</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.286</td>
<td style="vertical-align: top; text-align: left">.021</td>
<td style="vertical-align: top; text-align: left">.204</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.283</td>
<td style="vertical-align: top; text-align: left">.039</td>
<td style="vertical-align: top; text-align: left">−.235</td>
<td style="vertical-align: top; text-align: left">−.286</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.040</td>
<td style="vertical-align: top; text-align: left">.192</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.085</td>
<td style="vertical-align: top; text-align: left">.257</td>
<td style="vertical-align: top; text-align: left">.042</td>
<td style="vertical-align: top; text-align: left">−.252</td>
<td style="vertical-align: top; text-align: left">.026</td>
<td style="vertical-align: top; text-align: left">.205</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.085</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.081</td>
<td style="vertical-align: top; text-align: left">.104</td>
<td style="vertical-align: top; text-align: left">−.052</td>
<td style="vertical-align: top; text-align: left">−.023</td>
<td style="vertical-align: top; text-align: left">.195</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.257</td>
<td style="vertical-align: top; text-align: left">.081</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.075</td>
<td style="vertical-align: top; text-align: left">.221</td>
<td style="vertical-align: top; text-align: left">.024</td>
<td style="vertical-align: top; text-align: left">.205</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.042</td>
<td style="vertical-align: top; text-align: left">−.104</td>
<td style="vertical-align: top; text-align: left">−.075</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.265</td>
<td style="vertical-align: top; text-align: left">.009</td>
<td style="vertical-align: top; text-align: left">.202</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SWHYS</td>
<td style="vertical-align: top; text-align: left">.252</td>
<td style="vertical-align: top; text-align: left">.052</td>
<td style="vertical-align: top; text-align: left">−.221</td>
<td style="vertical-align: top; text-align: left">−.265</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.036</td>
<td style="vertical-align: top; text-align: left">.193</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CRCLT</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.093</td>
<td style="vertical-align: top; text-align: left">.279</td>
<td style="vertical-align: top; text-align: left">.043</td>
<td style="vertical-align: top; text-align: left">−.279</td>
<td style="vertical-align: top; text-align: left">.027</td>
<td style="vertical-align: top; text-align: left">.206</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UAMTR</td>
<td style="vertical-align: top; text-align: left">−.093</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">−.069</td>
<td style="vertical-align: top; text-align: left">.118</td>
<td style="vertical-align: top; text-align: left">−.049</td>
<td style="vertical-align: top; text-align: left">−.019</td>
<td style="vertical-align: top; text-align: left">.196</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">CWEMI</td>
<td style="vertical-align: top; text-align: left">−.279</td>
<td style="vertical-align: top; text-align: left">.069</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.059</td>
<td style="vertical-align: top; text-align: left">.219</td>
<td style="vertical-align: top; text-align: left">.014</td>
<td style="vertical-align: top; text-align: left">.203</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">SFETY</td>
<td style="vertical-align: top; text-align: left">−.043</td>
<td style="vertical-align: top; text-align: left">−.118</td>
<td style="vertical-align: top; text-align: left">−.059</td>
<td style="vertical-align: top; text-align: left">.000</td>
<td style="vertical-align: top; text-align: left">.281</td>
<td style="vertical-align: top; text-align: left">.012</td>
<td style="vertical-align: top; text-align: left">.202</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">SWHYS</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.279</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.049</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">−.219</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">−.281</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.000</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">−.035</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.193</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_021">
<label>Table A.15</label>
<caption>
<p>Averaged fuzzy numbers for overall performance of decision matrix with case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.60, .42, .31, .47, .70)</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .15, .68, .85)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .15, .68, .85)</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.60, .42, .31, .47, .70)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .34, .38, .62)</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .15, .68, .85)</td>
<td style="vertical-align: top; text-align: left">(.60, .42, .31, .47, .70)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, .34, .38, .62)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .37, .26, .57, .77)</td>
<td style="vertical-align: top; text-align: left">(.80, .33, .15, .68, .85)</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
<td style="vertical-align: top; text-align: left">(.90, .31, .06, .82, .92)</td>
<td style="vertical-align: top; text-align: left">(.60, .42, .31, .47, .70)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .33, .15, .68, .85)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .42, .31, .47, .70)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .42, .31, .47, .70)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .33, .15, .68, .85)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .31, .06, .82, .92)</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_022">
<label>Table A.16</label>
<caption>
<p>Averaged fuzzy numbers for overall performance of decision matrix with parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">(.90, .09, .24, .66, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .23, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .35, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .23, .88, .24, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .15, .57, .41, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">(.80, .22, .57, .43, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .29, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .29, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.70, .29, .89, .26, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .38, 1.00, .14, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .02, .24, .68, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .05, .56, .44, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .27, 1.00, .16, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.50, .50, 1.00, .08, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">(.70, .20, .88, .23, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.80, .12, .57, .40, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .07, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.90, .07, .24, .65, 1.00)</td>
<td style="vertical-align: top; text-align: left">(.60, .33, 1.00, .12, 1.00)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .11, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .33, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.60, .33, 1.00, .13, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.80, .11, .57, .41, 1.00)</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">(.90, .06, .24, .66, 1.00)</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_023">
<label>Table A.17</label>
<caption>
<p>Defuzzified decision matrix by the case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">NEGATIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.906</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.506</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.782</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.506</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.361</td>
<td style="vertical-align: top; text-align: left">.906</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.506</td>
<td style="vertical-align: top; text-align: left">.361</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.906</td>
<td style="vertical-align: top; text-align: left">.906</td>
<td style="vertical-align: top; text-align: left">.506</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.506</td>
<td style="vertical-align: top; text-align: left">.506</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.906</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">POSITIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.346</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.535</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.535</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.346</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.295</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.535</td>
<td style="vertical-align: top; text-align: left">.346</td>
<td style="vertical-align: top; text-align: left">.295</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.421</td>
<td style="vertical-align: top; text-align: left">.535</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.346</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.535</td>
<td style="vertical-align: top; text-align: left">.346</td>
<td style="vertical-align: top; text-align: left">.346</td>
<td style="vertical-align: top; text-align: left">.535</td>
<td style="vertical-align: top; text-align: left">.706</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UNSTABLE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.882</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.940</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.940</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.882</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.853</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.940</td>
<td style="vertical-align: top; text-align: left">.882</td>
<td style="vertical-align: top; text-align: left">.853</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.940</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.882</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.940</td>
<td style="vertical-align: top; text-align: left">.882</td>
<td style="vertical-align: top; text-align: left">.882</td>
<td style="vertical-align: top; text-align: left">.940</td>
<td style="vertical-align: top; text-align: left">.960</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">NATURAL</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.860</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.665</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.795</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.795</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.665</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.600</td>
<td style="vertical-align: top; text-align: left">.860</td>
<td style="vertical-align: top; text-align: left">.795</td>
<td style="vertical-align: top; text-align: left">.665</td>
<td style="vertical-align: top; text-align: left">.600</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.795</td>
<td style="vertical-align: top; text-align: left">.860</td>
<td style="vertical-align: top; text-align: left">.860</td>
<td style="vertical-align: top; text-align: left">.665</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.795</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.665</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.665</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.795</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.860</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_024">
<label>Table A.18</label>
<caption>
<p>Defuzzified decision matrix by the parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.898</td>
<td style="vertical-align: top; text-align: left">.680</td>
<td style="vertical-align: top; text-align: left">.586</td>
<td style="vertical-align: top; text-align: left">.680</td>
<td style="vertical-align: top; text-align: left">.790</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.802</td>
<td style="vertical-align: top; text-align: left">.696</td>
<td style="vertical-align: top; text-align: left">.696</td>
<td style="vertical-align: top; text-align: left">.696</td>
<td style="vertical-align: top; text-align: left">.605</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.534</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.815</td>
<td style="vertical-align: top; text-align: left">.625</td>
<td style="vertical-align: top; text-align: left">.534</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.663</td>
<td style="vertical-align: top; text-align: left">.778</td>
<td style="vertical-align: top; text-align: left">.891</td>
<td style="vertical-align: top; text-align: left">.891</td>
<td style="vertical-align: top; text-align: left">.565</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.791</td>
<td style="vertical-align: top; text-align: left">.586</td>
<td style="vertical-align: top; text-align: left">.586</td>
<td style="vertical-align: top; text-align: left">.791</td>
<td style="vertical-align: top; text-align: left">.898</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.852</td>
<td style="vertical-align: top; text-align: left">.596</td>
<td style="vertical-align: top; text-align: left">.526</td>
<td style="vertical-align: top; text-align: left">.596</td>
<td style="vertical-align: top; text-align: left">.718</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.715</td>
<td style="vertical-align: top; text-align: left">.599</td>
<td style="vertical-align: top; text-align: left">.599</td>
<td style="vertical-align: top; text-align: left">.599</td>
<td style="vertical-align: top; text-align: left">.540</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.532</td>
<td style="vertical-align: top; text-align: left">.910</td>
<td style="vertical-align: top; text-align: left">.813</td>
<td style="vertical-align: top; text-align: left">.623</td>
<td style="vertical-align: top; text-align: left">.532</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.589</td>
<td style="vertical-align: top; text-align: left">.716</td>
<td style="vertical-align: top; text-align: left">.854</td>
<td style="vertical-align: top; text-align: left">.854</td>
<td style="vertical-align: top; text-align: left">.510</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.737</td>
<td style="vertical-align: top; text-align: left">.539</td>
<td style="vertical-align: top; text-align: left">.539</td>
<td style="vertical-align: top; text-align: left">.737</td>
<td style="vertical-align: top; text-align: left">.866</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.865</td>
<td style="vertical-align: top; text-align: left">.632</td>
<td style="vertical-align: top; text-align: left">.568</td>
<td style="vertical-align: top; text-align: left">.632</td>
<td style="vertical-align: top; text-align: left">.743</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.729</td>
<td style="vertical-align: top; text-align: left">.618</td>
<td style="vertical-align: top; text-align: left">.618</td>
<td style="vertical-align: top; text-align: left">.618</td>
<td style="vertical-align: top; text-align: left">.562</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.534</td>
<td style="vertical-align: top; text-align: left">.912</td>
<td style="vertical-align: top; text-align: left">.815</td>
<td style="vertical-align: top; text-align: left">.625</td>
<td style="vertical-align: top; text-align: left">.534</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.641</td>
<td style="vertical-align: top; text-align: left">.752</td>
<td style="vertical-align: top; text-align: left">.872</td>
<td style="vertical-align: top; text-align: left">.872</td>
<td style="vertical-align: top; text-align: left">.571</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.760</td>
<td style="vertical-align: top; text-align: left">.577</td>
<td style="vertical-align: top; text-align: left">.577</td>
<td style="vertical-align: top; text-align: left">.760</td>
<td style="vertical-align: top; text-align: left">.878</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left"><bold>Balanced</bold></td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.874</td>
<td style="vertical-align: top; text-align: left">.634</td>
<td style="vertical-align: top; text-align: left">.557</td>
<td style="vertical-align: top; text-align: left">.634</td>
<td style="vertical-align: top; text-align: left">.752</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.744</td>
<td style="vertical-align: top; text-align: left">.629</td>
<td style="vertical-align: top; text-align: left">.629</td>
<td style="vertical-align: top; text-align: left">.629</td>
<td style="vertical-align: top; text-align: left">.562</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.533</td>
<td style="vertical-align: top; text-align: left">.911</td>
<td style="vertical-align: top; text-align: left">.815</td>
<td style="vertical-align: top; text-align: left">.624</td>
<td style="vertical-align: top; text-align: left">.533</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.631</td>
<td style="vertical-align: top; text-align: left">.750</td>
<td style="vertical-align: top; text-align: left">.874</td>
<td style="vertical-align: top; text-align: left">.874</td>
<td style="vertical-align: top; text-align: left">.547</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.764</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.566</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.566</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.764</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.882</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_025">
<label>Table A.19</label>
<caption>
<p>Normalized decision matrix by the case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">NEGATIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.704</td>
<td style="vertical-align: top; text-align: left">.559</td>
<td style="vertical-align: top; text-align: left">.704</td>
<td style="vertical-align: top; text-align: left">.863</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.863</td>
<td style="vertical-align: top; text-align: left">.704</td>
<td style="vertical-align: top; text-align: left">.704</td>
<td style="vertical-align: top; text-align: left">.704</td>
<td style="vertical-align: top; text-align: left">.559</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.399</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.863</td>
<td style="vertical-align: top; text-align: left">.559</td>
<td style="vertical-align: top; text-align: left">.399</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.704</td>
<td style="vertical-align: top; text-align: left">.863</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.559</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.863</td>
<td style="vertical-align: top; text-align: left">.559</td>
<td style="vertical-align: top; text-align: left">.559</td>
<td style="vertical-align: top; text-align: left">.863</td>
<td style="vertical-align: top; text-align: left">1.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">POSITIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.597</td>
<td style="vertical-align: top; text-align: left">.490</td>
<td style="vertical-align: top; text-align: left">.597</td>
<td style="vertical-align: top; text-align: left">.758</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.758</td>
<td style="vertical-align: top; text-align: left">.597</td>
<td style="vertical-align: top; text-align: left">.597</td>
<td style="vertical-align: top; text-align: left">.597</td>
<td style="vertical-align: top; text-align: left">.490</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.418</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.758</td>
<td style="vertical-align: top; text-align: left">.490</td>
<td style="vertical-align: top; text-align: left">.418</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.597</td>
<td style="vertical-align: top; text-align: left">.758</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.490</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.758</td>
<td style="vertical-align: top; text-align: left">.490</td>
<td style="vertical-align: top; text-align: left">.490</td>
<td style="vertical-align: top; text-align: left">.758</td>
<td style="vertical-align: top; text-align: left">1.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UNSTABLE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.950</td>
<td style="vertical-align: top; text-align: left">.919</td>
<td style="vertical-align: top; text-align: left">.950</td>
<td style="vertical-align: top; text-align: left">.980</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.980</td>
<td style="vertical-align: top; text-align: left">.950</td>
<td style="vertical-align: top; text-align: left">.950</td>
<td style="vertical-align: top; text-align: left">.950</td>
<td style="vertical-align: top; text-align: left">.919</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.889</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.980</td>
<td style="vertical-align: top; text-align: left">.919</td>
<td style="vertical-align: top; text-align: left">.889</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.950</td>
<td style="vertical-align: top; text-align: left">.980</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.919</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.980</td>
<td style="vertical-align: top; text-align: left">.919</td>
<td style="vertical-align: top; text-align: left">.919</td>
<td style="vertical-align: top; text-align: left">.980</td>
<td style="vertical-align: top; text-align: left">1.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">NATURAL EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.849</td>
<td style="vertical-align: top; text-align: left">.773</td>
<td style="vertical-align: top; text-align: left">.849</td>
<td style="vertical-align: top; text-align: left">.925</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.925</td>
<td style="vertical-align: top; text-align: left">.849</td>
<td style="vertical-align: top; text-align: left">.849</td>
<td style="vertical-align: top; text-align: left">.849</td>
<td style="vertical-align: top; text-align: left">.773</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.698</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.925</td>
<td style="vertical-align: top; text-align: left">.773</td>
<td style="vertical-align: top; text-align: left">.698</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.849</td>
<td style="vertical-align: top; text-align: left">.925</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.773</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.925</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.773</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.773</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.925</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">1.000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_026">
<label>Table A.20</label>
<caption>
<p>Normalized decision matrix by the parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.746</td>
<td style="vertical-align: top; text-align: left">.658</td>
<td style="vertical-align: top; text-align: left">.764</td>
<td style="vertical-align: top; text-align: left">.880</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.893</td>
<td style="vertical-align: top; text-align: left">.763</td>
<td style="vertical-align: top; text-align: left">.781</td>
<td style="vertical-align: top; text-align: left">.781</td>
<td style="vertical-align: top; text-align: left">.674</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.594</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.915</td>
<td style="vertical-align: top; text-align: left">.701</td>
<td style="vertical-align: top; text-align: left">.594</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.739</td>
<td style="vertical-align: top; text-align: left">.853</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.630</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.881</td>
<td style="vertical-align: top; text-align: left">.643</td>
<td style="vertical-align: top; text-align: left">.658</td>
<td style="vertical-align: top; text-align: left">.888</td>
<td style="vertical-align: top; text-align: left">1.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.655</td>
<td style="vertical-align: top; text-align: left">.616</td>
<td style="vertical-align: top; text-align: left">.699</td>
<td style="vertical-align: top; text-align: left">.829</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.839</td>
<td style="vertical-align: top; text-align: left">.658</td>
<td style="vertical-align: top; text-align: left">.702</td>
<td style="vertical-align: top; text-align: left">.702</td>
<td style="vertical-align: top; text-align: left">.624</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.625</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.952</td>
<td style="vertical-align: top; text-align: left">.730</td>
<td style="vertical-align: top; text-align: left">.615</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.691</td>
<td style="vertical-align: top; text-align: left">.787</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.588</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.865</td>
<td style="vertical-align: top; text-align: left">.592</td>
<td style="vertical-align: top; text-align: left">.631</td>
<td style="vertical-align: top; text-align: left">.864</td>
<td style="vertical-align: top; text-align: left">1.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.693</td>
<td style="vertical-align: top; text-align: left">.651</td>
<td style="vertical-align: top; text-align: left">.725</td>
<td style="vertical-align: top; text-align: left">.847</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.842</td>
<td style="vertical-align: top; text-align: left">.678</td>
<td style="vertical-align: top; text-align: left">.709</td>
<td style="vertical-align: top; text-align: left">.709</td>
<td style="vertical-align: top; text-align: left">.641</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.617</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.935</td>
<td style="vertical-align: top; text-align: left">.716</td>
<td style="vertical-align: top; text-align: left">.608</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.740</td>
<td style="vertical-align: top; text-align: left">.825</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.650</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.878</td>
<td style="vertical-align: top; text-align: left">.633</td>
<td style="vertical-align: top; text-align: left">.662</td>
<td style="vertical-align: top; text-align: left">.872</td>
<td style="vertical-align: top; text-align: left">1.000</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.696</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.726</td>
<td style="vertical-align: top; text-align: left">.852</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.851</td>
<td style="vertical-align: top; text-align: left">.691</td>
<td style="vertical-align: top; text-align: left">.720</td>
<td style="vertical-align: top; text-align: left">.720</td>
<td style="vertical-align: top; text-align: left">.637</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.610</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.932</td>
<td style="vertical-align: top; text-align: left">.714</td>
<td style="vertical-align: top; text-align: left">.604</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.721</td>
<td style="vertical-align: top; text-align: left">.823</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">1.000</td>
<td style="vertical-align: top; text-align: left">.620</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.874</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.621</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.648</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.874</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">1.000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="j_infor604_tab_027">
<label>Table A.21</label>
<caption>
<p>Weighted decision matrix by the case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">NEGATIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.222</td>
<td style="vertical-align: top; text-align: left">.132</td>
<td style="vertical-align: top; text-align: left">.115</td>
<td style="vertical-align: top; text-align: left">.135</td>
<td style="vertical-align: top; text-align: left">.166</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.192</td>
<td style="vertical-align: top; text-align: left">.132</td>
<td style="vertical-align: top; text-align: left">.145</td>
<td style="vertical-align: top; text-align: left">.135</td>
<td style="vertical-align: top; text-align: left">.108</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.088</td>
<td style="vertical-align: top; text-align: left">.187</td>
<td style="vertical-align: top; text-align: left">.178</td>
<td style="vertical-align: top; text-align: left">.108</td>
<td style="vertical-align: top; text-align: left">.077</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.156</td>
<td style="vertical-align: top; text-align: left">.161</td>
<td style="vertical-align: top; text-align: left">.206</td>
<td style="vertical-align: top; text-align: left">.192</td>
<td style="vertical-align: top; text-align: left">.108</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.192</td>
<td style="vertical-align: top; text-align: left">.104</td>
<td style="vertical-align: top; text-align: left">.115</td>
<td style="vertical-align: top; text-align: left">.166</td>
<td style="vertical-align: top; text-align: left">.193</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">POSITIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.211</td>
<td style="vertical-align: top; text-align: left">.114</td>
<td style="vertical-align: top; text-align: left">.101</td>
<td style="vertical-align: top; text-align: left">.121</td>
<td style="vertical-align: top; text-align: left">.144</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.160</td>
<td style="vertical-align: top; text-align: left">.114</td>
<td style="vertical-align: top; text-align: left">.123</td>
<td style="vertical-align: top; text-align: left">.121</td>
<td style="vertical-align: top; text-align: left">.093</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.088</td>
<td style="vertical-align: top; text-align: left">.191</td>
<td style="vertical-align: top; text-align: left">.156</td>
<td style="vertical-align: top; text-align: left">.099</td>
<td style="vertical-align: top; text-align: left">.079</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.126</td>
<td style="vertical-align: top; text-align: left">.145</td>
<td style="vertical-align: top; text-align: left">.205</td>
<td style="vertical-align: top; text-align: left">.202</td>
<td style="vertical-align: top; text-align: left">.093</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.160</td>
<td style="vertical-align: top; text-align: left">.094</td>
<td style="vertical-align: top; text-align: left">.101</td>
<td style="vertical-align: top; text-align: left">.153</td>
<td style="vertical-align: top; text-align: left">.190</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UNSTABLE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.202</td>
<td style="vertical-align: top; text-align: left">.189</td>
<td style="vertical-align: top; text-align: left">.184</td>
<td style="vertical-align: top; text-align: left">.190</td>
<td style="vertical-align: top; text-align: left">.195</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.198</td>
<td style="vertical-align: top; text-align: left">.189</td>
<td style="vertical-align: top; text-align: left">.190</td>
<td style="vertical-align: top; text-align: left">.190</td>
<td style="vertical-align: top; text-align: left">.183</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.180</td>
<td style="vertical-align: top; text-align: left">.199</td>
<td style="vertical-align: top; text-align: left">.196</td>
<td style="vertical-align: top; text-align: left">.184</td>
<td style="vertical-align: top; text-align: left">.177</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.192</td>
<td style="vertical-align: top; text-align: left">.195</td>
<td style="vertical-align: top; text-align: left">.200</td>
<td style="vertical-align: top; text-align: left">.200</td>
<td style="vertical-align: top; text-align: left">.183</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.198</td>
<td style="vertical-align: top; text-align: left">.183</td>
<td style="vertical-align: top; text-align: left">.184</td>
<td style="vertical-align: top; text-align: left">.196</td>
<td style="vertical-align: top; text-align: left">.199</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">NATURAL</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.207</td>
<td style="vertical-align: top; text-align: left">.166</td>
<td style="vertical-align: top; text-align: left">.156</td>
<td style="vertical-align: top; text-align: left">.169</td>
<td style="vertical-align: top; text-align: left">.182</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.191</td>
<td style="vertical-align: top; text-align: left">.166</td>
<td style="vertical-align: top; text-align: left">.172</td>
<td style="vertical-align: top; text-align: left">.169</td>
<td style="vertical-align: top; text-align: left">.152</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.144</td>
<td style="vertical-align: top; text-align: left">.196</td>
<td style="vertical-align: top; text-align: left">.187</td>
<td style="vertical-align: top; text-align: left">.154</td>
<td style="vertical-align: top; text-align: left">.137</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.175</td>
<td style="vertical-align: top; text-align: left">.181</td>
<td style="vertical-align: top; text-align: left">.202</td>
<td style="vertical-align: top; text-align: left">.199</td>
<td style="vertical-align: top; text-align: left">.152</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.191</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.151</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.156</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.184</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.197</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_028">
<label>Table A.22</label>
<caption>
<p>Weighted decision matrix by the parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CRCLT</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">UAMTR</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">CWEMI</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SFETY</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SWHYS</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.208</td>
<td style="vertical-align: top; text-align: left">.146</td>
<td style="vertical-align: top; text-align: left">.132</td>
<td style="vertical-align: top; text-align: left">.154</td>
<td style="vertical-align: top; text-align: left">.171</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.185</td>
<td style="vertical-align: top; text-align: left">.149</td>
<td style="vertical-align: top; text-align: left">.156</td>
<td style="vertical-align: top; text-align: left">.157</td>
<td style="vertical-align: top; text-align: left">.131</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.123</td>
<td style="vertical-align: top; text-align: left">.196</td>
<td style="vertical-align: top; text-align: left">.183</td>
<td style="vertical-align: top; text-align: left">.141</td>
<td style="vertical-align: top; text-align: left">.116</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.154</td>
<td style="vertical-align: top; text-align: left">.167</td>
<td style="vertical-align: top; text-align: left">.200</td>
<td style="vertical-align: top; text-align: left">.202</td>
<td style="vertical-align: top; text-align: left">.122</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.183</td>
<td style="vertical-align: top; text-align: left">.126</td>
<td style="vertical-align: top; text-align: left">.132</td>
<td style="vertical-align: top; text-align: left">.179</td>
<td style="vertical-align: top; text-align: left">.194</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.204</td>
<td style="vertical-align: top; text-align: left">.129</td>
<td style="vertical-align: top; text-align: left">.125</td>
<td style="vertical-align: top; text-align: left">.143</td>
<td style="vertical-align: top; text-align: left">.159</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.171</td>
<td style="vertical-align: top; text-align: left">.130</td>
<td style="vertical-align: top; text-align: left">.142</td>
<td style="vertical-align: top; text-align: left">.143</td>
<td style="vertical-align: top; text-align: left">.120</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.127</td>
<td style="vertical-align: top; text-align: left">.197</td>
<td style="vertical-align: top; text-align: left">.193</td>
<td style="vertical-align: top; text-align: left">.149</td>
<td style="vertical-align: top; text-align: left">.118</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.141</td>
<td style="vertical-align: top; text-align: left">.155</td>
<td style="vertical-align: top; text-align: left">.203</td>
<td style="vertical-align: top; text-align: left">.204</td>
<td style="vertical-align: top; text-align: left">.113</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.176</td>
<td style="vertical-align: top; text-align: left">.117</td>
<td style="vertical-align: top; text-align: left">.128</td>
<td style="vertical-align: top; text-align: left">.176</td>
<td style="vertical-align: top; text-align: left">.192</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.205</td>
<td style="vertical-align: top; text-align: left">.136</td>
<td style="vertical-align: top; text-align: left">.133</td>
<td style="vertical-align: top; text-align: left">.146</td>
<td style="vertical-align: top; text-align: left">.163</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.173</td>
<td style="vertical-align: top; text-align: left">.133</td>
<td style="vertical-align: top; text-align: left">.145</td>
<td style="vertical-align: top; text-align: left">.143</td>
<td style="vertical-align: top; text-align: left">.124</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.127</td>
<td style="vertical-align: top; text-align: left">.195</td>
<td style="vertical-align: top; text-align: left">.191</td>
<td style="vertical-align: top; text-align: left">.144</td>
<td style="vertical-align: top; text-align: left">.117</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.152</td>
<td style="vertical-align: top; text-align: left">.161</td>
<td style="vertical-align: top; text-align: left">.205</td>
<td style="vertical-align: top; text-align: left">.202</td>
<td style="vertical-align: top; text-align: left">.125</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.180</td>
<td style="vertical-align: top; text-align: left">.124</td>
<td style="vertical-align: top; text-align: left">.136</td>
<td style="vertical-align: top; text-align: left">.176</td>
<td style="vertical-align: top; text-align: left">.193</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.206</td>
<td style="vertical-align: top; text-align: left">.137</td>
<td style="vertical-align: top; text-align: left">.129</td>
<td style="vertical-align: top; text-align: left">.147</td>
<td style="vertical-align: top; text-align: left">.165</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.175</td>
<td style="vertical-align: top; text-align: left">.136</td>
<td style="vertical-align: top; text-align: left">.146</td>
<td style="vertical-align: top; text-align: left">.146</td>
<td style="vertical-align: top; text-align: left">.123</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.125</td>
<td style="vertical-align: top; text-align: left">.196</td>
<td style="vertical-align: top; text-align: left">.189</td>
<td style="vertical-align: top; text-align: left">.145</td>
<td style="vertical-align: top; text-align: left">.117</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.148</td>
<td style="vertical-align: top; text-align: left">.162</td>
<td style="vertical-align: top; text-align: left">.203</td>
<td style="vertical-align: top; text-align: left">.202</td>
<td style="vertical-align: top; text-align: left">.120</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.180</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.122</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.131</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.177</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.193</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_029">
<label>Table A.23</label>
<caption>
<p>SAW, WPN, and combining scores by the case-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SAW</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">WPN</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">Combining scores (<inline-formula id="j_infor604_ineq_098"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.5</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.5$]]></tex-math></alternatives></inline-formula>)</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">NEGATIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.770</td>
<td style="vertical-align: top; text-align: left">.683</td>
<td style="vertical-align: top; text-align: left">.727</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.711</td>
<td style="vertical-align: top; text-align: left">.638</td>
<td style="vertical-align: top; text-align: left">.675</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.638</td>
<td style="vertical-align: top; text-align: left">.537</td>
<td style="vertical-align: top; text-align: left">.587</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.824</td>
<td style="vertical-align: top; text-align: left">.729</td>
<td style="vertical-align: top; text-align: left">.776</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.770</td>
<td style="vertical-align: top; text-align: left">.678</td>
<td style="vertical-align: top; text-align: left">.724</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">POSITIVE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.691</td>
<td style="vertical-align: top; text-align: left">.472</td>
<td style="vertical-align: top; text-align: left">.581</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.611</td>
<td style="vertical-align: top; text-align: left">.427</td>
<td style="vertical-align: top; text-align: left">.519</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.614</td>
<td style="vertical-align: top; text-align: left">.407</td>
<td style="vertical-align: top; text-align: left">.510</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.772</td>
<td style="vertical-align: top; text-align: left">.524</td>
<td style="vertical-align: top; text-align: left">.648</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.698</td>
<td style="vertical-align: top; text-align: left">.474</td>
<td style="vertical-align: top; text-align: left">.586</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">UNSTABLE</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.960</td>
<td style="vertical-align: top; text-align: left">.921</td>
<td style="vertical-align: top; text-align: left">.940</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.950</td>
<td style="vertical-align: top; text-align: left">.911</td>
<td style="vertical-align: top; text-align: left">.930</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.935</td>
<td style="vertical-align: top; text-align: left">.897</td>
<td style="vertical-align: top; text-align: left">.916</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.970</td>
<td style="vertical-align: top; text-align: left">.930</td>
<td style="vertical-align: top; text-align: left">.950</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.959</td>
<td style="vertical-align: top; text-align: left">.920</td>
<td style="vertical-align: top; text-align: left">.940</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">NATURAL</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.880</td>
<td style="vertical-align: top; text-align: left">.753</td>
<td style="vertical-align: top; text-align: left">.817</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.850</td>
<td style="vertical-align: top; text-align: left">.729</td>
<td style="vertical-align: top; text-align: left">.790</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.818</td>
<td style="vertical-align: top; text-align: left">.696</td>
<td style="vertical-align: top; text-align: left">.757</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.909</td>
<td style="vertical-align: top; text-align: left">.778</td>
<td style="vertical-align: top; text-align: left">.844</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.879</td>
<td style="vertical-align: top; text-align: left">.752</td>
<td style="vertical-align: top; text-align: left">.816</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">OVERALL</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.846</td>
<td style="vertical-align: top; text-align: left">.713</td>
<td style="vertical-align: top; text-align: left">.780</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.807</td>
<td style="vertical-align: top; text-align: left">.683</td>
<td style="vertical-align: top; text-align: left">.745</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.775</td>
<td style="vertical-align: top; text-align: left">.646</td>
<td style="vertical-align: top; text-align: left">.710</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.885</td>
<td style="vertical-align: top; text-align: left">.745</td>
<td style="vertical-align: top; text-align: left">.815</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.847</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.712</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.780</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_030">
<label>Table A.24</label>
<caption>
<p>SAW, WPN, and combining scores by the parameter-based assessments.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">SAW</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">WPN</td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin">Combining scores (<inline-formula id="j_infor604_ineq_099"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.5</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.5$]]></tex-math></alternatives></inline-formula>)</td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Maximum variance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.811</td>
<td style="vertical-align: top; text-align: left">.720</td>
<td style="vertical-align: top; text-align: left">.766</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.780</td>
<td style="vertical-align: top; text-align: left">.697</td>
<td style="vertical-align: top; text-align: left">.739</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.760</td>
<td style="vertical-align: top; text-align: left">.666</td>
<td style="vertical-align: top; text-align: left">.713</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.845</td>
<td style="vertical-align: top; text-align: left">.747</td>
<td style="vertical-align: top; text-align: left">.796</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.814</td>
<td style="vertical-align: top; text-align: left">.720</td>
<td style="vertical-align: top; text-align: left">.767</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum entropy</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.760</td>
<td style="vertical-align: top; text-align: left">.648</td>
<td style="vertical-align: top; text-align: left">.704</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.706</td>
<td style="vertical-align: top; text-align: left">.609</td>
<td style="vertical-align: top; text-align: left">.658</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.785</td>
<td style="vertical-align: top; text-align: left">.666</td>
<td style="vertical-align: top; text-align: left">.725</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.816</td>
<td style="vertical-align: top; text-align: left">.692</td>
<td style="vertical-align: top; text-align: left">.754</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.790</td>
<td style="vertical-align: top; text-align: left">.671</td>
<td style="vertical-align: top; text-align: left">.730</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Maximum resistance</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.784</td>
<td style="vertical-align: top; text-align: left">.681</td>
<td style="vertical-align: top; text-align: left">.732</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.717</td>
<td style="vertical-align: top; text-align: left">.628</td>
<td style="vertical-align: top; text-align: left">.672</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.775</td>
<td style="vertical-align: top; text-align: left">.667</td>
<td style="vertical-align: top; text-align: left">.721</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.845</td>
<td style="vertical-align: top; text-align: left">.733</td>
<td style="vertical-align: top; text-align: left">.789</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.808</td>
<td style="vertical-align: top; text-align: left">.700</td>
<td style="vertical-align: top; text-align: left">.754</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Balanced</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.783</td>
<td style="vertical-align: top; text-align: left">.682</td>
<td style="vertical-align: top; text-align: left">.732</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.725</td>
<td style="vertical-align: top; text-align: left">.637</td>
<td style="vertical-align: top; text-align: left">.681</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.772</td>
<td style="vertical-align: top; text-align: left">.666</td>
<td style="vertical-align: top; text-align: left">.719</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.835</td>
<td style="vertical-align: top; text-align: left">.725</td>
<td style="vertical-align: top; text-align: left">.780</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">.803</td>
<td style="vertical-align: top; text-align: left">.697</td>
<td style="vertical-align: top; text-align: left">.750</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Overall</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">.782</td>
<td style="vertical-align: top; text-align: left">.679</td>
<td style="vertical-align: top; text-align: left">.731</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">.723</td>
<td style="vertical-align: top; text-align: left">.634</td>
<td style="vertical-align: top; text-align: left">.678</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">.774</td>
<td style="vertical-align: top; text-align: left">.666</td>
<td style="vertical-align: top; text-align: left">.720</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">.835</td>
<td style="vertical-align: top; text-align: left">.723</td>
<td style="vertical-align: top; text-align: left">.779</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.804</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.696</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">.750</td>
</tr>
</tbody>
</table>
</table-wrap> 
<table-wrap id="j_infor604_tab_031">
<label>Table A.25</label>
<caption>
<p>Comparative ranking results of the alternatives by the case-based assessments with the different combination parameters.</p>
</caption>
<table>
<thead>
<tr>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"/>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_100"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_101"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.1</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.1$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_102"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.2</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.2$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_103"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.3</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.3$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_104"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.4</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.4$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_105"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.5</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.5$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_106"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.6</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.6$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_107"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.7</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.7$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_108"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.8</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.8$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_109"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.9</mml:mn></mml:math><tex-math><![CDATA[$\gamma =0.9$]]></tex-math></alternatives></inline-formula></td>
<td style="vertical-align: top; text-align: left; border-top: solid thin; border-bottom: solid thin"><inline-formula id="j_infor604_ineq_110"><alternatives><mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn></mml:math><tex-math><![CDATA[$\gamma =1$]]></tex-math></alternatives></inline-formula></td>
</tr>
</thead>
<tbody>
<tr>
<td style="vertical-align: top; text-align: left">Negative</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Positive</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Unstable</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Natural</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
<td style="vertical-align: top; text-align: left">2</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">ESBST</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">Overall</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EVWHD</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
<td style="vertical-align: top; text-align: left">3</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">GSWCL</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
<td style="vertical-align: top; text-align: left">4</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">LCESM</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
<td style="vertical-align: top; text-align: left">5</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left">EPEWC</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
<td style="vertical-align: top; text-align: left">1</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">ESBST</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
<td style="vertical-align: top; text-align: left; border-bottom: solid thin">2</td>
</tr>
</tbody>
</table>
</table-wrap>
</app></app-group>
<ref-list id="j_infor604_reflist_001">
<title>References</title>
<ref id="j_infor604_ref_001">
<mixed-citation publication-type="journal"><string-name><surname>Ajibade</surname>, <given-names>H.</given-names></string-name>, <string-name><surname>Ujah</surname>, <given-names>C.O.</given-names></string-name>, <string-name><surname>Nnakwo</surname>, <given-names>K.C.</given-names></string-name>, <string-name><surname>Kallon</surname>, <given-names>D.V.</given-names></string-name> (<year>2024</year>). <article-title>Improvement in battery technologies as panacea for renewable energy crisis</article-title>. <source>Discover Applied Sciences</source>, <volume>6</volume>(<issue>7</issue>), <fpage>374</fpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_002">
<mixed-citation publication-type="journal"><string-name><surname>Altiparmak</surname>, <given-names>S.O.</given-names></string-name>, <string-name><surname>Waters</surname>, <given-names>K.</given-names></string-name>, <string-name><surname>Thies</surname>, <given-names>C.G.</given-names></string-name>, <string-name><surname>Shutters</surname>, <given-names>S.T.</given-names></string-name> (<year>2025</year>). <article-title>Cornering the market with foreign direct investments: China’s cobalt politics</article-title>. <source>Renewable and Sustainable Energy Transition</source>, <volume>7</volume>, <elocation-id>100113</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_003">
<mixed-citation publication-type="journal"><string-name><surname>Bican</surname>, <given-names>P.M.</given-names></string-name>, <string-name><surname>Caspary</surname>, <given-names>D.</given-names></string-name>, <string-name><surname>Guderian</surname>, <given-names>C.C.</given-names></string-name> (<year>2023</year>). <article-title>Cross-border dynamics of IP modularity: international patenting in LEDs and lithium-ion secondary battery technology</article-title>. <source>Management International Review</source>, <volume>63</volume>(<issue>2</issue>), <fpage>347</fpage>–<lpage>376</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_004">
<mixed-citation publication-type="journal"><string-name><surname>Chakraborty</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Zavadskas</surname>, <given-names>E.K.</given-names></string-name> (<year>2014</year>). <article-title>Applications of WASPAS method in manufacturing decision making</article-title>. <source>Informatica</source>, <volume>25</volume>(<issue>1</issue>), <fpage>1</fpage>–<lpage>20</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_005">
<mixed-citation publication-type="journal"><string-name><surname>Daniarta</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Kolasiński</surname>, <given-names>P.</given-names></string-name>, <string-name><surname>Imre</surname>, <given-names>A.R.</given-names></string-name> (<year>2024</year>). <article-title>Performance map and theoretical analysis of Carnot battery technology via novel reversible Rankine-based cycle</article-title>. <source>Energy Reports</source>, <volume>11</volume>, <fpage>4500</fpage>–<lpage>4514</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_006">
<mixed-citation publication-type="journal"><string-name><surname>De Luca</surname>, <given-names>G.</given-names></string-name>, <string-name><surname>Magnus</surname>, <given-names>J.R.</given-names></string-name>, <string-name><surname>Peracchi</surname>, <given-names>F.</given-names></string-name> (<year>2023</year>). <article-title>Weighted-average least squares (WALS): confidence and prediction intervals</article-title>. <source>Computational Economics</source>, <volume>61</volume>(<issue>4</issue>), <fpage>1637</fpage>–<lpage>1664</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_007">
<mixed-citation publication-type="journal"><string-name><surname>Deb</surname>, <given-names>P.P.</given-names></string-name>, <string-name><surname>Bhattacharya</surname>, <given-names>D.</given-names></string-name>, <string-name><surname>Chatterjee</surname>, <given-names>I.</given-names></string-name>, <string-name><surname>Chatterjee</surname>, <given-names>P.</given-names></string-name>, <string-name><surname>Zavadskas</surname>, <given-names>E.K.</given-names></string-name> (<year>2023</year>). <article-title>An intuitionistic fuzzy consensus WASPAS method for assessment of open-source software learning management systems</article-title>. <source>Informatica</source>, <volume>34</volume>(<issue>3</issue>), <fpage>529</fpage>–<lpage>556</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_008">
<mixed-citation publication-type="journal"><string-name><surname>Denisart</surname>, <given-names>L.</given-names></string-name>, <string-name><surname>Troncoso</surname>, <given-names>J.F.</given-names></string-name>, <string-name><surname>Loup-Escande</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Franco</surname>, <given-names>A.A.</given-names></string-name> (<year>2024</year>). <article-title>Breaking down the barriers between the digital and the real: mixed reality applied to battery manufacturing R&amp;D and training</article-title>. <source>Batteries &amp; Supercaps</source>, <volume>7</volume>(<issue>7</issue>), <elocation-id>e202400042</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_009">
<mixed-citation publication-type="journal"><string-name><surname>Dhairiyasamy</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Gabiriel</surname>, <given-names>D.</given-names></string-name>, <string-name><surname>Bunpheng</surname>, <given-names>W.</given-names></string-name>, <string-name><surname>Kit</surname>, <given-names>C.C.</given-names></string-name> (<year>2024</year>). <article-title>A comprehensive analysis of India’s electric vehicle battery supply chain: barriers and solutions</article-title>. <source>Discover Sustainability</source>, <volume>5</volume>(<issue>1</issue>), <fpage>361</fpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_010">
<mixed-citation publication-type="journal"><string-name><surname>Du</surname>, <given-names>R.</given-names></string-name> (<year>2024</year>). <article-title>Studying the impact of investments in critical minerals and energy transition in transportation sector in Asia</article-title>. <source>Resources Policy</source>, <volume>96</volume>, <elocation-id>105227</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_011">
<mixed-citation publication-type="journal"><string-name><surname>Etxandi-Santolaya</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Casals</surname>, <given-names>L.C.</given-names></string-name>, <string-name><surname>Montes</surname>, <given-names>T.</given-names></string-name>, <string-name><surname>Corchero</surname>, <given-names>C.</given-names></string-name> (<year>2023</year>). <article-title>Are electric vehicle batteries being underused? A review of current practices and sources of circularity</article-title>. <source>Journal of Environmental Management</source>, <volume>338</volume>, <elocation-id>117814</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_012">
<mixed-citation publication-type="journal"><string-name><surname>Fahma</surname>, <given-names>F.</given-names></string-name>, <string-name><surname>Sutopo</surname>, <given-names>W.</given-names></string-name>, <string-name><surname>Pujiyanto</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Nizam</surname>, <given-names>M.</given-names></string-name> (<year>2024</year>). <article-title>Dynamic open innovation to determine technology-based interoperability requirement for electric motorcycle swappable battery</article-title>. <source>Journal of Open Innovation: Technology, Market, and Complexity</source>, <volume>10</volume>(<issue>2</issue>), <elocation-id>100259</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_013">
<mixed-citation publication-type="journal"><string-name><surname>Kim</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Kim</surname>, <given-names>Z.</given-names></string-name>, <string-name><surname>Lee</surname>, <given-names>D.H.</given-names></string-name> (<year>2024</year>). <article-title>Prediction of the emergence of solid-state battery technology in the post-lithium ion battery era: a patent-based approach</article-title>. <source>International Journal of Green Energy</source>, <volume>21</volume>(<issue>6</issue>), <fpage>1210</fpage>–<lpage>1225</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_014">
<mixed-citation publication-type="journal"><string-name><surname>Kutlu Gundogdu</surname>, <given-names>F.</given-names></string-name>, <string-name><surname>Kahraman</surname>, <given-names>C.</given-names></string-name> (<year>2019</year>). <article-title>Extension of WASPAS with spherical fuzzy sets</article-title>. <source>Informatica</source>, <volume>30</volume>(<issue>2</issue>), <fpage>269</fpage>–<lpage>292</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_015">
<mixed-citation publication-type="journal"><string-name><surname>Lyu</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Zhang</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Li</surname>, <given-names>Z.</given-names></string-name>, <string-name><surname>Zou</surname>, <given-names>X.</given-names></string-name> (<year>2023</year>). <article-title>Impact of rexatory intervention on green technology and innovation investment of the NEV automaker</article-title>. <source>Computers &amp; Industrial Engineering</source>, <volume>184</volume>, <elocation-id>109439</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_016">
<mixed-citation publication-type="chapter"><string-name><surname>Maher</surname>, <given-names>K.</given-names></string-name>, <string-name><surname>Boumaiza</surname>, <given-names>A.</given-names></string-name> (<year>2024</year>). <chapter-title>October. Qatar’s energy future: challenges and opportunities in Lithium-Ion battery technology</chapter-title>. In: <source>2024 12th International Conference on Smart Grid and Clean Energy Technologies (ICSGCE)</source>. <publisher-name>IEEE</publisher-name>, pp. <fpage>60</fpage>–<lpage>65</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_017">
<mixed-citation publication-type="journal"><string-name><surname>Mohseni</surname>, <given-names>P.</given-names></string-name>, <string-name><surname>Husev</surname>, <given-names>O.</given-names></string-name>, <string-name><surname>Vinnikov</surname>, <given-names>D.</given-names></string-name>, <string-name><surname>Strzelecki</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Romero-Cadaval</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Tokarski</surname>, <given-names>I.</given-names></string-name> (<year>2023</year>). <article-title>Battery technologies in electric vehicles: improvements in electric battery packs</article-title>. <source>IEEE Industrial Electronics Magazine</source>, <volume>17</volume>(<issue>4</issue>), <fpage>55</fpage>–<lpage>65</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_018">
<mixed-citation publication-type="chapter"><string-name><surname>Moyo</surname>, <given-names>T.</given-names></string-name>, <string-name><surname>Onososen</surname>, <given-names>A.O.</given-names></string-name>, <string-name><surname>Musonda</surname>, <given-names>I.</given-names></string-name>, <string-name><surname>Muzioreva</surname>, <given-names>H.</given-names></string-name> (<year>2023</year>). <chapter-title>Advancements in E-mobility: a bibliometric literature review on battery technology, charging infrastructure, and energy management</chapter-title>. In: <source>Smart and Resilient Infrastructure For Emerging Economies: Perspectives on Building Better</source>, pp. <fpage>82</fpage>–<lpage>89</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_019">
<mixed-citation publication-type="journal"><string-name><surname>Naseri</surname>, <given-names>F.</given-names></string-name>, <string-name><surname>Gil</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Barbu</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Cetkin</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Yarimca</surname>, <given-names>G.</given-names></string-name>, <string-name><surname>Jensen</surname>, <given-names>A.C.</given-names></string-name>, <string-name><surname>Larsen</surname>, <given-names>P.G.</given-names></string-name>, <string-name><surname>Gomes</surname>, <given-names>C.</given-names></string-name> (<year>2023</year>). <article-title>Digital twin of electric vehicle battery systems: comprehensive review of the use cases, requirements, and platforms</article-title>. <source>Renewable and Sustainable Energy Reviews</source>, <volume>179</volume>, <elocation-id>11328</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_020">
<mixed-citation publication-type="journal"><string-name><surname>Overbeck</surname>, <given-names>L.</given-names></string-name>, <string-name><surname>Voigtländer</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Lanza</surname>, <given-names>G.</given-names></string-name> (<year>2023</year>). <article-title>Optimal line configurations for agile production systems for battery cell manufacturing</article-title>. <source>Procedia CIRP</source>, <volume>118</volume>, <fpage>976</fpage>–<lpage>981</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_021">
<mixed-citation publication-type="journal"><string-name><surname>Pesaran</surname>, <given-names>A.A.</given-names></string-name> (<year>2023</year>). <article-title>Lithium-ion battery technologies for electric vehicles: progress and challenges</article-title>. <source>IEEE Electrification Magazine</source>, <volume>11</volume>(<issue>2</issue>), <fpage>35</fpage>–<lpage>43</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_022">
<mixed-citation publication-type="journal"><string-name><surname>Plante</surname>, <given-names>M.</given-names></string-name> (<year>2025</year>). <article-title>Investing in the batteries and vehicles of the future: a view through the stock market</article-title>. <source>Energy Economics</source>, <volume>143</volume>, <elocation-id>108216</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_023">
<mixed-citation publication-type="journal"><string-name><surname>Rankin</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Bedrava</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Covington</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Johnson</surname>, <given-names>J.L.</given-names></string-name>, <string-name><surname>Pollard-Larkin</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Schipper</surname>, <given-names>M.J.</given-names></string-name>, <string-name><surname>Castillo</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Woodward</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Xing</surname></string-name>, <string-name><surname>Paradis K. C</surname>, <given-names>Y.-H.</given-names></string-name> (<year>2024</year>). <article-title>Women in the medical physics workforce: insights from membership trends of the American Association of Physicists in Medicine, 1993 to 2023</article-title>. <source>International Journal of Radiation Oncology, Biology, Physics</source>, <volume>119</volume>(<issue>5</issue>), <fpage>1336</fpage>–<lpage>1343</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_024">
<mixed-citation publication-type="journal"><string-name><surname>Rizos</surname>, <given-names>V.</given-names></string-name>, <string-name><surname>Urban</surname>, <given-names>P.</given-names></string-name> (<year>2024</year>). <article-title>Barriers and policy challenges in developing circularity approaches in the EU battery sector: an assessment</article-title>. <source>Resources, Conservation and Recycling</source>, <volume>209</volume>, <elocation-id>107800</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_025">
<mixed-citation publication-type="journal"><string-name><surname>Schulz-Mönninghoff</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Neidhardt</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Niero</surname>, <given-names>M.</given-names></string-name> (<year>2023</year>). <article-title>What is the contribution of different business processes to material circularity at company-level? A case study for electric vehicle batteries</article-title>. <source>Journal of Cleaner Production</source>, <volume>382</volume>, <elocation-id>135232</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_026">
<mixed-citation publication-type="chapter"><string-name><surname>Şensoy</surname>, <given-names>N.</given-names></string-name> (<year>2023</year>). <chapter-title>Determination of optimal battery and renewable capacity investment for hybrid energy storage systems</chapter-title>. In: <source>2023 19th International Conference on the European Energy Market (EEM)</source>. <publisher-name>IEEE</publisher-name>, pp. <fpage>1</fpage>–<lpage>6</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_027">
<mixed-citation publication-type="chapter"><string-name><surname>Shaji</surname>, <given-names>K.M.</given-names></string-name>, <string-name><surname>Dudhe</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Alex</surname>, <given-names>A.F.</given-names></string-name> (<year>2023</year>). <chapter-title>Neoteric innovations concerning battery technology and lubricants for electric vehicles</chapter-title>. In: <source>2023 Advances in Science and Engineering Technology International Conferences (ASET)</source>. <publisher-name>IEEE</publisher-name>, pp. <fpage>1</fpage>–<lpage>6</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_028">
<mixed-citation publication-type="chapter"><string-name><surname>Suhail</surname>, <given-names>A.H.</given-names></string-name>, <string-name><surname>Guangul</surname>, <given-names>F.M.</given-names></string-name>, <string-name><surname>Nazeer</surname>, <given-names>A.</given-names></string-name> (<year>2024</year>). <chapter-title>Pushing boundaries: advancements and challenges in electric vehicle battery technology</chapter-title>. In: <source>Solving Fundamental Challenges of Electric Vehicles</source>. <publisher-name>IGI Global</publisher-name>, pp. <fpage>282</fpage>–<lpage>313</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_029">
<mixed-citation publication-type="journal"><string-name><surname>Vásquez</surname>, <given-names>L.O.P.</given-names></string-name>, <string-name><surname>Chavarría-Hernández</surname>, <given-names>J.C.</given-names></string-name>, <string-name><surname>Trinidad</surname>, <given-names>A.A.</given-names></string-name>, <string-name><surname>Ordóñez-López</surname>, <given-names>L.C.</given-names></string-name>, <string-name><surname>Sosa</surname>, <given-names>S.F.</given-names></string-name>, <string-name><surname>Pool</surname>, <given-names>P.Y.C.</given-names></string-name>, <string-name><surname>Barrera-Cabrera</surname>, <given-names>J.N.</given-names></string-name> (<year>2025</year>). <article-title>Life cycle assessment of electric and gasoline moto-taxis in Yucatán, México: impact of battery technology and social considerations</article-title>. <source>Energy for Sustainable Development</source>, <volume>85</volume>, <elocation-id>101614</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_030">
<mixed-citation publication-type="journal"><string-name><surname>Wang</surname>, <given-names>H.</given-names></string-name>, <string-name><surname>Dai</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Wei</surname>, <given-names>H.</given-names></string-name>, <string-name><surname>Lu</surname>, <given-names>Q.</given-names></string-name> (<year>2023</year>). <article-title>Understanding technological innovation and evolution of energy storage in China: spatial differentiation of innovations in lithium-ion battery industry</article-title>. <source>Journal of Energy Storage</source>, <volume>66</volume>, <elocation-id>107307</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_031">
<mixed-citation publication-type="journal"><string-name><surname>Watabe</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Leaver</surname>, <given-names>J.</given-names></string-name> (<year>2023</year>). <article-title>Transitioning to battery electric vehicles in Japan: impact of promotion policy, battery performance and carbon neutrality on greenhouse gas emissions reduction</article-title>. <source>Journal of Cleaner Production</source>, <volume>430</volume>, <elocation-id>13968</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_032">
<mixed-citation publication-type="journal"><string-name><surname>Yalcin Kavus</surname>, <given-names>B.</given-names></string-name>, <string-name><surname>Ayyildiz</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Gulum Tas</surname>, <given-names>P.</given-names></string-name>, <string-name><surname>Taskin</surname>, <given-names>A.</given-names></string-name> (<year>2023</year>). <article-title>A hybrid Bayesian BWM and Pythagorean fuzzy WASPAS-based decision-making framework for parcel locker location selection problem</article-title>. <source>Environmental Science and Pollution Research</source>, <volume>30</volume>(<issue>39</issue>), <fpage>90006</fpage>–<lpage>90023</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_033">
<mixed-citation publication-type="journal"><string-name><surname>Yang</surname>, <given-names>H.</given-names></string-name>, <string-name><surname>Fulton</surname>, <given-names>L.</given-names></string-name> (<year>2023</year>). <article-title>Decoding US investments for future battery and electric vehicle production</article-title>. <source>Transportation Research Part D: Transport and Environment</source>, <volume>118</volume>, <elocation-id>103693</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_034">
<mixed-citation publication-type="journal"><string-name><surname>Zavadskas</surname>, <given-names>E.K.</given-names></string-name>, <string-name><surname>Turskis</surname>, <given-names>Z.</given-names></string-name>, <string-name><surname>Antucheviciene</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Zakarevicius</surname>, <given-names>A.</given-names></string-name> (<year>2012</year>). <article-title>Optimization of weighted aggregated sum product assessment</article-title>. <source>Elektronika ir elektrotechnika</source>, <volume>122</volume>(<issue>6</issue>), <fpage>3</fpage>–<lpage>6</lpage>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_035">
<mixed-citation publication-type="journal"><string-name><surname>Zeng</surname>, <given-names>Z.</given-names></string-name>, <string-name><surname>Qu</surname>, <given-names>X.</given-names></string-name> (<year>2023</year>). <article-title>What’s next for battery-electric bus charging systems</article-title>. <source>Communications in Transportation Research</source>, <volume>3</volume>, <elocation-id>100094</elocation-id>.</mixed-citation>
</ref>
<ref id="j_infor604_ref_036">
<mixed-citation publication-type="journal"><string-name><surname>Zhao</surname>, <given-names>X.</given-names></string-name>, <string-name><surname>Wu</surname>, <given-names>W.</given-names></string-name>, <string-name><surname>Wu</surname>, <given-names>D.</given-names></string-name> (<year>2024</year>). <article-title>Technological trajectory analysis in lithium battery manufacturing: based on patent claims perspective</article-title>. <source>Journal of Energy Storage</source>, <volume>98</volume>, <elocation-id>112894</elocation-id>.</mixed-citation>
</ref>
</ref-list>
</back>
</article>
