An organized method for identifying client needs or requirements and converting them into detailed plans for producing goods that would satisfy those demands is known as Quality Function Deployment (QFD) which was introduced by Mizuno and Akao (1978). These explicit and implicit client needs or demands are referred to as the “voice of the customer”. Several techniques are used to record the voice of the consumer, including direct conversation or interviews, surveys, focus groups, customer specifications, observation, warranty information, and field reports, etc. Hence, the “Voice of the Customer” is translated via QFD into the precise technical specifications and standards that the design must meet in order to be successful on the market. Especially in product planning and new product development, QFD is frequently utilized.

A product planning matrix, often known as a “house of quality”, is then created to compile this understanding of the needs of the customers. These matrices are used to translate higher level “what’s” into lower level “how’s” – product specifications or technological features—that can be used to meet those needs (Song et al., 2014).

Experts mostly prefer to use linguistic variables such as Certainly Low Importance (CLI) and Certainly High Importance (CHI) to explain the importance of the customer requirements. The relationships between whats and hows can also be evaluated by a different linguistic term set such as Certainly High Relation (CHR) and Certainly Low Relation (CLR). Apart from these, organizational difficulty explains the difficulty of technical requirements to be realized. Organizational difficulties are appraised by linguistic terms as well, and located at the bottom of the House of Quality. In this part, absolute importance values are also computed, which indicates the technical aspects of the considered product taking the most attention from the customers. Next, relative absolute importance values are calculated pointing out the relative importance degrees of the design requirements where the sum of these relative values equals to “1”.

At the roof of the House of Quality, correlations between the hows are indicated by linguistic sets ranging from Certainly Low Positive Correlation (CLPC) to Certainly High Positive Correlation (CHPC). The wall on the very right side points out the customer ratings with respect to customer requirements using the terms such as Certainly Low Satisfactory (CLS), or Certainly High Satisfactory (CHS). Similarly, at the very bottom of the House of Quality, engineering assessments of the companies/organizations are performed with regard to design requirements using the terms such as Certainly Low Satisfactory (CLS), or Certainly High Satisfactory (CHS). Corresponding numerical values of linguistic terms can be assigned from linguistic scales generally including five to nine fuzzy levels.

Linguistic terms can be transformed to their corresponding numerical values by utilizing the fuzzy set theory developed by Zadeh (1965). Ordinary fuzzy sets have been expanded to several new extensions with the aim of defining more detailed membership functions including decision makers’ hesitancies. These recent extensions can be listed as Intuitionistic Fuzzy Fets (IFS), Pythagorean Fuzzy Sets (PFS), Fermatean Fuzzy Sets (FFS), Neutrosophic Sets (NS), and Picture Fuzzy Sets (PiFS) etc. In this paper, we employ PFS in order to capture vagueness and ambiguities in the linguistic assessments with a larger domain to assign membership degrees (Akram et al., 2024).

Generally, the importance degrees of customer requirements are different since a disparate linguistic assessment is made by the customers for each requirement. The weights of customer requirements can be determined by various techniques such as Analytic Hierarchy Process (AHP) (Saaty, 1980), Analytic Network Process (ANP) (Saaty, 1996), the CRiteria Importance Through Intercriteria Correlation (CRITIC) (Diakoulaki et al., 1995), Step-wise weight assessment ratio analysis (SWARA) (Kersuliene et al., 2010) and Simple Multi-attribute Rating Technique (SMART) (Edwards and Barron, 1994).

One of the frequently used weighting method is Best-Worst Method (BWM) (Rezai, 2015) which is an optimization-based method differing from the above techniques with this feature (Gul et al., 2024). BWM provides a list of advantages as comprehensive view of the evaluation range allowing researchers the ability of verifying the coherence of pairwise comparisons. In order to reduce potential bias in decision making, BWM uses a dual pairwise comparison model in a single optimization framework. It is also capable of producing multiple optimal solutions under the scenarios having at least three criteria or alternatives. In order to cope with uncertainties and ambiguity, there have been a number of versions of the classical BWM by utilizing different fuzzy set extensions such as intuitionistic fuzzy sets and spherical fuzzy sets. We employ Pythagorean fuzzy sets for the extensions of BWM and QFD methods. The advantage of Pythagorean fuzzy sets over intuitionistic fuzzy sets is that they allow membership degrees to be assigned from a broader domain. This allows the expert to be more comfortable and flexible in assigning membership degrees. The preference between Pythagorean Fuzzy Sets (PFS) and Spherical Fuzzy Sets (SFS) relies heavily on the type of uncertainty the experts deal with, mathematical flexibility, and interpretability in decision-making problems. PFS has been more widely adopted and studied compared to SFS. SFS allows more flexibility by including hesitancy, but this can also introduce ambiguity or overfitting in modelling if the hesitancy degree isn’t well-defined.

In this paper, an interval-valued Pythagorean fuzzy (IVPF) BWM is introduced to determine the weights of the customer requirements. This process is applied for each of the multiple experts; and later the set of weights obtained from BWM are aggregated and used as an input for IVPF QFD analysis. According to the best knowledge of the authors, this is the first time to develop IVPF BWM and integrate it into IVPF QFD analysis for solving a real life product design problem.

E-scooters are one of the most common micro-mobility vehicles. Shared e-scooters are frequently preferred because of their affordable travel costs, easy availability, and easy progress in crowded traffic. There are several different e-scooters in the global market each having different features. In the literature, few studies conducted on e-scooter design through MCDM methods exist (Torrisi et al., 2025; Sonawane et al., 2025).

In this paper, a new scooter is aimed to be designed based on QFD analysis integrated with BWM including 12 customer and 12 design requirements. In this design, customer requirements such as “Long lasting electric scooter charge”, “fast charging”, “Bluetooth Internet connection”, and “Climbing ramps with ease” are involved while design requirements such as “Lithium ion (Li-Ion) batteries”, “Charging rate”, “Wi-Fi Bluetooth assembly”, and “Stainless adjustable umbrella holder” are handled to meet the customer requirements. Herein, linguistic assessments are employed for customer and design requirements, and then these assessments are converted to their corresponding IVPF numbers. House of Quality computations are realized based on these Pythagorean fuzzy numbers. Besides, competitive and sensitivity analyses are also implemented to illustrate the position of our company among the competitors and monitor how this position is affected based on the different values of a coefficient which is used to compile the Overall Performance Rating scores based on the DRs and CRs.

Organization of the study is as follows: Section 2 provides a detailed literature review on fuzzy BWM and QFD. Section 3 gives the preliminaries of IVPF sets while Section 4 displays the steps of the proposed IVPF BWM and QFD methodology. Section 5 demonstrates the application of the proposed IVPF methodology, sensitivity and comparative analyses. Finally, Section 6 presents conclusions and states the future remarks.

In this section, a comprehensive literature review on fuzzy BWM method and fuzzy QFD method is separately presented. The section focuses on MCDM methods integrated with BWM and QFD studies under fuzzy environment.

In this section, an IVPF BWM & QFD methodology is presented step by step. In Fig. 4, the proposed two-phase IVPF BWM & QFD methodology is demonstrated.

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Phase 1: IVPF BWM

Step 1. Decision makers ( D M k = { D M 1 , D M 2 , … , D M K } ) and a criteria set ( C i = { C 1 , C 2 , … , C n } ) are identified.

Step 2. Decision makers determines the most important (MI) criterion and the most unimportant (MU) criterion as denoted by C M I and C M U , respectively. Table 1 lists the linguistic scale for determining the C M I and C M U values.

Step 3. IVPF MI to Others vector ( S ˜ M I P k ) is identified by Pythagorean fuzzy evaluations of other criteria compared to the most important one for the kth decision maker utilizing Table 1.

The S ˜ M I P k vector is illustrated as in Eq. (15): (15) S ˜ M I P k = ( s ˜ M I 1 P k , s ˜ M I 2 P k , … , s ˜ M I n P k ) , where s ˜ M I i P k = ( [ μ M I i P L , μ M I i P U ] , [ v M I i P L , v M I i P U ] ) is the preference of C M I over C i based on DM_k’s judgment.

Step 4. IVPF MU to Others vector ( S ˜ M U P k ) is identified by Pythagorean fuzzy evaluations of other criteria compared to the most unimportant one utilizing Table 1. The S ˜ M U P k vector is presented in Eq. (16): (16) S ˜ M U P k = ( s ˜ M U 1 P k , s ˜ M U 2 P k , … , s ˜ M U n P k ) , where s ˜ M U i P k = ( [ μ M U i P L , μ M U i P U ] , [ v M U i P L , v M U i P U ] ) is the preference of C M U over C i based on DM_k’s judgment.

Step 5. In this step, based on DMs’ judgments, the optimal IVPF weight of each criterion is computed. The weights of the most important and the most unimportant criteria are shown in Eqs. (17)–(18), respectively. (17) w ˜ M I P k = ( [ μ M I P L , μ M I P U ] , [ v M I P L , v M I P U ] ) , (18) w ˜ M U P k = ( [ μ M U P L , μ M U P U ] , [ v M U P L , v M U P U ] ) . The optimal weights of the criteria should satisfy the following conditions: deff ( w ˜ M I P k ) / deff ( w ˜ i P k ) = a M I i and deff ( w ˜ i P k ) / deff ( w ˜ M U P k ) = a M U i . In order to obtain the best possible solution, the maximum absolute differences of | w ˜ M I P k / w ˜ i P k − r ˜ M I i P k | and | w ˜ i P k / w ˜ M U P k − r ˜ M U i P k | for all is’ are minimized. The optimization problem in Eq. (19) provides the optimal weights w ˜ i P k = ( w ˜ 1 ∗ , w ˜ 2 ∗ , … , w ˜ n ∗ ) k for each DM and for each criterion analysed. In Eq. (19), the minimum ε points out the consistency of the comparison matrices. The closer values of ε to “0” demonstrate a more consistent matrix. (19) min ε s.t. | μ M I P L ( k ) + v i P L ( k ) − μ M I P L ( k ) . v i P L ( k ) − μ M I i P L ( k ) | ⩽ ε , for all i | μ M I P U ( k ) + v i P U ( k ) − μ M I P U ( k ) . v i P U ( k ) − μ M I i P U ( k ) | ⩽ ε , for all i , | μ i P L ( k ) + v M U P L ( k ) − μ i P L ( k ) . v M U P L ( k ) − μ M U i P L ( k ) | ⩽ ε , for all i , | μ i P U ( k ) + v M U P U ( k ) − μ i P U ( k ) . v M U P U ( k ) − μ M U i P U ( k ) | ⩽ ε , for all i , | μ i P L ( k ) + v M I P L ( k ) − v M I i P L ( k ) | ⩽ ε , for all i , | μ i P U ( k ) + v M I P U ( k ) − v M I i P U ( k ) | ⩽ ε , for all i , | μ M U P L ( k ) + v i P L ( k ) − v M U i P L ( k ) | ⩽ ε , for all i , | μ M U P U ( k ) + v i P U ( k ) − v M U i P U ( k ) | ⩽ ε , for all i , 0 ⩽ ( μ i P U ( k ) ) 2 + ( v i P U ( k ) ) 2 ⩽ 1 , ∑ i = 1 n S c ( w ˜ i P k ) = 1 , S c ( w ˜ i P k ) ⩾ 0 , for all i .

Step 6. IVPFWG operator (Eq. (12)) aggregates the DMs judgments. Thus, the optimal weights of criteria w ˜ i P are calculated.

Step 7. Finally, the IVPF weights of criteria are defuzzified through Eq. (13). Then, the weights are normalized by Eq. (20). (20) w i N = w i ∑ i = 1 n w i . •

Phase 2: IVPF QFD

CR&DR Relation Analysis

Step 8: Linguistic CRs are defined and customer importance ratings are assigned by means of Pythagorean fuzzy scale presented in Table 2. This linguistic scale satisfies the following conditions: systematic behaviour, intersection between intervals, and replacement of membership and non-membership intervals for reciprocal terms. Herein, CRs are rated by three DMs as in Fig. 5 by using Table 2 (Haktanir and Kahraman, 2019). Figure 5 is designed for n customer requirements together with their Importance Evaluations ( IE). In this step, the solutions of IVPF BWM are used as the importance evaluations ( IE i , i = 1 , 2 , … , n).

Step 9: In this step, the DRs (Hows) are defined and the direction of improvement of DRs are determined. Next, the relationship matrix for m design requirements and n customer requirements, is constructed as presented in Fig. 6.

Step 10: The levels of organizational difficulty of the hows are identified at the bottom part of Fig. 7. Organizational Difficulty ( OD ˜) means how difficult to achieve a certain DR for an organization. Afterwards, target values of DRs utilizing classical numbers as denoted with Greek letters α, β, … , and η are given in the same figure.

Step 11: The correlation matrix among DRs (at the roof of HoQ) is designed as in Fig. 8. The correlations are evaluated based on the judgments of three DMs by using the IVPF scale shown in Table 3. In Figs. 7 and 8, positive and negative correlations are shown by blue and red colour arrows, respectively. In Fig. 8, empty cells point out no correlation among DR pairs. The cells with only two linguistic terms indicate that only two experts state their opinions.

Step 12: In this step, Absolute Importance ( A I ˜) value of each DR is computed by Eq. (21): (21) A I ˜ j = { ( ⨁ i = 1 n IE i ⊗ R ˜ j ) ⊗ ( 1 + CI ˜ j ) } ⊘ ( 1 + ROD ˜ j ) , j = 1 , 2 , … , m , where R ˜ is the aggregated linguistic terms in the relationship matrix; C I ˜ is the aggregated Correlation Impact factor (see Eq. (22)), and ROD ˜ is Relative Organizational Difficulty (see Eq. (23)).

In Eq. (21), the aggregated values of R ˜ are calculated by means of aggregation operator in Eq. (12), while the values of IE are the crisp importance weights of CRs obtained from Pythagorean fuzzy BWM in Phase 1. The OD ˜ linguistic assessments for each DR are aggregated using Eq. (12) in order to calculate ROD ˜ later. Herein, also Relative Absolute Importance ( RAI ˜) is derived through Eq. (24). Since IVPFS division and subtraction operations have not been explicitly defined in the literature, defuzzification formula is employed as given in Eq. (13). Absolute Importance ( A I ˜ ) and Relative Absolute Importance ( RAI ˜ ) values are shown in Fig. 9. (22) C I ˜ j = ( n c j / ( j − 1 ) ) ∗ ( p c ‾ ˜ j ⊖ n c ‾ ˜ j ) , − 1 ˜ ⩽ C I ˜ j ⩽ + 1 ˜ , (23) ROD ˜ j = ( O D ˜ i j ⨁ i = 1 n O D ˜ i j ) , j = 1 , 2 , … , m , (24) RAI ˜ j = A I ˜ j ⊘ ( ⨁ j = 1 m A I ˜ j ) , j = 1 , 2 , … , m , where n c j : the number of correlations of D R j with the other DRs; p c ‾ ˜ j : average of the positive correlations of D R j , and n c ‾ ˜ j : average of the negative correlations of D R j .

Step 13: The DRs are ranked with respect to RAI ˜ j where R A ˜ I j = ⟨ [ μ R A ˜ j L , μ R A ˜ j U ] , [ v R A ˜ j L , v R A ˜ j U ] ⟩ values with the hesitancy interval [ π R A ˜ j L , π R A ˜ j U ]. The highest RAI j value indicates the most important DRs that should be focused on during the design phase of a new product.

Competitive Analysis

Step 14: The linguistic ratings for competition with respect to CRs, as shown in Fig. 10, are evaluated by multiple decision makers using the IVPF scale in Table 2.

In this step, linguistic ratings with regard to the corresponding CRs are aggregated through Eq. (12). Then, the weighted comparison score ( I O − ϕ C R ) between our company O and company ϕ with regard to CRs are computed by Eq. (25). (25) I O − ϕ C R = ∑ i = 1 n ( ξ O − ϕ C R × d i C R ( O , ϕ ) × IE i ) , ϕ = φ 1 , … , φ y , where (26) ξ O − ϕ C R = + 1 , if O is better than ϕ , − 1 , if ϕ is better than O , 0 , if O is equal to ϕ and (27) d i C R ( O , ϕ ) = 2 4 ( ( μ O L − μ ϕ L ) 2 + ( v O L − v ϕ L ) 2 + ( μ O U − μ ϕ U ) 2 + ( v O U − v ϕ U ) 2 ) , i = 1 , 2 , … , n .

Step 15: Next, competitive analysis is conducted this time with respect to the DRs employing Table 2, as illustrated in Fig. 11.

Linguistic ratings with regard to the corresponding DRs are integrated via Eq. (12). Afterwards, the weighted comparison score ( I ˜ O − ϕ D R ) between our company O and company ϕ with regard to DRs are computed via Eq. (28). (28) I ˜ O − ϕ D R = ⨁ j = 1 m ( ξ O − ϕ D R × d j D R ( O , ϕ ) × A I ˜ j ) , ϕ = φ 1 , … , φ y where (29) ξ O − ϕ D R = + 1 , if O is better than ϕ , − 1 , if ϕ is better than O , 0 , if O is equal to ϕ and (30) d j D R ( O , ϕ ) = 2 4 ( ( μ O L − μ ϕ L ) 2 + ( v O L − v ϕ L ) 2 + ( μ O U − μ ϕ U ) 2 + ( v O U − v ϕ U ) 2 ) , j = 1 , 2 , … , m

Step 16: To see our position among the competitors, Overall Performance Rating ( OPR ˜) score of our company is obtained utilizing Eq. (31) by considering weighted comparison score assessments of both CRs and DRs. (31) OPR ˜ = κ I O − ϕ C R ⊕ ( 1 − κ ) I ˜ O − ϕ D R , where κ and ( 1 − κ) are the importance coefficients of CRs and DRs, respectively.

Step 17: As conclusion, the relative position of our company with respect to competitive companies is determined through the value of OPR ˜. Larger positive OPR ˜ value points out that our company performs much better than Company ϕ while larger absolute negative OPR ˜ value indicates that our company performs much worse than Company ϕ. If defuzzified OPR value equals to “0”, equal performances of our company and the competitive companies are observed.

Scooters are one of the most used micromobility vehicles in all over the world. An electric scooter (motor scooter) is a motorcycle with a seat, a platform for the rider’s feet, and an underbone or step-through frame, with an emphasis on comfort and fuel efficiency. Electric scooters (ESs), often known as e-scooters, are environmentally beneficial; can easily avoid traffic; and are space and money-saving devices. Nowadays, ESs are available for a pursuit of short-term rentals through a scooter-sharing system, which is a shared transportation service. E-scooters are picked up and dropped off at certain points within the service area, rather than having a permanent home address. Scooter-sharing programs aim to give the general population a quick and practical means of transportation for last-mile mobility in cities. In this case study, an e-scooter design is tried to be optimized by a QFD analysis under Pythagorean fuzzy environment. This e-scooter design will be used in a scooter-sharing system.

A manufacturer of micromobility vehicles in Istanbul is designing an e-scooter that they plan to manufacture. As a result of the interviews with the customers, the following 12 CRs were determined as listed in Table 4. During the technical meetings held with engineers and product development experts in the company on how to meet these customer needs, the following DRs were determined for each customer requirement. Table 4 presents the CRs and the corresponding DRs.