Quality function deployment (QFD) was first introduced by Akao (1972) for designing new products systematically, which can translate customer requirements (CRs) into engineering characteristics (ECs) for maximum customer satisfaction (Bevilacqua et al., 2006). Nowadays, the QFD has become a powerful tool for designing and developing products or services (Huang et al., 2019). It can not only improve customer satisfaction, but also reduce cycle-time of product development, cut down production cost and enhance the performance of manufacturing process. Due to its effectiveness and benefits, the QFD method has been applied for product design and quality improvement in various areas, such as construction (Fargnoli et al., 2020; Lapinskienė and Motuzienė, 2021), manufacturing (Neramballi et al., 2020; Shi and Peng, 2020) and service (Lee et al., 2020; Park et al., 2021) industries.

When implementing QFD, house of quality (HOQ) occupies a central position, which assists designers in translating CRs into ECs through explicit assessment matrix of users and products. In this way, the QFD method serves as a valuable tool for managers or designers to develop products. However, when used in real situations, the traditional QFD method has some inherent deficiencies (Huang et al., 2019; Jia et al., 2016; Ping et al., 2020; Wu et al., 2020). On the one hand, crisp values are utilized to deal with the relationships between CRs and ECs in the traditional QFD. However, in the real world, it is often hard for experts to give accurate numerical values on the relationships between CRs and ECs due to the uncertainty and fuzziness of human perception (Aliev and Huseynov, 2014; Lorkowski et al., 2014). Instead, they prefer to use linguistic terms to express their opinions (Liu et al., 2019; Tian et al., 2019; Liu et al., 2021). Based on linguistic term sets (Zadeh, 1975) and Z-numbers (Zadeh, 2011), the concept of linguistic Z-numbers was introduced by Wang et al. (2017) to express both vagueness and randomness of uncertain linguistic information. For a linguistic Z-number, the two components (i.e. restriction and reliability measure) are represented with linguistic terms. Compared to other linguistic computing methods, the linguistic Z-numbers can not only describe decision-making information more flexibly, but also avoid the distortion and loss of original information effectively (Peng and Wang, 2017; Wang et al., 2017). Hence, it is promising to employ the linguistic Z-numbers to represent experts’ uncertain and vague evaluation information on the relationships between CRs and ECs in QFD.

On the other hand, the ranking of ECs in QFD can be considered as a multiple criteria decision making (MCDM) problem because it involves multiple and conflicting CRs (Ping et al., 2020). Accordingly, many MCDM methods have been adopted to improve the performance of QFD in previous researches (Mistarihi et al., 2020; Ocampo et al., 2020; Yazdani et al., 2016). As an effective MCDM method, the evaluation based on distance from average solution (EDAS) was put forward by Ghorabaee et al. (2015) to address MCDM problems. The EDAS includes two measures, i.e. positive distance from average (PDA) and negative distance from average (NDA), for dealing with the desirability of alternatives (Keshavarz-Ghorabaee et al., 2018; Keshavarz Ghorabaee et al., 2017). It has simple logic and is especially useful for decision making problems with conflicting criteria (Darko and Liang, 2020). Since its introduction, the EDAS method has been broadly adopted to solve MCDM problems in many areas, which include supplier selection (Ghorabaee et al., 2016), manufacturer selection (Stević et al., 2018), health-care waste disposal technology selection (Ju et al., 2020), typhoon disaster assessment (Tan and Zhang, 2021), car selection (Yanmaz et al., 2020) and logistics centre location (Özmen and Aydoğan, 2020). Therefore, it is of vital importance to adopt the EDAS method to determine the ranking of ECs in QFD analysis.

Based on the aforementioned discussions, an approach combining linguistic Z-numbers with EDAS method is presented in the study to improve the effectiveness of QFD. Specifically, the linguistic Z-numbers are used to cope with the vague and uncertain assessments provided by experts on the relationships among CRs and ECs, and the EDAS method is utilized to acquire the priority orders of ECs in the process of product development. Moreover, the weights of CRs are obtained by the use of stepwise weight assessment ratio analysis (SWARA) method. Finally, a practical case of product design for Panda shared cars is introduced to testify the effectiveness and efficiency of the proposed QFD approach.

The remainder of the article is organized as follows: Section 2 briefly reviews research progress of the QFD method. The preliminaries of linguistic Z-numbers are presented in Section 3. Then the new integrated QFD approach combining linguistic Z-numbers and EDAS method is developed in Section 4. In Section 5, a practical example is given to demonstrate the proposed QFD framework. Lastly, conclusions of this study and outlines for future research are discussed in Section 6.

In the past decade, an increasing number of improved QFD methods have been developed to eliminate the deficiencies and enhance the performance of the traditional QFD. For instance, Li et al. (2014) introduced analytical network process (ANP) into QFD for deciding the importance of CRs and evaluating corresponding characteristics of software quality. Jia et al. (2016) proposed an integrated QFD method combining fuzzy evidence reasoning theory with fuzzy discrete Choquet integral to determine the importance value of design characteristics. Integrating QFD and decision-making trial and evaluation laboratory (DEMATEL) technique, Ramezankhani et al. (2018) designed a hybrid model and applied it to supply chain performance measurement. Liu et al. (2019) proposed a QFD approach by using partitioned Bonferroni mean operator and interval type-2 fuzzy sets to select a better solution from various green suppliers. Vats and Vaish (2019) employed QFD in combination with vlseKriterijumska optimisacija I kompromisno resenje (VIKOR) approach to select smart materials for thermal energy efficient architecture. Based on cloud model and grey relational analysis, Wang et al. (2020) put forward an integrated QFD model to control the quality of the rotor used in air compressor. Via integrating interval type-2 fuzzy sets and DEMATEL, Yazdani et al. (2020) designed a QFD approach to evaluate and rank sustainable supply chain drivers.

Recently, it has become a trend to integrate the advantages of different MCDM approaches for the improvement of traditional QFD. For example, by using DEMATEL and VIKOR, Wu et al. (2016) developed a QFD model for the product development of electric vehicle. Combining fuzzy BWM, fuzzy maximizing deviation method and fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA), Tian et al. (2018) established a hybrid QFD model to assess the performance of a smart bike-sharing program. Huang et al. (2019) constructed a QFD technique to design manufacture system, in which the relationships between CRs and ECs were expressed by hesitant fuzzy linguistic term sets, the weights of CRs were derived by the best-worst method (BWM) and the ranking order of ECs were determined by the prospect theory. Lu et al. (2019) presented a QFD model by combining fuzzy analytic hierarchy process (AHP) with fuzzy ANP for the design of brand revitalization. A QFD model integrating TOPSIS and EDAS method was proposed by Ping et al. (2020) for a product-service system design.

As reviewed previously, many studies handled the uncertainty and vagueness of experts’ assessments in QFD using fuzzy sets, interval type-2 fuzzy sets and hesitant fuzzy linguistic term sets. However, the reliability of experts’ assessment information cannot be reflected in the processes of QFD. Besides, although different types of MCDM methods have been proposed to obtain the EC prioritization in QFD, they are extremely complex or not considering the conflict of CRs. To overcome these issues, in this paper, we develop a novel QFD approach integrating linguistic Z-numbers and an extended EDAS method to determine the priorities of ECs. Our proposed QFD model can not only represent experts’ evaluation information flexibly, but also provide engineers more practical and reliable solutions for identifying critical ECs to improve product or service.

In this section, some basic concepts of linguistic term sets and linguistic Z-numbers are introduced to aid in understanding the proposed QFD model. Definition 1

Let S = { s 0 , s 1 , … , s 2 t } be a finite and ordered linguistic term set with odd cardinality, where s i is the possible value for a linguistic variable and t is a nonnegative integer. In this linguistic term set S, s i and s j are required to satisfy the following characteristics: (1)

The set is ordered: s i > s j {s_{j}}$]]>, if and only if i > jj$]]>;

In this section, a new comprehensive QFD model combining linguistic Z-numbers and EDAS method is devised to acquire the ranking of ECs. Specially, linguistic Z-numbers are utilized to evaluate the relationships between CRs and ECs, the relative weights of CRs are computed by the SWARA method, and an extended EDAS method is employed to estimate the final priority ratings of ECs. Flowchart for the developed QFD model consisting of three phases is depicted in Fig. 1.

For a QFD analysis problem, suppose that there are m engineering characteristics EC i ( i = 1 , 2 , … , m ) and n customer requirements CR j ( j = 1 , 2 , … , n ). Meanwhile, l experts E k ( k = 1 , 2 , … , l ) are invited to provide their assessments for the relationships between CRs and ECs, and each expert is assigned a weight λ k satisfying λ k > 00$]]> and ∑ k = 1 l λ k = 1 to describe his/her relative importance in the QFD analysis. Let Z k = [ z i j k ] m × n be the linguistic assessment matrix of E k , where z i j k = ( A ϕ ( i j k ) , B φ ( i j k ) ) is the linguistic Z-number evaluation EC i with respect to CR j provided by E k . Based on the above assumptions, the proposed QFD model is described as follows:

Stage 1. Evaluate the relationships between ECs and CRs using linguistic Z-numbers.

Step 1: Establish the collective linguistic evaluation matrix Z.

By using the LZWA operator, the individual linguistic evaluation matrices Z k ( k = 1 , 2 , … , l ) can be aggregated to obtain the collective linguistic evaluation matrix Z = ( z i j ) m × n , in which (9) z i j = LZWA ( z i j 1 , z i j 2 , … , z i j l ) = ( f ∗ − 1 ( ∑ k = 1 l λ k f ∗ ( A ϕ ( i j k ) ) ) , g ∗ − 1 ( ∑ k = 1 l λ k f ∗ ( A ϕ ( i j k ) ) g ∗ ( B φ ( i j k ) ) ∑ k = 1 l λ k f ∗ ( A ϕ ( i j k ) ) ) ) .

Stage 2. Acquire the weights of CRs by the SWARA method.

The SWARA method proposed by Keršuliene et al. (2010) is a powerful weighting method in solving MCDM problems. The superiority of the SWARA is that it is uncomplicated, straightforward and involves less comparisons compared with other weighing methods (Hashemkhani Zolfani et al., 2013; Karabasevic et al., 2016; Ruzgys et al., 2014; Stanujkic et al., 2017). Given its strength, it has been used to find the relative weights of evaluation criteria in many researches (Duan et al., 2019; Liu et al., 2020; Naeini et al., 2020). Therefore, the SWARA method is introduced to acquire the weights of CRs in this study. The detailed steps are listed as follows:

Step 2: Sort CRs in a descending order.

The n customer requirements CR j ( j = 1 , 2 , … , n ) are sorted in a descending order according to their expected importance. Then, newly ranked CRs are denoted as CR j ′ ( j = 1 , 2 , … , n ).

Step 3: Determine the comparative importance of CRs.

Starting from the second CR, experts are invited to assess the relative importance of CR j ′ to CR j − 1 ′ ( j = 2 , 3 , … , n ). Then the comparative importance of CRs ρ j is obtained.

Step 4: Calculate the CR coefficient k j by (10) k j = 1 , j = 1 , ρ j + 1 , j > 1 . 1.\end{array}\right.\]]]>

Step 5: Compute the recalculated CR weights q j by (11) q j = 1 , j = 1 , q j − 1 k j , j > 1 . 1.\end{array}\right.\]]]>

Step 6: Determine the final weight of each CR w j ′ by (12) w j ′ = q j ∑ k = 1 n q j .

Finally, the weight vector of the n customer requirement CR j ( j = 1 , 2 , … , n ), i.e. w = ( w 1 , w 2 , … , w n ), can be derived by rearranging the weights w j ′ ( j = 1 , 2 , … , n ).

Stage 3. Rank the ECs through EDAS method.

In this part, we extend the EDAS method with linguistic Z-numbers, and adopt the linguistic Z-EDAS to obtain the ranking of ECs. The detail steps for ranking ECs are as follows.

Step 7: Determine the linguistic average EC.

The linguistic average engineering characteristics EC is defined as z A = ( z A 1 , z A 2 , … , z A n ), which can be derived by (13) z A j = 1 m ⨁ i = 1 m z i j .

Step 8: Compute the matrices of PDA and NDA.

The PDA matrix D + = [ d i j + ] m × n and the NDA matrix D − = [ d i j − ] m × n are, respectively, computed by (14) d i j + = max { 0 , ( s ( z i j ) − s ( z A j ) ) } s ( z A j ) , if z i j > z A j , 0 , if z i j ⩽ z A j , {z_{Aj}},\\ {} 0,\hspace{1em}& \text{if}\hspace{2.5pt}{z_{ij}}\leqslant {z_{Aj}},\end{array}\right.\end{aligned}\]]]> (15) d i j − = max { 0 , ( s ( z i j ) − s ( z A j ) ) } s ( z A j ) , if z i j < z A j , 0 , if z i j ⩾ z A j .

Step 9: Calculate the weighted sum of PDA and NDA for each EC.

Considering the weight of each customer requirement w, the weighted sums of PDA and NDA for each EC are calculated by (16) SP i = ∑ j = 1 n w j d i j + , i = 1 , 2 , … , m , (17) SN i = ∑ j = 1 n w j d i j − , i = 1 , 2 , … , m .

Step 10: Normalize the weighted sums of PDA and NDA for each EC.

The normalized values of SP i and SN i for each EC can be derived by (18) SP ‾ i = SP i max i SP i , i = 1 , 2 , … , m , (19) SN ‾ i = 1 − SN i max i SN i , i = 1 , 2 , … , m .

Step 11. Compute the important score for all ECs.

The importance scores for the m ECs can be computed by (20) IS i = 1 2 ( SP ‾ i + SN ‾ i ) , i = 1 , 2 , … , m .

In the process of QFD analysis, the larger the important score IS i , the higher the importance of the engineering characteristics EC i is. Therefore, the priority of all the ECs can be obtained according to the descending order of the values of IS i ( i = 1 , 2 , … , m ).

In this section, the designing process of Panda shared cars (Wu and Liao, 2018) is provided to illustrate the feasibility and applicability of our proposed QFD approach.