The CE is an important research area as an approach aimed at using resources more efficiently, increasing the lifespan of products, and consequently reducing waste generation (Lieder and Rashid, 2016). Kirchherr et al. (2017) defined CE as a transformation model leading to sustainable development and proposed a broad systems approach encompassing the process from design to post-use through the 3R-9R concepts. Based on this, material circularity, less carbon emissions in production processes, life cycle design, reverse logistics, and closed-loop supply chain have become important topics in the CE literature (Almusaed et al., 2024; Mishra et al., 2022).

The construction industry is critical for CE applications because it is a resource-intensive industry with high material consumption and, consequently, a high level of waste generation. While prominent themes related to the construction industry includes waste management, life cycle assessment (LCA), and the use of recycled materials (Jeon et al., 2025), carbon emissions (Iqbal et al., 2025), and clean production technologies (Alam et al., 2024; Giannetti et al., 2023), circularity is not limited to these themes. Prefabrication, modular construction, and off-site construction practices (Obi et al., 2025) enable the reduction of material waste and the improvement of energy efficiency, and are seen as important steps in line with these circular economy principles. In addition, aerated concrete, steel, and composite materials play a strategic role in supplier selection processes in terms of material-based circularity due to their recyclability and low carbon levels (Ghisellini et al., 2018). Aerated concrete, in particular, is a significant alternative in sustainable building applications due to its energy efficiency, lightness, thermal performance, and recycling potential (Rafiza et al., 2022). These studies demonstrate that circularity is not limited to design and material selection, but encompasses a holistic structure, including production methods and logistics processes.

In supplier selection studies conducted during periods when sustainable development is not given the necessary importance, they fully concentrated on operational criteria such as cost, quality, and delivery. However, increasing sustainability pressures broadened this framework in later stages. Today, circular supplier selection groups drivers under economic, operational, environmental, social, and organizational headings. Factors such as cost, quality, and flexibility remain key drivers in almost all supplier selection work, whether traditional or circular (Alavi et al., 2021; Liu et al., 2022). Similarly, criteria such as delivery performance, on-time delivery, and capacity efficiency stand out as parameters reflecting operational performance and are commonly used in many studies (Govindan et al., 2020; Tushar et al., 2022). These criteria remain highly important and are still considered even under the pressures of sustainability. Environmental criteria, which are critical for the circular economy, are among the most extensively discussed topics in the supplier selection literature. Drivers, including eco-design, modularity, product disassembly, use of recyclable materials, energy efficiency, reduction of carbon emissions, waste management, and integration of green technology, are frequently preferred as circular indicators (Khalili Nasr et al., 2021; Kusi-Sarpong et al., 2023; Masoomi et al., 2022). They are the most decisive components of circular supplier selection, as they aim to increase resource use efficiency in the process from production to distribution. Besides, reverse logistics, remanufacturing, take-back systems, and processes aimed at closing the product cycle are other drivers that reveal the extent to which suppliers aid circular economy principles (Koc et al., 2023; Tramarico et al., 2025). The literature indicates that they are utilized to measure a supplier’s involvement in post-lifecycle processes, how they manage the recovery process, and their adaptation to closed-loop systems (Bai et al., 2024; Demirbağ et al., 2025). However, the social dimension is less emphasized than the other dimensions and is considered in a limited number of works. Some drivers, including occupational health and safety, employee welfare, and social responsibility, are usually included in the social sustainability aspect of circular supplier evaluation (Laosirihongthong et al., 2019; Luthra et al., 2017). Besides, organizational readiness, environmental management systems (EMS), level of LCA usage, and circular economy awareness are highlighted in the literature as key drivers (Amarasinghe et al., 2024; Bai et al., 2024). Consequently, Table 1 presents a summary of the criteria used.

The subsection presents a method-oriented literature survey. For this purpose, we consider HyFS-based decision models, LOPCOW, RANCOM, and DEPART studies from the literature.

A review of the current literature reveals that research on supplier selection within the scope of CE has been conducted in the fields of electronics (Kannan et al., 2020; Menon and Ravi, 2022), chemistry (Alavi et al., 2021), automotive (Haleem et al., 2021), textile (Khalili Nasr et al., 2021; Kusi-Sarpong et al., 2023), and manufacturing (Liu et al., 2022; Tong et al., 2022) sectors using multidimensional fuzzy MCDM approaches. Moreover, most current studies on supplier selection in the construction sector focus on sustainability indicators such as environmental certification, occupational health and safety, green design, and the use of recyclable materials. However, CE’s more technical sub-components, including material cycles, component recovery, modularity, and material passports, are generally overlooked (Perçin, 2022; Tushar et al., 2022). In a recent study, Demirbağ et al. (2025) addressed CE in terms of functional, product, component, material, and energy circularity dimensions, presenting a comprehensive model aimed at addressing one of the significant gaps in this field. However, there is still very little literature on the application of this approach at the level of construction materials, particularly materials with high circularity potential such as aerated concrete. Particularly in material-intensive sectors such as construction, there are very few studies that address supplier and material selection in an integrated manner with CE principles. Furthermore, there are almost no examples in the literature of applied supplier selection models focusing on critical building materials such as aerated concrete in terms of energy efficiency and environmental performance. Consequently, this study aims to fill this gap and provide a concrete framework for how the circular economy can be integrated into the construction material supply chain. On the other hand, a significant portion of existing studies limit their evaluation criteria to environmental indicators only, failing to sufficiently integrate economic, technological, and managerial dimensions. The number of studies in which the CE criteria are systematically determined based on the opinions of industry experts and tested in real-world applications is also quite limited. Furthermore, it is observed that studies on CE-based supplier selection in the literature are largely addressed in the context of developed countries and general building materials. However, in developing countries such as Türkiye, there are very few models for building materials of strategic importance for sustainable building applications, particularly aerated concrete, due to its energy efficiency, light weight, and low carbon potential.

From a methodological perspective, most existing studies address uncertainty in a limited manner; expert opinions are mostly evaluated with equal weight and rely on a single weighting approach. However, since the evaluation of supplier performance in the construction industry is largely based on experience and perception, uncertainty and differences in the level of knowledge among experts must be explicitly reflected in decision models. Besides, the interpretation of data in terms of an orthopair fuzzy construct is subtle, and the flexibility for expressing choices is restricted in earlier studies. Moreover, the weights or importance of decision experts are either neglected or assigned directly without methodical determinations. Also, the weights of criteria are calculated, but the determination of both subjective and objective weights is lacking in extant studies. Additionally, ranks are determined in extant frameworks, but due consideration to each expert’s data for the rank determination of suppliers and the combined rank of suppliers is missing.

As a result, this research aims to fill the aforementioned gaps by: (i) focusing on the construction sector, (ii) addressing strategic building materials such as aerated concrete, and (iii) addressing uncertainty with hyperbolic fuzzy sets, integrating the LOPCOW, RANCOM, and DEPART methods, and incorporating expert weighting. Thus, this work presents a comprehensive circular supplier selection model.

We review the hyperbolic fuzzy set and its operations here. Definition 1

R is a reference set. q-ROFS Q on R is given by, (1) Q = ( r , μ Q ( r ) , υ Q ( r ) ∨ r ∈ R ) , where μ Q ( r ) is the degree of preference or membership, υ Q ( r ) is the degree of non-preference or non-membership.

Note that μ Q ( r ) and υ Q ( r ) are in the unit interval. Also 0 ⩽ μ Q q + υ Q q ⩽ 1 with q ⩾ 1.

We present the orthopair fuzzy conditions for clarity to readers in Eq. (2). (2) Conditions = 0 ⩽ μ q 1 + υ Q 1 ⩽ 1 q = 1 ( Intuitionistic fuzzy set ( IFS ) ) , 0 ⩽ μ Q 2 + υ Q 2 ⩽ 1 q = 2 ( Pythagorean fuzzy set ( PFS ) ) , 0 ⩽ μ Q 3 + υ Q 3 ⩽ 1 q = 3 ( Fermatean fuzzy set ( FFS ) ) .

In the orthopair fuzzy set family, HyFS is a recent inception that is gaining attention from researchers considering its flexibility in choice elicitation, which is restricted or constrained by certain inequalities in the predecessor forms, such as IFS, PFS, FFS, and, in general, q-ROFS. Such inequalities are relaxed in HyFS, and a broader window for choice expression is provided with a two-dimensional representation – both preference and non-preference grades. Driven by the flexibility, we consider HyFN for the study. It must be noted that the earlier fuzzy variants in the orthopair family followed additive constraints, while the HyFS followed multiplicative constraints, and it is based on the concept of a hyperbola as suggested by Dutta and Borah (2023). Specifically, Dutta and Bahrami (2025) argued that HyFS incorporates a hyperbolic geometric boundary that facilitates expressiveness and adaptability. Furthermore, it can be noted that in qROFS, there is a need to choose q a priori, which is a crucial tuning parameter. Choosing a lesser q blocks several orthopair values (membership and non-membership), while a larger q requires changing the semantic interpretation of all values simultaneously. As a result, it is more about robustness of representation rather than ranking accuracy when it comes to HyFS versus qROFS. The questions these two sets address are different. In qROFS, the question is ‘what must be the value of q so that the expert’s choice can be represented?’, whereas in HyFS, the question is ‘what is the expert’s opinion?’ From this, we gain clarity that it is about representational robustness rather than decision accuracy, which motivated authors to choose HyFS for data or rating interpretation. Methodical superiority of the proposed framework can be noticed in Section 1.

If two HyFNs must be compared, then do the following: •

Check the score, if S ( B 1 ) > S ( B 2 ), then B 1 > B 2 ; If S ( B 1 ) = S ( B 2 ), then go to accuracy measure.

In this section, we present the feature reduction module by considering the Laplacian score. The presented procedure is capable of feature selection with no requirement for class labels. As a result, for decision problems, the Laplacian score is viable. Furthermore, the score retains the local structure or patterns, which mitigates information loss and efficiently reduces complexity or computational overhead.

This score considers alignment with the intrinsic geometry of data. Generally, criteria with low scores are preferred as they retain information about the neighborhood, and so, the top k criteria are selected based on the arrangement of the scores in ascending order. The method performs feature reduction that helps in reducing dimensionality.

The procedure for determining the reduced set of features is:

Input: Experts’ rating criteria – k × n matrix

Process: •

Construct the similarity matrix

Output: A revised criteria set (feature reduced) – k × c where c < n.

It must be noted that each criterion is assigned a score, and based on the importance, the top k criteria are chosen. This helps in feature reduction and facilitates local structure intactness.

In this section, we present a detailed step-by-step procedure for determining the weights of the criteria and the experts involved in the decision process. It must be noted that the weights or relative importance of a decision entity are not equal, and methodical determination of such values reduces bias and subjectivity (Kao, 2010; Koksalmis and Kabak, 2019). Driven by these studies, we present a methodical setup for determining the weights of the criteria and experts.

In general, weights are determined either with partial a priori information or no such information. The former type incurs a certain level of additional overhead, which in many situations is not practically possible. As a result, the latter type is presented by researchers. In the latter context, objective and subjective weight types exist. Subjective types directly consider ranks or priority to determine the weights (importance), while objective types consider opinions from stakeholders to determine the weights. Since both these types have their own benefits, we consider both types in this study to determine the weights of the criteria. Further, experts’ weights are determined objectively.

LOPCOW and RANCOM methods are extended to HyFS for determining the objective and subjective weights of criteria. LOPCOW follows a logarithmic function that is capable of reducing the scale-size effect, thus making the approach balanced without being affected by value spikes. Also, RANCOM considers ordinal data and pair-wise constructs, enabling careful consideration of each decision entity. Besides, it is intuitive, less impacted by inconsistencies, and computationally feasible. The combination of these two methods yields a holistic criterion weight, which can be further used for rank determination. The entropy approach is extended to HyFS for determining the weights of experts. Entropy determines the uniformity that exists in the construct or entity that is being measured. As a result, a high entropy value indicates high uniformity – less variability. So, there is a tendency for perceived consistency in the rating that would facilitate rational decision-making.

Detailed steps for the calculation are given below:

In this section, we present a HyFS extension of the DEPART method (Keshavarz-Ghorabaee et al., 2025), which is a recently developed ranking approach for determining the priority of alternatives. The method follows relational pairwise comparison, which sets it apart from other popular methods in the decision-making field. Most extant methods follow distance measure or uni-directed utility measure, which lack careful consideration of the decision entities.

DEPART, in contrast, considers a pairwise approach and hence, every entity in the set is given due consideration. The main philosophy of DEPART is to calculate deviation from best and worst and determine ratios that are finally aggregated to form scores. As a result, DEPART is fully relative, unlike other rank methods that are either partially relative or non-relative.

Driven by these merit points, in this work, we extend DEPART to HyFS for ranking. The steps involved in the ranking are clarified below:

Step 1: Consider d experts who rate a alternatives over c criteria. The decision matrices are formed with qualitative ratings, and the entries are transformed to HyFN, and the score is determined by using Eq. (8).

Step 2: Form positive and negative deviation matrices by using Eqs. (15)–(16). These are matrices of order a × c. (15) p i j = | a i j − a j + | , (16) n i j = | a i j − a j − | , where a i j is the score value.

Here, a j + = max ( a i j ) for benefit and min ( a i j ) for cost. It is the opposite for a j − .

Step 3: Form a pairwise positive and negative ratio of deviation by using Eqs. (17)–(18). These are square matrices of order a × a. (17) p d f g = ∑ j = 1 c ( p g j + P p f j + P ) , (18) n d f g = ∑ j = 1 c ( p f j + N p g j + N ) , where f and g are any two alternatives.

Here, P = max ( p i j ) and N = max ( n i j ).

Step 4: Determine the net pairwise deviation by using Eq. (19). Determine the score and arrange alternatives in descending order of score. (19) D f g = z · p d f g + ( 1 − z ) · n d f g , (20) Score i = ∑ g D f g .

Arrange the score in descending order of values. A higher score is highly preferred, and so on.

From Eq. (20), d vectors of 1 × a order are obtained. These are rank orders of alternatives based on data from each expert. To combine the ordering and obtain a net rank vector, the Copeland procedure is presented. Steps are given below:

By applying the procedure mentioned above, a combined rank order is obtained that yields a vector of 1 × a order. A single aggregated rank vector is obtained by considering rank vectors from d experts’ rating data.

To illustrate how the framework operates, the principal computational steps are demonstrated below using the case-study data; the complete intermediate values are reported in Tables 3–16. (a)

From linguistic rating to a normalized score. Each linguistic rating is converted to a hyperbolic fuzzy number (HyFN) and then to a crisp score using the score function in Eq. (8). The resulting score vector of every criterion is rescaled by the min–max normalization in Eq. (10). For criterion CRT4, the five expert ratings (5, 7, 2, 5, 7) give, after the HyFN transformation and Eq. (10), the normalized vector (0.773, 1.000, 0.000, 0.773, 1.000), as reported in Table 9.

This section determines the effect of a change in strategy values on the ranking of alternative suppliers. Likewise, we also infer the effect of the change of criteria weights on the ranking of alternative suppliers. We refer to these two types as intra-sensitivity analysis and inter-sensitivity analysis. In the former, we vary the strategy values in the unit interval with a step size of 0.10. Hence, we consider nine episodes from 0.10 to 0.90 for the rank value of alternative suppliers based on data from each expert. Table 16 shows the results of the sensitivity analysis of strategy values.

Table 16 shows the results of the intra-sensitivity analysis – strategy values are altered from 0.10 to 0.90, and it is inferred that for data from EXT1: AL1, AL2; EXT2: AL2, AL5; EXT3: AL5; EXT4: AL4; and EXT5: AL3 are the best suppliers. This information is crucial in a decision process, and extant models cannot reveal this insight. So, each expert yields different preferences for different suppliers, and it is evident from Table 16. As a result, understanding the ranking from each expert’s viewpoint is crucial.

To further validate the proposed framework, the supplier ranking obtained from HyF-DEPART with Copeland aggregation is compared with five established MCDM methods: TOPSIS, WASPAS, ARAS, CoCoSo, and SAW, computed from the complete decision matrix over the ten retained criteria with the combined criteria weights. As in the proposed framework, each method ranks the suppliers for every expert, and the five per-expert rankings are fused by the Copeland strategy with the expert weights; all ten criteria are treated as cost-type, consistent with their definitions in Table 2. Table 17 and Fig. 5 report the resulting rankings. All six methods identify AL3 as the best supplier and rank AL4 second or third, while AL1, AL2, and AL5 occupy the lower positions. The Spearman rank correlations with the proposed ranking range from 0.40 (TOPSIS) to 0.70 (WASPAS, ARAS, CoCoSo, and SAW), with the agreement strongest at the top and the divergences confined to the middle and lower ranks. The unanimous selection of AL3 as the best supplier across all methods confirms the robustness and reliability of the proposed supplier ranking.

In this study, a practical and flexible decision-support system has been developed for supplier evaluation in circular economy-based supply chains under uncertainty. The proposed approach is based on the LOPCOW–RANCOM and DEPART-based MCDM methodology integrated under a hyperbolic fuzzy set structure. This multi-layered structure provides a more balanced and reliable supplier selection model in selection processes where subjective evaluations and uncertainty are high.

The driver weights clearly indicate the effect of circular economy principles on the supplier selection for building construction processes. More clearly, corporate reputation and reliability (CRT15) is the foremost driver (0.152). This means that, in terms of long-term business relationships, supply continuity, and risk reduction, reliability is still a decisive factor in the construction industry. Some papers emphasized that supplier reliability plays a critical role in sustainable supply chains (Kannan et al., 2020; Luthra et al., 2017). Technological capability and innovation (CRT11) is the second-crucial driver (0.140), meaning that in building materials with technology-intensive production processes, such as aerated concrete, clean production technologies, process optimization, and innovative applications play a central role in aiding the circular economy. This finding is also consistent with previous studies (Haleem et al., 2021). The third-highest priority belongs to the deferred payment option (CRT4; 0.126), indicating that supplier selection decisions are shaped by economic and environmental sustainability concerns, particularly in emerging markets such as Türkiye, in which financing costs are high. Furthermore, circular economy-based supplier selection does not completely exclude traditional economic drivers; rather, it offers a holistic approach that considers these criteria together with environmental and managerial factors.

The findings present that energy efficiency (CRT5) and managerial compliance and top management support (CRT16) have medium-high weights. Thus, energy consumption, operational control, and corporate ownership are perceived as key factors in circular economy applications in the aerated concrete sector. As a result, energy-focused environmental policies and managerial commitment are becoming increasingly crucial in the production of building materials (GABC, 2025).

Furthermore, the relatively high weight of the green supply chain and logistics practices (CRT10) remarks that the CE approach is addressed holistically, encompassing production processes, logistics, and distribution stages together (Mishra et al., 2022). Regarding the findings, using recycled materials (CRT6) and waste management and recovery (CRT7) are given relatively lower weight than others. Though material circularity is considered a core concept in CE research, in practice, decision-makers prioritize other drivers, such as energy efficiency, technological competence, and regulatory compliance, over CRT 6 and CRT 7. Studies supporting this finding depict that drivers such as recycling and waste management could be prioritized lower due to structural, technical, and especially economic constraints (Ghisellini et al., 2018; Timm et al., 2023). This finding could also reveal that material-based circularity has not yet matured sufficiently.

The combined ranking obtained using the Copeland technique brought together the different situations that emerged in expert opinion-based rankings, thereby achieving consensus. The different rankings obtained with each expert’s evaluation in the previous steps made it difficult to determine the final priority, but with Copeland, the relative advantages of the alternatives are presented more clearly and comparably. This process shows that in decision-making processes involving subjective evaluations, the ranking technique is as important as weighting. The fact that AL3 ranked first illustrates the importance of considering not only environmental criteria but also multidimensional factors such as governance compliance, operational stability, and balanced performance. In contrast, AL2’s relatively low performance indicates that strong corporate perception, brand awareness, or technical advantages alone are not sufficient. This finding reveals that supplier selection focused on the circular economy can produce different results than conventional selection models.

As discussed above, the proposed framework helps a real-world logistics manager make better decisions. This study also has crucial managerial implications for companies operating in the aerated concrete industry and their supplier decision-makers. Firstly, the selection of suppliers based on a CE approach should not be limited to environmental indicators alone, but should also consider factors such as corporate reputation, technological competence, and financial flexibility. In other words, the flexibility a company offers in payment, its position within the sector, and its technological capabilities are as important as environmental indicators in aerated concrete supply. Therefore, companies should increase their technological capacity and demonstrate a strong corporate stance to establish sustainable business relationships. Additionally, the high importance of criteria such as energy efficiency and compliance with environmental regulations will require manufacturing companies to revise their production processes to produce energy-efficient and regulatory-compliant products. Companies that implement this will both gain a cost advantage and become an important link in the supply chain. Companies operating in compliance with environmental regulations and legislation will both overcome increasing public pressure and position themselves well in the face of legal regulations, and be preferred due to the trust they build. The research results also show an increasing importance of green supply chain and logistics processes. In this situation, manufacturers need to consider environmental impacts not only during the product’s manufacturing phase but also during its delivery to the customer. Optimal route selection in logistics processes, and the use of gasoline, hybrid, or electric vehicles instead of diesel vehicles, stand out as elements that strengthen CE performance in the supply chain. However, the fact that criteria such as recycling of material or waste management are given less importance compared to others indicates a lack of sufficient awareness in this area. Therefore, suppliers prioritizing this area will help decision-makers achieve circular economy goals. Furthermore, the proposed framework helps a real-world logistics manager make better decisions.

This study offers important insights for public authorities and regulators on how to more effectively implement CE-focused criteria in building construction processes. Firstly, the importance of criteria such as energy efficiency and environmental compliance has begun to influence current selection decisions. This necessitates a firm commitment to achieving public goals such as energy efficiency and carbon emission reduction, and the strengthening of regulations in this direction. The significant role of certification and regulatory compliance criteria in supplier selection suggests that policymakers can guide suppliers by developing standards in this area. Labelling systems that measure and numerically compare the circular performance of building materials can be an incentive for companies to achieve these goals. Once such regulations are implemented, a more transparent market environment will be created, and environmentally friendly companies will gain a competitive advantage under increasing cost pressures. Besides, the research findings show that areas such as the use of recycled materials or waste management are not yet sufficiently emphasized in supplier selection. This creates an important area for intervention for authorities. Through regulations, authorities can implement incentives, tax breaks, or priority in public procurement for the use of such materials. This could pave the way for the development of these areas through public means.

The framework proposed in this work combines different decision methods to arrive at a rational decision by reducing human intervention. Specifically, decision parameters such as weights or importance of experts, weights or importance of criteria, and ranks of alternative suppliers are determined methodically, which eventually reduces inaccuracies and bias in value assignment to decision parameters. By extending a decision method to the HyFS, we make the choice to extend considering the merit value it adds to the decision process. Entropy is used for expert weight calculation, as it captures hesitation and the depth of information an expert offers to the decision process. Likewise, LOPCOW and RANCOM are extended for determining the combined criteria weights, as LOPCOW has the ability to nullify extreme values and offers effective discrimination of criteria. RANCOM is a simple and straightforward subjective method, which outperforms different state-of-the-art subjective methods as clarified by Wieckowski et al. (2023). Finally, suppliers are ranked based on expert-wise data and combined grading by HyF-DEPART, which offers both individualistic and cumulative sense of ranking of alternative suppliers.

By calculating key decision parameters, we not only reduce subjectivity/bias but also make the process explainable, which is currently essential in AI systems. The step-by-step procedure offers transparency in the process, and stakeholders can readily apply changes to realize its impact on the final choices. Such perturbations are computationally viable given the flexible design of the proposed framework, which is both scalable and logically connected to yield rational decisions.