A Hybrid Approach for Battery Selection Based on Green Criteria in Electric Vehicles: DEMATEL-QFD-Interval Type-2 Fuzzy VIKOR

Abstract

Production involves processes such as raw material extraction, energy consumption, and waste management, which can lead to significant environmental consequences. Therefore, supplier selection based not only on technical performance but also on environmental sustainability criteria has become a fundamental component of eco-friendly manufacturing strategies. Moreover, in the selection of electric vehicle batteries, it is essential to consider customer demands alongside environmental factors. Accordingly, selected suppliers should fulfill company expectations while also reflecting the “voice” of the customer. The objective of this study is to propose an integrated approach for green supplier selection by taking into account various environmental performance requirements and criteria. The proposed approach evaluates battery suppliers with respect to both customer requirements and green criteria. To construct the relational structure, the DEMATEL method was employed to analyze the interrelationships among customer requirements (CRs). Subsequently, the Quality Function Deployment (QFD) model was used to establish a central relational matrix that captures the degree of correlation between each pair of supplier selection criteria and CRs. Finally, to evaluate and rank alternative suppliers, the Interval Type-2 Fuzzy VIKOR (IT2 F-VIKOR) method was applied. The hybrid approach proposed by us, integrating DEMATEL, QFD, and IT2 F-VIKOR, offers significant improvements over traditional methods. Unlike previous approaches that focus independently on customer preferences or supplier criteria, our model provides a unified evaluation by considering both dimensions simultaneously. Furthermore, the use of Interval Type-2 Fuzzy Logic enables the model to better manage uncertainty and ambiguity in expert judgments, yielding more reliable results compared to conventional fuzzy approaches. Additionally, the applicability of the model has been demonstrated through a real-world case study, confirming its practical relevance and robustness in the selection of green suppliers for electric vehicle battery procurement.

1. Introduction

Increasing environmental concerns, the depletion risks of fossil fuels, and issues such as global warming have led the transportation sector to seek more sustainable solutions. In this context, Electric Vehicles (EVs) have emerged as an eco-friendly alternative and are rapidly gaining popularity. However, when evaluating the environmental impact of EVs, it is not sufficient to consider only zero tailpipe emissions. The production, use, and disposal of batteries, which serve as the energy storage systems of these vehicles, also represent significant environmental and sustainability criteria. Therefore, the selection of batteries for electric vehicles should not only consider performance and cost but also take into account environmental impacts, sustainability of raw material sources, recyclability, and life cycle assessments.

The electric vehicle (EV) industry is experiencing rapid growth, driven by increasing environmental awareness and the need for sustainable transportation solutions. As the adoption of EVs accelerates, the selection of appropriate battery systems has become one of the most critical challenges for manufacturers. Battery performance directly impacts the driving range, safety, cost, and overall sustainability of electric vehicles, making it a pivotal factor in determining the success of the EV market. Additionally, the growing concern for environmental sustainability, energy efficiency, and green supply chains has further intensified the focus on selecting battery suppliers who meet both technical and environmental criteria. Despite advances in battery technology, challenges such as raw material sourcing, energy consumption during production, and waste management persist, which necessitate a comprehensive evaluation process. This research addresses these challenges by proposing a novel approach that integrates multiple decision-making criteria, thus offering a more holistic solution to the battery selection process.

The rapid advancements in electric vehicle technologies have made it essential to consider not only technical performance criteria but also environmental sustainability and customer-oriented expectations when selecting batteries. Sustainable green battery selection is a complex decision problem that requires the evaluation of numerous conflicting criteria. In this context, in recent years, Multi-Criteria Decision-Making (MCDM) methods have been frequently used in the literature, with fuzzy logic-based approaches emerging as particularly prominent in situations dominated by uncertainty and complexity. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) method has been utilized as an effective tool to analyze causal relationships and interactions among criteria, providing decision-makers with a systematic perspective. Through this method, not only the importance levels of the criteria but also their interdependencies can be identified. Thus, the DEMATEL method enables the identification of cause-and-effect relationships between customer and environmental criteria, allowing for the distinction between the influencing and influenced criteria in the system. This is a crucial step in identifying which criteria are more critical. In this study, the DEMATEL method was specifically selected due to its unique capability to identify and model causal relationships among customer requirements in a structured and interpretable manner. DEMATEL enables the construction of an influence matrix that clearly distinguishes between cause and effect groups, which is a fundamental feature for prioritizing customer requirements in QFD models. In contrast, although methods such as SITW (Stochastic Identification of Weights) and RANCOM (Ranking Comparison) are valuable for weight estimation and ranking, they do not provide a transparent mapping of causal linkages among factors. Moreover, DEMATEL aligns well with fuzzy logic frameworks, allowing for seamless integration with the subsequent fuzzy QFD and IT2 F-VIKOR phases of our hybrid model. Compared to other approaches that address causal relationships, DEMATEL offers greater interpretability, ease of integration, and analytical clarity, particularly in fuzzy multi-criteria decision-making environments characterized by high levels of uncertainty.

The QFD method is regarded as an effective tool for associating customer requirements (CRs) with technical characteristics, offering the advantage of integrating user expectations into technical parameters, especially in the selection of sustainable technological products. Through the integration of DEMATEL and QFD, a bi-directional interaction analysis between stakeholder expectations and technical criteria (green criteria) can be conducted, enabling the creation of more balanced decision models.

The VIKOR method enables the ranking of alternative battery options based on a compromise approach in relation to the ideal solution. Interval Type-2 fuzzy sets, an advanced extension of fuzzy logic, provide higher sensitivity in managing uncertainty in expert opinions and linguistic variables, offering more flexible results compared to classical Type-1 fuzzy sets. This provides a more realistic and adaptable evaluation capability compared to classical fuzzy approaches. In this context, the VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method, while offering a compromise-based solution for alternative ranking, allows for more reliable outcomes in decision environments characterized by high uncertainty when combined with the interval Type-2 fuzzy extension. Thus, with IT2 F-VIKOR, the ranking process becomes more precise and dependable under uncertain conditions. The integration of DEMATEL, QFD, and IT2 F-VIKOR methods will add methodological depth and analytical rigor to the decision-making process. By combining these methods, a holistic, systematic, and reliable battery selection process can be designed, which aligns with both customer-centric and environmental sustainability principles. This approach will not only reduce environmental impacts but also enable more sustainable product and supplier decisions that increase stakeholder satisfaction. Additionally, the development of decision-making approaches for selecting alternatives through integrated methods may be highly specific, as each individual method contains general functions that only provide stable solutions when appropriately integrated.

This study addresses the key factors to be considered in the sustainable “green” battery selection for electric vehicles and compares existing battery technologies in terms of environmental sustainability. The aim is to identify battery alternatives that are less harmful both environmentally and economically, more efficient in terms of resource usage, and compatible with a circular economy. While numerous applications exist in the literature where DEMATEL, QFD, and VIKOR methods are used either individually or in combination, there appears to be a lack of studies focusing on the integrated DEMATEL-QFD-IT2 F-VIKOR model specifically for green battery selection for electric vehicles. Therefore, it is expected that the integrated model proposed in this study will fill the existing gap in the literature and contribute to the development of sustainable decision support systems.

The core novelty and potential contributions of our study can be summarized as follows:

• Hybrid Methodological Integration: Our study proposes a novel hybrid decision-making framework that integrates DEMATEL, QFD, and IT2 F-VIKOR methods to solve the complex and uncertainty-driven problem of green battery selection for electric vehicles. Although these methods have been applied separately in various domains, their integration in the specific context of EV battery supplier evaluation under green criteria has not been previously explored in the literature.
• Dual-Dimensional Criteria Evaluation: In this study, the proposed hybrid approach simultaneously considers customer requirements and green supplier criteria, going beyond traditional evaluations that typically focus on a single dimension. This dual-layered assessment provides a more comprehensive and sustainable decision-making model for electric vehicle manufacturers.
• Use of IT2 Fuzzy Logic in a Real-World Case: To effectively handle uncertainty and imprecision in expert judgments, it is essential to employ Interval Type-2 fuzzy sets (IT2 FSs), which offer a more robust modeling of linguistic assessments compared to conventional fuzzy logic. The use of IT2 F-VIKOR within this integrated framework is novel and enhances the reliability of the decision-making process.
• Application to a Critical and Emerging Domain: The study focuses on a timely and impactful area—green supplier selection for EV batteries—which is of strategic importance for sustainable manufacturing and environmental policy. The results offer actionable insights for EV manufacturers to align with green supply chain strategies.
• Unidimensional Evaluation Methods: Traditional methods typically address criteria independently and evaluate decisions on a single dimension. However, in the context of battery supplier selection, a multidimensional decision process is involved, where economic, environmental, and technical factors interact. The integration of DEMATEL-QFD-IT2 F-VIKOR provides a more comprehensive evaluation by considering these interactions and uncertainties.
• Fuzzy AHP, TOPSIS: Although these methods are frequently used, the integration of DEMATEL-QFD-IT2 F-VIKOR allows for a more coherent combination of causal analysis and customer requirements with green supplier criteria.
• Application to Multi-Criteria Decision Analysis (MCDA): Moreover, QFD and DEMATEL, within the context of multi-criteria decision analysis, effectively integrate both customer requirements and green supplier criteria, while the integration of IT2 F-VIKOR with fuzzy logic enables more effective management of uncertainties within this process.

In conclusion, traditional approaches that typically focus on a single evaluation dimension, the proposed model simultaneously considers both customer requirements and green supplier criteria, offering a dual-perspective assessment to support more sustainable decision-making. Furthermore, by utilizing IT2 fuzzy logic, the model captures the vagueness and imprecision inherent in expert judgments more effectively than conventional fuzzy methods, thereby improving the reliability of the evaluations. Given the increasing global emphasis on sustainable manufacturing and environmental responsibility, the application of this hybrid approach to green supplier selection in EV battery production provides timely and actionable insights for both industry and policy makers.

The remainder of this study is structured as follows: The literature review is presented in Section 2. Section 3 introduces the proposed approaches for the five alternatives discussed. Section 4 outlines the steps for applying the proposed integrated approach to green supplier selection. In Section 5, the integrated method proposed is applied to the five alternatives, based on customer and environmental criteria, and the selection and ranking of these alternatives are performed. Section 6 provides an analysis of the application results, while Section 7 concludes with the results and discussions.

2. Literature Review

This section briefly discusses studies related to the use of DEMATEL, QFD, and IT2 F-VIKOR methods in the selection and ranking of alternative suppliers, with a particular focus on their applications in the automotive industry as well as other sectors.

In a study conducted by [1], a decision framework integrating fuzzy DEMATEL, fuzzy QFD, fuzzy TOPSIS, and fuzzy VIKOR methods was proposed for the selection and ranking of five suppliers under 15 criteria in a detergent factory, for the first time in an uncertain environment. In a study by [2], fuzzy DEMATEL and fuzzy QFD methods were used to determine the weights of customer requirements and technical criteria in the product development process for electric vehicles. They also proposed an integrated model using fuzzy VIKOR to scale and evaluate engineering characteristics related to the product development process of electric vehicles. In a study by [3], a hybrid integrated model combining QFD, DEMATEL, and MULTIMOORA methods was used for product design in CNC machine tools. In a study by [4], a hybrid decision-making model combining DEMATEL and VIKOR methods for sustainable supplier selection was proposed, and the model was applied in supplier selection evaluation for a company. In a study by [5], strategic part prioritization for quality improvement applications in an automotive factory was conducted. A multi-criteria decision-making approach was used, integrating fuzzy DEMATEL, the anti-entropy weighting method, and fuzzy VIKOR methods. In a study by [6], multi-criteria decision-making methods were used for appropriate supplier selection in the automotive sector. Initially, the DEMATEL approach was applied to reveal the cause-and-effect relationships between the main criteria, followed by the Analytical Network Process (ANP) to calculate the weights of sub-criteria. Finally, alternative suppliers were evaluated using the TOPSIS method, and suppliers with the highest performance index were selected. In a study by [6], a new interval Type-2 fuzzy evaluation model utilizing group decision-making analysis for green supplier selection in the automotive sector was proposed. The study was validated with a case study in the battery industry. In the model, the evaluation criteria provided by decision-makers were specified as linguistic terms, which were then converted into interval Type-2 fuzzy expressions. The importance of the evaluation criteria was calculated using the interval Type-2 fuzzy TOPSIS method, and potential alternatives were ranked using the interval Type-2 fuzzy Hamming distance criterion. In a study by [7], a decision support model developed for determining sustainable strategies in the EV adoption process was presented. The approach introduces an interval Type-2 fuzzy MEREC-VIKOR approach based on confidence level. The proposed approach allows decision-makers to make evaluations in a more flexible and uncertain environment. The approach used the MEREC (Minimum Removal Effects Criteria) method to determine the importance of criteria in the ranking of strategies, followed by the VIKOR method for the ranking of alternatives.

Also, recent developments in MCDA have introduced innovative approaches for managing uncertainty, structure identification, and subjective weighting in complex decision environments. For instance, [8] proposed a Fuzzy normalization-based Multi-Attributive Border Approximation Area Comparison (F-MABAC) method, which provides a robust alternative to classical normalization techniques by addressing fuzziness and ambiguity in input data—an aspect also central to our use of Interval Type-2 fuzzy sets. Moreover, the pymcdm—reidentify tool introduced by [9] represents a notable advancement in MCDA model re-identification, offering algorithmic insights into model structure and robustness under different scenarios. This contributes significantly to the understanding of how model architecture affects decision outcomes, reinforcing the value of hybrid approaches such as ours. Finally, the systematic review by [10] on subjective weight determination methods provides a comprehensive taxonomy and evaluation of existing strategies for expert-based weighting, which complements our own expert-driven weighting procedures embedded within DEMATEL and QFD stages.

From the literature review (see

Table 1. Summary of previous research on electric vehicles and battery selection.

Author/Authors	Applied Method	Application Area
[11]	ORESTE method	Automotive—Battery Supplier Selection
[12]	Fuzzy QFD—Multiple regression Method	Automotive—Hybrid electric vehicles
[13]	Type-2 Fuzzy TOPSIS, Type-2 Fuzzy Hamming	Energy–Battery industry
[14]	Classical VIKOR—Fuzzy VIKOR	Transportation—Energy Sensors
[15]	Fuzzy DEMATEL—LPWBN	Automotive—Electric vehicle—Battery supplier selection
[16]	DEMATEL-ISM	Automotive—Electric vehicle selection

), it is observed that many researchers in the past have used a variety of methods and integrated approaches for evaluating and selecting suitable alternatives. However, there is a noticeable lack of studies in the transportation-automotive sector, where customer and environmental criteria are considered in battery selection using the hybrid DEMATEL-QFD-IT2 F-VIKOR method.

Also, despite the increasing interest in sustainable decision-making for electric vehicle components, the current body of literature reveals several limitations. Many existing studies either concentrate solely on customer preferences or focus exclusively on supplier-side green criteria, lacking an integrated perspective that accounts for both dimensions simultaneously. Moreover, most of the previous approaches rely on Type-1 fuzzy logic, which falls short in capturing the uncertainty and imprecision inherent in expert evaluations. Additionally, hybrid methodological integrations that connect causal analysis (e.g., DEMATEL), requirement mapping (e.g., QFD), and robust optimization methods (e.g., IT2 F-VIKOR) remain underexplored. This study addresses these critical gaps by introducing a novel hybrid approach that not only improves uncertainty modeling through interval Type-2 fuzzy sets but also provides a structured framework for incorporating both technical and sustainability-related decision parameters. The proposed model is further validated through a practical case study, demonstrating its applicability in real-world supplier selection problems.

3. Preliminaries

This section first presents the concept of Type-2 fuzzy sets and the mathematical operations performed within these sets. Subsequently, the steps and definitions of the IT2 F-VIKOR method are outlined, followed by the steps and definitions of the DEMATEL method. Finally, the steps and definitions of the QFD method are presented.

3.1. General Type-2 Fuzzy Sets

Type-2 fuzzy sets are a type of fuzzy set developed to better model uncertainty compared to classical or Type-1 fuzzy sets. Type-2 fuzzy sets are characterized by membership degrees that are themselves fuzzy and are defined by an upper membership function (UMF) and a lower membership function (LMF).

Definition 1. 

A Type-2 fuzzy set $\widetilde{\stackrel{~}{A}}$ is defined on the universal set  $X$ as follows:

$$\widetilde{\stackrel{~}{A}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{A}}}\left(x,u\right)\right)∣x\in X,u\in J_x\subseteq \left[\mathrm{0,1}\right]\right\}$$

(1)

Here, $x$ is an element of the universal set $X$.

$u$: The membership degree is the internal variable that varies. $J_x$: The range to which the value of  $u$  belongs for each $x$. ${\mu }_{\widetilde{\stackrel{~}{A}}}(x,u)$: The second-order membership function that denotes the membership degree of the element  $x,$ and this function defines the Type-2 fuzzy set function instead of the Type-1 fuzzy set function.

Definition 2. 

Type-2 fuzzy sets are defined by UMF and LMF. Any Type-2 fuzzy set  $\widetilde{\stackrel{~}{A}}$  is expressed as follows:

$$\widetilde{\stackrel{~}{A}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{A}}}\left(x,u\right)\right)\mid x\in X\right\}$$

(2)

Here,  ${\mu }_{\widetilde{\stackrel{~}{A}}}(x)=[{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}(x),{\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}(x)]$ is expressed in terms of the lower and upper membership functions.

Here,  ${\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ represents the UMF.

${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$  represents the LMF. This definition demonstrates that Type-2 fuzzy sets encompass a broader range of uncertainty compared to Type-1 fuzzy sets. For this reason, Type-2 fuzzy sets can be used to better model uncertainty in fuzzy systems and improve the accuracy of expert opinions.

3.2. Interval Type-2 Fuzzy Sets

Interval Type-2 fuzzy sets (IT2 FSs) are a subclass of Type-2 fuzzy sets in which the membership function varies within a specific interval. In these sets, the membership degree of each element is characterized by a lower and upper bound, forming an interval rather than a precise value. This allows for better modeling of uncertainty compared to classical Type-1 fuzzy sets, particularly in situations where information is vague or expert evaluations are imprecise.

Definition 3. 

Interval Type-2 fuzzy sets are defined as follows:

$$\widetilde{\stackrel{~}{A}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)\right)\mid x\in X\right\}$$

(3)

Here,  $x$  denotes an element of the universal set  $X$. ${\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)$is the secondary membership function that defines the degree of membership for each element  $x$, represented by a bounded interval between a lower and an upper value. These bounds reflect a certain degree of uncertainty.

Definition 4. 

An interval Type-2 fuzzy set represents each membership value as an interval, and can be expressed as follows:

$${\mu }_{\widetilde{\stackrel{~}{A}}}(x)=[{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}(x),{\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}(x)]$$

(4)

Here,  ${\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$,  Upper Membership Function (UMF), represents the highest degree of membership for the element  $x$.

${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$,  Lower Membership Function (LMF), represents the lowest degree of membership for the element  $x$.

The lower and upper membership functions represent the fuzzy value range assigned to an element, which is particularly useful for modeling more complex and uncertain systems.

3.3. Arithmetic Operations in Type-2 Fuzzy Sets

Definition 5. 

Addition Operation: In Type-2 fuzzy sets, the addition operation is performed between the lower and upper membership functions of each set.

If $\widetilde{\stackrel{~}{A}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)\right)\right\}$ and $\widetilde{\stackrel{~}{B}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{B}}}\left(x\right)\right)\right\}$ are Type-2 fuzzy sets, the membership function of the set $\widetilde{\stackrel{~}{C}}=\widetilde{\stackrel{~}{A}}+\widetilde{\stackrel{~}{B}}$ is calculated as follows:

$${\mu }_{\widetilde{\stackrel{~}{C}}}\left(x\right)={\mu }_{\widetilde{\stackrel{~}{A}}}(x)+{\mu }_{\widetilde{\stackrel{~}{B}}}(x)=[{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}(x)+{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}(x),{\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}(x)+{\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}(x)]$$

(5)

Here, ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ and ${\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ are the lower and upper membership functions of the set $\widetilde{\stackrel{~}{A}}$. ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(\mathrm{x}\right)$ and ${\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(\mathrm{x}\right)$ are the lower and upper membership functions of the set $\widetilde{\stackrel{~}{B}}$.

Definition 6. 

Subtraction Operation: The subtraction operation allows for finding the difference between two Type-2 fuzzy sets. This operation is performed between the lower and upper membership functions of both sets.

If we are working with Type-2 fuzzy sets $\widetilde{\stackrel{~}{A}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)\right)\right\}$ and $\widetilde{\stackrel{~}{B}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{B}}}\left(x\right)\right)\right\}$ the membership function of set $\widetilde{\stackrel{~}{C}}=\widetilde{\stackrel{~}{A}}-\widetilde{\stackrel{~}{B}}$ is calculated as follows:

$${\mu }_{\widetilde{\stackrel{~}{C}}}\left(x\right)={\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)-{\mu }_{\widetilde{\stackrel{~}{B}}}(x)=[{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)-{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right),{\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)-{\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}(x)]$$

(6)

Here, ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ and ${\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ are the lower and upper membership functions of set $\widetilde{\stackrel{~}{A}}$. ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right)$ ve ${\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right)$ are the lower and upper membership functions of set $\widetilde{\stackrel{~}{B}}$.

Definition 7. 

Multiplication Operation: The multiplication operation is performed between the lower and upper membership functions of Type-2 fuzzy sets. This operation yields the result obtained by multiplying the membership degrees of the two Type-2 fuzzy sets.

If we are working with Type-2 fuzzy sets $\widetilde{\stackrel{~}{A}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)\right)\right\}$ and $\widetilde{\stackrel{~}{B}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{B}}}\left(x\right)\right)\right\}$, the membership function of set $\widetilde{\stackrel{~}{C}}=\widetilde{\stackrel{~}{A}}\times \widetilde{\stackrel{~}{B}}$ is calculated as follows:

$${\mu }_{\widetilde{\stackrel{~}{C}}}\left(x\right)={\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)\times {\mu }_{\widetilde{\stackrel{~}{B}}}(x)=[{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)\times {\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right),{\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)\times {\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}(x)]$$

(7)

Here, ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ and ${\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ are the lower and upper membership functions of set $\widetilde{\stackrel{~}{A}}$. ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right)$ and ${\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right)$ are the lower and upper membership functions of set $\widetilde{\stackrel{~}{B}}$.

Definition 8. 

Division operation. The division operation is also performed between the membership functions of two Type-2 fuzzy sets, where the membership function of one set is divided by the membership function of the other set.

If we are working with Type-2 fuzzy sets $\widetilde{\stackrel{~}{A}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)\right)\right\}$ and $\widetilde{\stackrel{~}{B}}=\left\{\left(x, {\mu }_{\widetilde{\stackrel{~}{B}}}\left(x\right)\right)\right\}$, the membership function of set $\widetilde{\stackrel{~}{C}}=\widetilde{\stackrel{~}{A}} /\widetilde{\stackrel{~}{ B}}$ is calculated as follows:

$${\mu }_{\widetilde{\stackrel{~}{C}}}\left(x\right)={\mu }_{\widetilde{\stackrel{~}{A}}}\left(x\right)/{\mu }_{\widetilde{\stackrel{~}{B}}}(x)=[{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)/{\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right),{\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)/{\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}(x)]$$

(8)

Here, ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ and ${\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ are the lower and upper membership functions of set $\widetilde{\stackrel{~}{A}}$. ${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right)$ and ${\overline{\mu }}_{\widetilde{\stackrel{~}{B}}}\left(x\right)$ are the lower and upper membership functions of set $\widetilde{\stackrel{~}{B}}$.

Definition 9. 

Multiplying a Type-2 fuzzy set by a constant  $k$. The operation of multiplying a Type-2 fuzzy set by a constant  $k$ is performed as follows:

$$\widetilde{\stackrel{~}{B}}=k\times \widetilde{\stackrel{~}{A}}$$

(9)

Similarly, the membership function of set  $\widetilde{\stackrel{~}{B}}$ is calculated as follows:

$${\mu }_{\widetilde{\stackrel{~}{B}}}\left(x\right)=[k\times {\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right), k\times {\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)]$$

(10)

Here,  $k is$ a constant number (usually a positive real number).

${\underset{\_}{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$  and  ${\overline{\mu }}_{\widetilde{\stackrel{~}{A}}}\left(x\right)$ $\widetilde{\stackrel{~}{A}}$  are the lower and upper membership functions of set. $\widetilde{\stackrel{~}{B}}$  is the new Type-2 fuzzy set multiplied by the constant  $k$.

Definition 10. 

Triangular Type-2 fuzzy sets: Triangular Type-2 fuzzy sets are typically defined by their lower and upper membership functions. Although they have a triangular shape, similar to Type-1 fuzzy sets, they contain two membership functions: UMF and LMF. A triangular Type-2 fuzzy set is defined by the following parameters:

UMF: A triangular fuzzy number is denoted as ${(a_{i1}^u,a_{i2}^u,a_{i3}^u;h}_1({\widetilde{\stackrel{~}{A}}}_i^U),h_2({\widetilde{\stackrel{~}{A}}}_i^U)$).

LMF: It is typically defined as a smaller triangular fuzzy number within the UMF, for example, denoted as ${(a_{i1}^l,a_{i2}^l,a_{i3}^l;h}_1({\widetilde{\stackrel{~}{A}}}_i^L),h_2({\widetilde{\stackrel{~}{A}}}_i^L)$). In a Type-2 triangular fuzzy set, the horizontal axis represents the variable $x$ value, and the vertical axis represents the membership degree $\mu \left(x\right)$ value. A Type-2 triangular fuzzy set is shown in Figure 1.

3.4. Interval Type-2 Fuzzy VIKOR Method (IT2 F-VIKOR)

This section will discuss the steps involved in the IT2 F-VIKOR method.

Step 1: First, the number of decision makers, alternatives, and criteria are determined.

Step 2: Determining Fuzzy Data. In this step, decision makers evaluate each alternative for each criterion using interval Type-2 fuzzy numbers. Interval Type-2 fuzzy numbers are typically expressed with lower and upper bounds that are defined within specific intervals. The alternatives (A₁, A₂,…, A_n) and criteria (C₁, C₂,…, C_m) are determined. The decision matrix is created as follows:

$$\widetilde{\stackrel{~}{X}}=\left[\begin{array}{cccc}{\widetilde{\stackrel{~}{x}}}_{11}& {\widetilde{\stackrel{~}{x}}}_{12}& \dots & {\widetilde{\stackrel{~}{x}}}_{1m}\\ {\widetilde{\stackrel{~}{x}}}_{21}& {\widetilde{\stackrel{~}{x}}}_{22}& \dots & {\widetilde{\stackrel{~}{x}}}_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ {\widetilde{\stackrel{~}{x}}}_{n1}& {\widetilde{\stackrel{~}{x}}}_{n2}& \dots & {\widetilde{\stackrel{~}{x}}}_{nm}\end{array}\right]$$

(11)

Step 3: Calculation of the ideal (positive) and anti-ideal (negative) solutions. At this stage, the ideal solution (${\widetilde{\stackrel{~}{f}}}_j^{\ast }$) and the anti-ideal solution (${\widetilde{\stackrel{~}{f}}}_j^{-}$) values are calculated for each criterion. The ideal solution (${\widetilde{\stackrel{~}{f}}}_j^{\ast }$): It takes the best (maximum) values for each criterion. The anti-ideal solution (${\widetilde{\stackrel{~}{f}}}_j^{-}$): It takes the worst (minimum) values for each criterion. The ideal and anti-ideal solution values are calculated as shown in Equations (12) and (13) below:

$$\mathrm{I}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l} \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}:{\widetilde{\stackrel{~}{f}}}_j^{\ast }=max x_{ij}$$

(12)

$$\mathrm{A}\mathrm{n}\mathrm{t}\mathrm{i}\text{-}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l} \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}:{\widetilde{\stackrel{~}{f}}}_j^{-}=min x_{ij}$$

(13)

Here, for Type-2 fuzzy numbers, the upper and lower membership functions are normalized separately.

Step 4: Fuzzy data normalization. In this step, the fuzzy data for each alternative and criterion are typically normalized to a specific range. Normalization converts the value of each criterion to a range between 0 and 1, ensuring comparability among criteria. The formulas for normalization are given in Equations (14) and (15) as follows:

$${\widetilde{\stackrel{~}{S}}}_i={\sum }_{j=1}^m{w}_j{\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-x_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}$$

(14)

$${\widetilde{\stackrel{~}{R}}}_i=\begin{array}{c}max\\ j\end{array}\left(w_j{\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-x_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}\right)$$

(15)

Here,

${\widetilde{\stackrel{~}{S}}}_i$: It is a measure of the total difference (the overall distance of the alternative in relation to all criteria).

${\widetilde{\stackrel{~}{R}}}_i$: It is the maximum criterion difference (the distance of the alternative in the worst criterion).

$w_j$: It is the weight of the criterion.

Here, for Type-2 fuzzy numbers, the upper and lower membership functions are normalized separately.

Step 5: The calculation of the fuzzy VIKOR scores $\left({\widetilde{\stackrel{~}{Q}}}_i\right)$. The fuzzy VIKOR score is calculated based on the distances of each alternative from the ideal and anti-ideal solutions. This computation incorporates the decision-maker’s compromise parameter $\left(v\right)$, which reflects the balance between the proximity to the ideal solution and the remoteness from the anti-ideal solution. The VIKOR score is calculated as shown in Equation (16) below.

$${\widetilde{\stackrel{~}{Q}}}_i=v{\displaystyle \frac{{\widetilde{\stackrel{~}{S}}}_i-{\widetilde{\stackrel{~}{S}}}^{\ast }}{{\widetilde{\stackrel{~}{S}}}^{-}-{\widetilde{\stackrel{~}{S}}}^{\ast }}}+\left(1-v\right){\displaystyle \frac{{\widetilde{\stackrel{~}{R}}}_i-{\widetilde{\stackrel{~}{R}}}^{\ast }}{{\widetilde{\stackrel{~}{R}}}^{-}-{\widetilde{\stackrel{~}{R}}}^{\ast }}}$$

(16)

Here,

${\widetilde{\stackrel{~}{S}}}_i$: The total disadvantage of the alternative;

${\widetilde{\stackrel{~}{R}}}_i$: The worst criterion performance of the alternative;

${\widetilde{\stackrel{~}{S}}}^{\ast }$: $\min {\widetilde{\stackrel{~}{S}}}_i$, $S^{-}$: $\max {\widetilde{\stackrel{~}{S}}}_i$, ${\widetilde{\stackrel{~}{R}}}^{\ast }$: $\min {\widetilde{\stackrel{~}{R}}}_i$, $R^{-}$: $\max {\widetilde{\stackrel{~}{R}}}_i$;

$v$: The compromise coefficient (usually set to 0.5).

Step 6: Defuzzification of the Calculated Fuzzy VIKOR Scores. In this step, the fuzzy VIKOR scores computed in step 5 are defuzzified to obtain crisp values. The defuzzification of the Type-2 fuzzy VIKOR scores will be carried out using the average Type-1 fuzzy approach. This method involves a two-step defuzzification process.

• Transformation of Upper and Lower Membership Functions into Type-1 Fuzzy Sets: Here, to obtain a Type-1 fuzzy set, the average of the upper and lower membership functions is calculated.

$$\widetilde{\stackrel{~}{x}}=\left({\displaystyle \frac{{\widetilde{\stackrel{~}{x}}}_{U1}+{\widetilde{\stackrel{~}{x}}}_{L1}}{2}},{\displaystyle \frac{{\widetilde{\stackrel{~}{x}}}_{U2}+{\widetilde{\stackrel{~}{x}}}_{L2}}{2}},{\displaystyle \frac{{\widetilde{\stackrel{~}{x}}}_{U3}+{\widetilde{\stackrel{~}{x}}}_{L3}}{2}}\right)$$

(17)

Here, ${\widetilde{\stackrel{~}{x}}}_{U1}, {\widetilde{\stackrel{~}{x}}}_{U2},{ \widetilde{\stackrel{~}{x}}}_{U3}$ represents the value of the upper membership function, and ${\widetilde{\stackrel{~}{x}}}_{L1}, {\widetilde{\stackrel{~}{x}}}_{L2},{ \widetilde{\stackrel{~}{x}}}_{L3}$ represents the value of the lower membership function.

As a result of this process, our Type-2 fuzzy set is transformed into a Type-1 fuzzy set.

2.

Defuzzification: Here, the Weighted Average (Centroid) Method is applied to defuzzify the Type-1 fuzzy set. This significantly simplifies the computation required to find the center of a two-dimensional shape, thus enhancing the efficiency of the defuzzification process [17].

$$Defuzzification value=\left({\displaystyle \frac{{\widetilde{\stackrel{~}{x}}}_1+{\widetilde{\stackrel{~}{x}}}_2+{\widetilde{\stackrel{~}{x}}}_3}{3}}\right)$$

(18)

Thus, using Equations (17) and (18), the Type-2 fuzzy values calculated in Step 5 are defuzzified and converted into crisp values.

Step 7: Ranking of Alternatives. In Step 6, alternatives are ranked based on the VIKOR scores ($Q_i$) calculated. The alternative with the smallest VIKOR score is considered the best solution.

Here, two conditions are checked for the $Q_i$ value:

Condition 1 (Acceptable Advantage):

$$Q\left(A2\right)-Q\left(A1\right)\ge {\displaystyle \frac{1}{m-1}}$$

(19)

Here, A1 represents the best alternative, A2 represents the second-best alternative, and m represents the total number of alternatives considered.

Condition 2 (Acceptable Stability): The best alternative must be ranked first in both the ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ rankings. If these conditions are not met, a compromise can be made to select the best alternative.

3.5. DEMATEL Method (The Decision Making Trial and Evaluation Laboratory Method)

The DEMATEL method was developed between 1972 and 1976 by the Battelle Memorial Institute in Geneva, under the Science and Human Relations Program, for solving complex and interrelated problem groups [18]. The DEMATEL method consists of seven consecutive steps. The solution is achieved with the effect-cause graph diagram obtained at the end of Step 5.

Step 1: The creation of the direct relationship matrix (A):

To create the direct relationship matrix (A), a five-level binary comparison scale is used. The levels are represented as 0 (Ineffective), 1 (Low Impact), 2 (Moderate Impact), 3 (High Impact), and 4 (Very High Impact). The relationships between criteria are determined by an expert group using the binary comparison scale [19]. As a result of the comparisons, the direct relationship matrix (A) is obtained. A sample A matrix is shown in Equation (20).

$$\mathrm{A}=\left[\begin{array}{cccccc}0& {\mathrm{a}}_{12}& \dots & {\mathrm{a}}_{1\mathrm{j}}& \dots & {\mathrm{a}}_{1\mathrm{n}}\\ {\mathrm{a}}_{21}& 0& \dots & {\mathrm{a}}_{2\mathrm{j}}& \dots & {\mathrm{a}}_{2\mathrm{n}}\\ \dots & \dots & \dots & \dots & \dots & \dots \\ \dots & \dots & \dots & \dots & \dots & \dots \\ {\mathrm{a}}_{\mathrm{n}1}& {\mathrm{a}}_{\mathrm{n}2}& \dots & {\mathrm{a}}_{\mathrm{n}\mathrm{j}}& \dots & 0\end{array}\right]$$

(20)

Step 2: The creation of the normalized direct-relation matrix (X):

After the creation of the direct-relation matrix (A), the normalized matrix (X) is obtained using Equation (21). Each element in the X matrix is between 0 and 1.

$$X=k\times A$$

(21)

Here,

$$k={\displaystyle \frac{1}{{}_{1\le i\le n}{}^{max}\left({\sum }_{j=1}^n{a}_{ij}\right)}}, i,j=1,2,\dots ,n$$

(22)

In Equations (21) and (22), the normalization factor is used to standardize the values of various criteria, ensuring they are comparable even when measured using different units or scales. This factor is crucial for adjusting the values to a common scale, preventing any one criterion from dominating the decision-making process due to its units or magnitude. The impact of the normalization factor on the final results is significant, as it influences the rankings of alternatives and the overall outcome of the decision process.

Step 3: Calculation of the total relation matrix (T):

After obtaining the normalized direct-relation matrix, the total relation matrix is derived using Equation (23). In this equation, the identity matrix (I) is denoted.

$T={\left[t_{ij}\right]}_{n\times n},i,j=1,2,\dots ,nise$ $T=X+X^2+X^3+...+X^k$

T  $=X(I+X+X^2+...+X^{k-1})\left[(I-X){(I-X)}^{-1}\right]$

T $=X(I-X^k){(I-X)}^{-1}$ then,

$$T=X{(I-X)}^{-1}T, k\to \infty , X^k={\left[0\right]}_{n\times n} \mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{s};T=X{(I-X)}^{-1}$$

(23)

Step 4: Determination of the row and column sums of the T matrix:

In the total relation matrix (T), the sums of the rows and columns are obtained using Equations (24) and (25), and these are represented by the vectors D and R, respectively.

$$D_i={\left[{\sum }_{j=1}^n{t}_{ij}\right]}_{n\times 1}={\left[t_i\right]}_{n\times 1}, i=1,2,\dots ,n$$

(24)

$$R_j={\left[{\sum }_{j=1}^n{t}_{ij}\right]}_{1\times n}={\left[t_i\right]}_{n\times 1}, j=1,2,\dots ,n$$

(25)

Step 5: Adjustment of the threshold value (α):

To obtain an appropriate cause-effect graph, decision-makers need to adjust a threshold value for the impact level. Elements with impact values greater than the threshold in the T matrix are selected and transformed into a cause-effect graph diagram. The threshold value is determined by the decision maker or experts. The value of $\alpha$ is calculated using Equation (26). Here, N represents the total number of elements in the T matrix.

$$\alpha ={\displaystyle \frac{\sum _{i=1}^n\sum _j^n\left[t_{ij}\right]}{N}}$$

(26)

In this study, the threshold $\left(\alpha \right)$ is calculated as the average of the total relation matrix (Equation (26)) to provide a reasonable and consistent cut-off point for the causal relationships. The choice of threshold is critical, as it determines the strength of the connections represented in the causal diagram. We chose this approach for its simplicity and to ensure that the threshold reflects the overall intensity of interrelationships among the criteria.

Step 6: Development of a Causal Diagram:

A causal diagram is a classification of the degree of each criterion. It shows the criteria that can easily be classified as passive or active. The influence diagram is obtained by plotting the points (D + R, D − R) on a coordinate plane, where the horizontal axis represents D + R and the vertical axis represents D − R.

Step 7: Calculation of criteria weights:

The criteria weights $\left(C_i\right)$ are calculated by normalizing the prominence vector (D_k + R_k), ensuring that the sum of the normalized weights equals 1.

3.6. QFD Model

In a general QFD model, the following elements are incorporated into the House of Quality (HoQ), as illustrated in Figure 2. Here,

A: the matrix of WHATs; B: the matrix of HOWs; C: the relationship matrix between WHATs and HOWs; D: the relative importance or weights of the WHATs; E: the relationship among the HOWs; F: the weights of the HOWs.

The general QFD model is shown in Figure 2 below.

The general steps in applying the QFD model are as follows:

Step 1: The definition of the WHATs is made.

Step 2: The definition of the HOWs is made. The supplier selection criteria are specified as HOWs in the HoQ and placed in the area marked ‘B’ in Figure 2.

Step 3: The development of the HOWs matrix (E) showing the internal dependencies among the HOWs.

Step 4: Assigning priority weights to customer requirements: A binary comparison scale consisting of 5 levels is used to assign priority values to customer requirements. The levels are defined as 1 (not important), 2 (important), 3 (very important), 4 (much more important), and 5 (most important).

Step 5: The development of the relationship matrix (C) or HoQ by evaluating the degree of impact between the WHATs and HOWs, using an appropriate scale to express how much each WHATs affects the HOWs. Here, a four-point scale of 1, 3, 6, and 9 is used, addressing weak, medium, strong, and very strong relationships, respectively.

Step 6: After the HoQ matrix is developed, the overall priorities of the supplier selection criteria or HOWs are calculated, showing the synthesized importance of the supplier selection criteria.

In QFD, the output of each stage (HOWs) is transformed into the inputs of the next stage (new WHATs). The advantages of implementing the QFD model include higher customer satisfaction, shorter delivery times, better flexibility, promotion of quality, reduced time to market, and information protection, among others [20].

4. A Combined Selection Method for Green Supplier Selection

The proposed hybrid approach will provide the following contributions to the literature. The first contribution is the integration of customer requirements and green supplier selection criteria. The second contribution is the presentation of DEMATEL, QFD, and IT2 F-VIKOR methods as an integrated framework. The DEMATEL-QFD component of the proposed hybrid method provides a practical and effective approach for performing customer-oriented criteria weighting in situations where customer satisfaction is directly involved in the decision-making process. The IT2 F-VIKOR method, on the other hand, has been applied to evaluate and rank suppliers based on each selection criterion. The complete approach, which is being proposed for the first time, is summarized below in a four-stage structure:

4.1. Stage I: Identification of Customer, Green Supplier Selection Requirements, and Alternatives

In this stage, a two-person expert committee was formed. Then, based on the literature review and the characteristics of the analyzed supplier companies, CRs and supplier selection criteria related to sustainable green factors were determined in collaboration with the expert committee. The customer criteria determined in this stage represent the answers to the “What” questions of the problem at hand. The green supplier selection criteria include all the criteria that need to be considered for ranking the candidate suppliers, i.e., all the CRs to be fulfilled, and these criteria represent the answers to the “HOW” questions of QFD in the addressed problem. Based on the literature review and the views and recommendations of the expert committee, the CRs, green supplier criteria, and the evaluated alternatives, along with their explanations, are provided in

Table 2. Customer requirements and green supplier criteria.

Customer Requirements (Customer Demands) (CRs)	Explanation
Long range (LR)	It is the maximum distance that an electric vehicle can travel on a single full charge.
Fast charging time (FCT)	It refers to the time required for the battery to reach a specific charge level.
Safety (S)	It refers to the level of protection the vehicle and battery provide to the user against physical hazards.
Environmental friendliness and recyclability (EFR)	It refers to the minimal environmental impact of the battery’s production, use, and disposal processes, as well as the inclusion of recyclable materials.
Low cost (LC)	It refers to the minimal impact of the battery on the vehicle’s price or ensuring that its total cost remains at an acceptable level.
Green Supplier Selection Criteria	Explanation
Carbon Footprint (CO2 Emissions) (CF)	It refers to the total greenhouse gas emissions (especially CO2) generated throughout the process from raw material extraction to production, transportation, and usage of the battery. Low emissions are crucial for reducing environmental impacts.
Waste Management and Recycling Rate (WMRR)	It refers to how much of the battery can be recycled when its lifespan ends and how environmentally friendly this process is. A high recycling rate reduces resource waste and environmental pollution.
Use of Toxic and Critical Materials (TCMU)	It refers to the amount and type of materials used in the battery that are harmful to the environment and human health (e.g., cobalt, lead, fluoride electrolytes) or are at risk in terms of sourcing. Reducing the use of such materials is important both environmentally and ethically.
Use of Green Energy (GEU)	It refers to whether renewable energy sources (such as solar, wind, etc.) are used in the battery production processes. The use of green energy significantly reduces the environmental impact of the production process.
Energy Efficiency and Lifetime Impact (EELI)	It refers to how efficiently the battery provides energy and the total environmental impact throughout its entire life cycle. Long-lasting and highly efficient batteries reduce resource usage and waste generation.

and

Table 3. The evaluated alternatives and the characteristics of the alternatives according to the green supplier criteria.

Abbreviation of the Alternatives	Battery Type/Criteria	Carbon Footprint (CO2 Emissions)	Recycling and Waste Management	Use of Toxic/Critical Materials	Use of Green Energy	Energy Efficiency and Lifetime Impact
A1	NMC (Li-ion)	High Intensive mining and processing process	Medium It has existing infrastructure but is costly	High Contains Cobalt and Nickel	Low-Medium Typically produced using fossil energy	Medium-High Good range but limited cycle life
A2	LFP (LiFePO4)	Medium Simpler structure, production with lower energy	High Easy and safe recycling	Low Does not contain critical materials	Medium-High Production is increasing with solar energy	High Long cycle life and stable performance
A3	Solid-State	Medium-High Its production is complex; however, there is potential for cost reduction	Medium As an emerging system, it encompasses both advantages and disadvantages	Low-Medium It may vary depending on the material selection	High The objective is to increase the use of clean energy in production processes in the future.	Very High Very long lifespan and high energy density
A4	Li-S (Lithium Sulfur)	Medium Lightweight material but inefficient production	Low Sulfur-based structure poses challenges in recycling	Low Does not contain critical materials	Low In R&D-focused production, conventional energy is typically used	Medium High capacity but short lifespan
A5	Sodium-Ion	Low Abundant resources, low-temperature production	High Easy recycling due to its simple structure	Low Does not contain toxic materials	High Low temperature and production are easy with green energy	Medium Low energy density, but durable structures are possible

below.

4.2. Stage II: Weighting of Customer and Green Supplier Selection Criteria

In this stage, the DEMATEL method is used to establish the causal and perceptual relationship between the CRs and the green supplier selection criteria, assigning overall weights. Subsequently, the normalized values of the CRs, obtained through the DEMATEL method in the previous stage, are considered as the CRs’ weights to be used later in the QFD-based analysis. These weights are then used to weight the green supplier selection criteria in the QFD. The QFD model is defined as follows by [21]: QFD transformations are typically represented by a matrix known as the House of Quality (HoQ). This matrix expresses the relationship between the CRs (WHATs) and the green supplier selection criteria (HOWs), containing the following elements. Here, (A) the matrix of WHATs, (B) the importance (weights) of the WHATs, (C) the matrix of HOWs (green supplier selection criteria), (D) the relationship matrix between WHATs and HOWs, (E) the matrix to relate HOWs, (F) the relative importance or weights of HOWs (the weights of green supplier selection criteria), and (G) it represents the competitive evaluation matrix [21]. The working principle of QFD is provided in Figure 3.

4.3. Stage III: Weighting of Suppliers According to Each Green Supplier Selection Criterion

In this stage, the expert committee evaluates the alternatives according to each green supplier selection criterion in order to determine the performance score of the candidate suppliers based on green criteria. For this, the expert committee will assess each candidate supplier separately according to the green supplier selection criteria using interval Type-2 triangular fuzzy numbers.

4.4. Stage IV: Ranking Alternatives Using the IT2 F-VIKOR Method

In this phase, the IT2 F-VIKOR method is applied to rank the suppliers. To implement this method, both the weights of all green supplier selection criteria from the second phase and the priority values of each candidate supplier according to each green supplier selection criterion obtained in the third phase will be used to evaluate and rank the candidate suppliers.

In summary, the proposed hybrid DEMATEL–QFD–IT2 F-VIKOR approach offers a comprehensive and structured framework for green supplier evaluation:

• Integrating both customer requirements and sustainability criteria in a unified decision model;
• Capturing uncertainty and vagueness in expert judgments through interval Type-2 fuzzy logic;
• Establishing causal relationships among customer needs via DEMATEL;
• Mapping customer needs to technical criteria using QFD;
• Ranking supplier alternatives with IT2 F-VIKOR to reflect real-world complexity and ambiguity.

This integrated framework enhances the objectivity, robustness, and applicability of green supplier selection decisions, particularly in high-stakes industries such as electric vehicles.

5. Application of the Proposed Method

In this section, the steps of the DEMATEL-QFD-IT2 F-VIKOR hybrid method are applied to a supplier selection problem. The application process consists of three stages: In the first stage, the criteria and alternatives related to the problem are defined. Then, a committee consisting of experts is formed, and the evaluation process begins. During this stage, the criteria and alternatives are assessed by the experts in accordance with the purpose of the problem. In the third stage, based on the experts’ evaluations, the method(s) applied result in the selection and ranking of the alternatives.

Based on expert opinions and a literature review, five CR criteria, five sustainable green supplier criteria, and five alternatives have been identified. In this study, all five CRs defined are considered vital, and therefore, identifying the most important requirement of the evaluation system and measuring the relationships between them is essential. For this reason, the DEMATEL method was used to measure the causal relationships among the CRs. As explained in the DEMATEL steps in Section 3.5, the integer scale is used to determine the relationships between different CRs. After the relationships are measured, the initial direct relationship matrix (A) is created, as shown in

Table 4. The initial basic relationship matrix (A).

CRs	LR	FCT	S	EFR	LC
LR	0	1	2	2	3
FCT	2	0	1	1	3
S	3	2	0	1	2
EFR	3	3	3	0	3
LC	1	1	1	2	0

. Matrix A is a 5 × 5 matrix obtained through bidirectional comparisons, representing the effects and directions between the CRs.

The normalized direct-relation matrix (X) is calculated from the A matrix in Table 4, as presented in

Table 5. The normalized direct relationship matrix (X) for CRs.

CRs	LR	FCT	S	EFR	LC
LR	0.0000	0.0833	0.1667	0.1667	0.2500
FCT	0.1667	0.0000	0.0833	0.0833	0.2500
S	0.2500	0.1667	0.0000	0.0833	0.1667
EFR	0.2500	0.2500	0.2500	0.0000	0.2500
LC	0.0833	0.0833	0.0833	0.1667	0.0000

.

Subsequently, the total relation matrix (T) is derived from Table 5, as illustrated in

Table 6. The total impact matrix (T) for CRs. (t_ij* > 0.3704).

CRs	LR	FCT	S	EFR	LC
LR	0.2810	0.3055	0.3752 *	0.3619	0.5497 *
FCT	0.3732 *	0.1844	0.2693	0.2668	0.5010 *
S	0.4791 *	0.3575	0.2233	0.2926	0.4862 *
EFR	0.6029 *	0.5221 *	0.5279 *	0.3038	0.6952 *
LC	0.2782	0.2409	0.2436	0.2941	0.2439

(* Represents significant relationships between criteria. That is, it indicates the significant (direct and indirect) influence of criterion ${CR}_i$ on criterion ${CR}_i$).

.

Now, the row and column totals, represented by the D and R vectors, are calculated as shown in

Table 7. The calculation of D and R vectors.

CRs	Dk (Influencing)	Rk (Influenced)
LR	1.8733	2.0144
FCT	1.5947	1.6104
S	1.8387	1.6393
EFR	2.6519	1.5192
LC	1.3007	2.4760

.

Using Table 7, the total and net impact values (D + R) and (D − R) for each CR are calculated as shown in

Table 8. The total and net impact values for each CRs.

CRs	D + R	D − R	Group
LR	3.8877	−0.1411	Conclusion
FCT	3.2051	−0.0157	Conclusion
S	3.4780	0.1994	Reason
EFR	4.1711	1.1327	Reason
LC	3.7767	−1.1753	Conclusion

.

The values of (D + R) and (D − R) in Table 8 represent the degree of total impact levels and, respectively, the degree of net impact levels. Positive values here indicate that they will affect other requirements more. Table 8 shows that the EFR customer demand has the highest impact level, followed by the LR demand. The causal diagram of DEMATEL for CRs.

Looking at the causal diagram in Figure 4, it can be seen that the CRs are visually divided into cause and effect groups. The causal group is formed by S and EFR, while the effect group is formed by LR, FCT, and LC. It is credible that the requirements of S and EFR are the main driving factors for LR, FCT, and LC. Among these five CRs, EFR is considered the most important value because it has the maximum D + R value and thus has the strongest relationship intensity with the others. Additionally, EFR is also the most convincing factor due to its highest D-R value. Therefore, EFR plays a significant role in the supplier evaluation problem and has the greatest impact on the others. On the other hand, LC, with the lowest (D − R) value, is the customer demand most affected by the other factors.

The threshold value (α) is calculated by taking the average of the elements in the T matrix using Equation (26). Here, the α value is calculated as 0.3704. The t_ij values in Table 6 represent the relationship between two CRs, and the relationships are compared with the cause-effect values t_ij^* value. For example, since $t_{13}$ (0.3752) > α (0.3704), the arrow in the diagram is drawn from LR to S as shown in Figure 5. The contextual relationships among the CRs are presented in Figure 5.

The weights of the CRs are calculated by normalizing the (D + R) values presented in Table 8 and are shown in

Table 9. Weights of the CRs.

CRs	LR	FCT	S	EFR	LC
Ağırlıklar	0.2099	0.1731	0.1878	0.2252	0.2039

. As can be seen from Table 9, EFR has the highest weight and the greatest impact among the other factors.

As shown in Table 9, among the CRs, the highest weight is assigned to the EFR criterion, indicating that it has the greatest overall impact on the system.

Following the calculation of the weights of the CRs, and in accordance with the QFD process (see Section 3.6), a central relationship matrix is constructed to illustrate the interactions and correlations between each pair of CRs and the green supplier selection criteria. This relationship matrix, presented in

Table 10. QFD model for green supplier selection problem.

HOWs (CRs)	WHATs (Green Supplier Selection Criteria)					Weights of CRs
	CF	WMRR	TCMU	GEU	EELI
LR	3	1	1	1	9	0.2099
FCT	1	1	1	1	6	0.1731
S	3	3	9	1	6	0.1878
EFR	9	9	3	6	6	0.2252
LC	3	3	6	3	3	0.2039
Absolute Importance Values	4.0047	3.2093	3.9722	2.5337	6.0174
Normalized Criterion Weights	0.2029	0.1626	0.2013	0.1284	0.3049

, is developed by the decision-making team based on the available data regarding green suppliers. Essentially, this step addresses how the CRs and the green supplier selection criteria interact and influence each other, based on expert evaluations. As shown in Table 10, values are assigned within the matrix to represent how well each green supplier selection criterion satisfies each CR. Using both the weights of the CRs and the expert assessments, the weights of each green supplier selection criterion are calculated. The normalized weights of all green supplier selection criteria are obtained and presented in Table 10. It is clearly observed that the EELI criterion emerges as the most critical green supplier evaluation criterion among the listed criteria.

After calculating the weights of the green supplier selection criteria using the QFD model, the IT2 F-VIKOR method will be employed to evaluate the alternatives based on each green supplier evaluation criterion.

Ranking of Alternatives Using IT2 VIKOR

In this section, the applicability of the IT2 F-VIKOR method to the battery selection problem in electric vehicles based on green criteria is demonstrated step by step. The objective of the decision problem is to select and rank five alternatives (A1, A2, A3, A4, A5) (see Table 3) under five green criteria (CF, WMRR, TCMU, GEU, EELI) (see Table 2), which are defined by the expert committee. Here,

CF: Carbon footprint (CO₂ Emissions) (g CO₂/kWh) (to be minimized) (1–10 points).

WMRR: Waste management and recycling rate (to be maximized) (1–10 points).

TCMU: Use of toxic and critical materials (Yıl) (to be minimized) (1–10 points).

GEU: Use of green energy (to be maximized) (1–10 points).

EELI: Energy efficiency and lifetime impact (to be maximized) (1–10 points).

Here, 1 represents the lowest—10: Represents the highest score.

The green supplier criteria weights $\left(w_j\right)$ obtained from the DEMATEL-QFD hybrid method were presented in Table 10. Now, let us explain step by step the application of the IT2 F-VIKOR method to the alternative selection problem at hand:

Step 1: The decision matrix creation. In this step, the decision matrix for evaluating the five alternatives according to the criteria, formed by a two-person expert committee, is provided in

Table 11. The triangular fuzzy numbers that determine the importance levels of the criteria.

Alternatives	Criteria
	CF (Minimize) (0–10)	WMRR (Maximize) (0–10)	TCMU (Minimize) (0–10)	GEU (Maximize) (0–10)	EELI (Maximize) (0–10)
A1	(2, 3.5, 5; 1, 1) (2.5, 3.5, 4.5; 0.8, 0.8)	(4, 5.5, 7; 1, 1) (4.4, 5.5, 6.6; 0.8, 0.8)	(1, 2.5, 4; 1, 1) (1.3, 2.5, 3.7; 0.8, 0.8)	(4, 5, 6; 1, 1) (4.2, 5, 5.8; 0.8, 0.8)	(5, 6, 7; 1, 1) (5.2, 6, 6.8;0.8, 0.8)
A2	(5, 6.5, 8; 1, 1) (5.4, 6.5, 7.6; 0.8, 0.8)	(7, 8.5, 10; 1, 1) (7.3, 9, 9.7; 0.8, 0.8)	(8, 9, 10; 1, 1) (8.4, 9, 9.6; 0.8, 0.8)	(5, 7, 8; 1, 1) (5.6, 7, 7.4; 0.8, 0.8)	(7, 9, 10; 1, 1) (7.3, 9, 9.7; 0.8, 0.8)
A3	(5, 6, 7; 1, 1) (5.5, 6, 6.5; 0.8, 0.8)	(4.5, 5.5, 6.5; 1, 1) (5, 5.5, 6; 0.8, 0.8)	(4.5, 6, 7.5; 1, 1) (5, 6, 7; 0.8, 0.8)	(7, 9, 10; 1, 1) (7.6, 9, 9.4; 0.8, 0.8)	(8, 9, 10; 1, 1) (8.3, 9, 9.7; 0.8, 0.8)
A4	(5.5, 6.4, 8; 1, 1) (6, 6.4, 7.5; 0.8, 0.8)	(3, 4, 5.5; 1, 1) (3.3, 4, 5.2; 0.8, 0.8)	(6, 7.5, 9; 1, 1) (6.6, 7.5, 8.4; 0.8, 0.8)	(3, 4, 5; 1, 1) (3.4, 4, 4.6; 0.8, 0.8)	(2, 3.5, 5;1, 1) (2.5, 4, 4.5; 0.8, 0.8)
A5	(8, 9, 10; 1, 1) (8.5, 9, 9.5; 0.8, 0.8)	(9, 9.5, 10; 1, 1) (9.2, 9.5, 9.8; 0.8, 0.8)	(9, 9.5, 10; 1, 1) (9.3, 9.5, 9.7; 0.8, 0.8)	(9, 9.5, 10; 1, 1) (9.2, 9.5, 9.8; 0.8, 0.8)	(5, 6, 7; 1, 1) (5.5, 6, 6.5; 0.8, 0.8)

. Interval Type-2 triangular fuzzy numbers were used to construct the decision matrix.

Step 2: Calculation of ideal (positive) and anti-ideal (negative) solutions. In this step, the ideal solution ${\widetilde{\stackrel{~}{f}}}_j^{\ast }$ and the anti-ideal solution ${\widetilde{\stackrel{~}{f}}}_j^{-}$ for each criterion are calculated. The ideal solution ${\widetilde{\stackrel{~}{f}}}_j^{\ast }$ is calculated using Equation (12), and the anti-ideal solution ${\widetilde{\stackrel{~}{f}}}_j^{-}$ is calculated using Equation (13). The calculated values are presented in

Table 12. Best $\left({\widetilde{\stackrel{~}{f}}}_j^{\ast }\right)$ and worst $\left({\widetilde{\stackrel{~}{f}}}_j^{-}\right)$ values calculated for each criterion.

Criterion	$\mathbf{Best} \mathsf{\left(}{\widetilde{\stackrel{~}{\mathbf{f}}}}_{\mathbf{j}}^{\mathsf{\ast }}\mathsf{\right)}$	$\mathbf{W}\mathbf{o}\mathbf{r}\mathbf{s}\mathbf{t} \mathsf{\left(}{\widetilde{\stackrel{~}{\mathbf{f}}}}_{\mathbf{j}}^{-}\mathsf{\right)}$
CF (Minimize)	(2, 3.5, 5; 1, 1) (2.5, 3.5, 4.5; 0.8, 0.8)	(8, 9, 10; 1, 1) (8.5, 9, 9.5; 0.8, 0.8)
WMRR (Maximize)	(9, 9.5, 10; 1, 1) (9.2, 9.5, 9.8; 0.8, 0.8)	(3, 4, 5.5; 1, 1) (3.3, 4, 5.2; 0.8, 0.8)
TCMU (Minimize)	(1, 2.5, 4; 1, 1) (1.3, 2.5, 3.7; 0.8, 0.8)	(9, 9.5, 10; 1, 1) (9.3, 9.5, 9.7; 0.8, 0.8)
GEU (Maximize)	(9, 9.5, 10; 1, 1) (9.2, 9.5, 9.8; 0.8, 0.8)	(3, 4, 5; 1, 1) (3.4, 4, 4.6; 0.8, 0.8)
EELI (Maximize)	(8, 9, 10; 1, 1) (8.3, 9, 9.7; 0.8, 0.8)	(2, 3.5, 5; 1, 1) (2.5, 4, 4.5; 0.8, 0.8

.

Step 3: The calculation of normalized fuzzy values. In this step, fuzzy ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values, which represent the deviation measures for each alternative, will be calculated using Equations (14) and (15). Since the detailed calculations are quite lengthy, only the calculation process for alternative A1 will be performed. The fuzzy ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values for the other alternatives are calculated similarly. Now, let us calculate the preliminary ${\widetilde{\stackrel{~}{w}}}_j\times {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}$ values for alternative A1 based on the fuzzy ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values.

For alternative A1, the upper membership values for CF (the criterion to be minimized) are as follows:

$$\begin{gathered} {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\tilde{f}}_j^{-}}}={\displaystyle \frac{\left(2, 3.5, 5;1, 1\right)-\left(2, 3.5, 5;1, 1\right)}{\left(2, 3.5, 5;1, 1\right)-(8, 9, 10;1, 1)}}={\displaystyle \frac{(0, 0, 0;1, 1)}{(-6,-5.5,-5;1, 1)}} \\ =(0, 0, 0;1, 1) \end{gathered}$$

Now, if we multiply the value calculated above by the weight $\left(w_j\right)$ (see Table 10):

$${\widetilde{\stackrel{~}{w}}}_j\ast {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}=\left(0.2029\right)\times \left(0, 0, 0;1, 1\right)=(0, 0, 0;1, 1)$$

For alternative A1, the lower membership values for CF (the criterion to be minimized) are as follows:

$${\displaystyle \frac{{\tilde{f}}_j^{\ast }-{\tilde{x}}_{ij}}{{\tilde{f}}_j^{\ast }-{\tilde{f}}_j^{-}}}={\displaystyle \frac{\left(2.5, 3.5.4.5;0.8, 0.8\right)-\left(2.5, 3.5.4.5;0.8, 0.8\right)}{\left(2.5, 3.5.4.5;0.8, 0.8\right)-(8.5, 9,9.5;0.8, 0.8)}}={\displaystyle \frac{(0, 0, 0;0.8, 0.8)}{(-6,-5.5,-5;0.8, 0.8)}}=(0, 0, 0;0.8, 0.8)$$

Now, if we multiply the value calculated above by the weight $\left(w_j\right)$ (see Table 10):

$${\widetilde{\stackrel{~}{w}}}_j\ast {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}=\left(0.2029\right)\times \left(0, 0, 0;0.8, 0.8\right)=(0, 0, 0;0.8, 0.8)$$

Thus, the interval Type-2 fuzzy membership value calculated for CF of alternative A1 is found to be $(0, 0, 0;1, 1) (0, 0, 0;0.8, 0.8)$.

For alternative A1, the upper membership function for WMRR (criterion to be maximized) is as follows:

$$\begin{gathered} {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}={\displaystyle \frac{\left(9, 9.5, 10;1, 1\right)-(4, 5.5, 7;1, 1)}{\left(9, 9.5, 10;1, 1\right)-(3, 4, 5.5;1, 1)}}={\displaystyle \frac{(5, 4, 3;1, 1)}{(6, 5.5, 4.5;1, 1)}} \\ =(0.8333, 0.7273, 0.6667;1, 1) \end{gathered}$$

(27)

Now, if we multiply the value calculated above by the weight $\left(w_j\right)$ (see Table 10), it is calculated as

$$\begin{gathered} {\tilde{w}}_j\times {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}=\left(0.1626\right)\times \left(0.8333, 0.7273, 0.6667;1, 1\right) \\ =\left(0.1355, 0.1183, 0.1084;1, 1\right) \end{gathered}$$

For the A1 alternative, the lower membership function for WMRR (the criterion to be maximized) is calculated as follows:

$${\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}={\displaystyle \frac{\left(9.2, 9.5, 9.8;0.8, 0.8\right)-(4.4,5.5,6.6;0.8, 0.8)}{\left(9.2, 9.5, 9.8;0.8, 0.8\right)-(3.3, 4,5.2;0.8, 0.8)}}={\displaystyle \frac{(4.8, 4.3.2;0.8, 0.8)}{(5.9, 5.5, 4.6;0.8, 0.8)}}=(0.8136, 0.7273, 0.6957;0.8, 0.8)$$

Now, if we multiply the value calculated above by the weight $\left(w_j\right)$ (see Table 10),

$${\widetilde{\stackrel{~}{w}}}_j\times {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}=\left(0.1626\right)\times (0.8136, 0.7273, 0.6957;0.8, 0.8)=(0.1323, 0.1183, 0.1131;0.8, 0.8)$$

Thus, the interval Type-2 fuzzy membership value calculated for WMRR of the A1 alternative is computed as $\left(0.1355, 0.1183, 0.1084;1, 1\right)(0.1323, 0.1183, 0.1131;0.8, 0.8)$. Similarly, the calculated interval Type-2 fuzzy upper and lower membership values for the TCMU, GEU, and EELI criteria are provided below:

The calculated interval Type-2 fuzzy membership value for the TCMU criterion: $(0, 0, 0;1, 1) (0, 0, 0;0.8, 0.8)$.

The calculated interval Type-2 fuzzy membership value for the GEU criterion: (0.1070, 0.1051, 0.1027; 1, 1) (0.1107, 0.1051, 0.0988; $0.8, 0.8$).

The calculated interval Type-2 fuzzy membership value for the EELI criterion: (0.1525, 0.1663, 0.1829; 1, 1) (0.1630, 0.1829, 0.1700; $0.8, 0.8$).

Similarly, the preliminary ${\widetilde{\stackrel{~}{w}}}_j\times {\displaystyle \frac{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{x}}}_{ij}}{{\widetilde{\stackrel{~}{f}}}_j^{\ast }-{\widetilde{\stackrel{~}{f}}}_j^{-}}}$ values for the fuzzy ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values of the remaining alternatives have been calculated through similar procedures as described above, and the calculated preliminary interval Type-2 fuzzy membership values for ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ are presented in

Table 13. Interval Type-2 fuzzy membership values calculated for the prior ${\tilde{S}}_i$ and ${\tilde{R}}_i$ values of each alternative.

Alternatives	CF (Minimize)	WMRR (Maximize)	TCMU (Minimize)	GEU (Maximize)	EELI (Maximize)
A1	(0, 0, 0; 1, 1) (0, 0, 0; 0.8, 0.8)	(0.1355, 0.1183, 0.1084; 1, 1) (0.1323, 0.1183, 0.1131; 0.8, 0.8)	(0, 0, 0; 1, 1) (0, 0, 0; 0.8, 0.8)	(0.1070, 0.1051, 0.1027; 1, 1) (0.1107, 0.1051, 0.0988; 0.8, 0.8)	(0.1525, 0.1663, 0.1829; 1, 1) (0.1630, 0.1829, 0.1700; 0.8, 0.8)
A2	(0.1015, 0.1107, 0.1217; 1, 1) (0.0981, 0.1107, 0.1258; 0.8, 0.8)	(0.0542, 0.0296, 0.0000; 1, 1) (0.0524, 0.0148, 0.0035; 0.8, 0.8)	(0.1761, 0.1869, 0.2013; 1, 1) (0.1787, 0.1869, 0.1979; 0.8, 0.8)	(0.0856, 0.0584, 0.0514; 1, 1) (0.0797, 0.0584, 0.0593; 0.8, 0.8)	(0.0508, 0.0000, 0.0000; 1, 1) (0.0526, 0.0000, 0.0000; 0.8, 0.8)
A3	(0.1015, 0.0922, 0.0812; 1, 1) (0.1015, 0.0922, 0.0812; 0.8, 0.8)	(0.1220, 0.1183, 0.1138; 1, 1) (0.1157, 0.1183, 0.1343; 0.8, 0.8)	(0.0881, 0.1007, 0.1174; 1, 1) (0.0931, 0.1007, 0.1107; 0.8, 0.8)	(0.0428, 0.0117, 0.0000; 1, 1) (0.0354, 0.0117, 0.0099; 0.8, 0.8)	(0, 0, 0; 1, 1) (0, 0, 0; 0.8, 0.8)
A4	(0.2367, 0.2213, 0.2029; 1, 1) (0.2266, 0.2213, 0.2151; 0.8, 0.8)	(0.1626, 0.1626, 0.1463; 1, 1) (0.1626, 0.1626, 0.1626; 0.8, 0.8)	(0.1258, 0.1438, 0.1678; 1, 1) (0.1334, 0.1438, 0.1577; 0.8, 0.8)	(0.1284, 0.1284, 0.1284; 1, 1) (0.1284, 0.1284, 0.1284; 0.8, 0.8)	(0.3049, 0.3049, 0.3049; 1, 1) (0.3049, 0.3049, 0.3049; 0.8, 0.8)
A5	(0.2029, 0. 2029, 0. 2029; 1, 1) (0.1961, 0.2029, 0.2110; 0.8, 0.8)	(0, 0, 0; 1, 1) (0, 0, 0; 0.8, 0.8)	(0.2013, 0.2013, 0.2013; 1, 1) (0.2013, 0.2013, 0.2013; 0.8, 0.8)	(0, 0, 0; 1, 1) (0, 0, 0; 0.8, 0.8)	(0.1525, 0.1663, 0.1839; 1, 1) (0.1472, 0.1829, 0.1876; 0.8, 0.8)

.

Now, based on Table 13, the final ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values for each alternative have been calculated (according to Equations (14) and (15)). The calculated final ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values are presented in

Table 14. Interval Type-2 fuzzy ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values calculated for each alternative.

Alternatives	${\widetilde{\stackrel{~}{\mathit{S}}}}_{\mathit{i}}$ (The Sum of All Criteria)	${\widetilde{\stackrel{~}{\mathit{R}}}}_{\mathit{i}}$ (The Largest Criterion Value)
A1	(0.3950, 0.3897, 0.3940; 1, 1) (0.4060, 0.4063, 0.3819; 0.8, 0.8)	(0.1525, 0.1663, 0.1829; 1, 1) (0.1630, 0.1829, 0.1700; 0.8, 0.8)
A2	(0.4682, 0.3856, 0.3744; 1, 1) (0.4615, 0.3708, 0.3865; 0.8, 0.8)	(0.1761, 0.1869, 0.2013; 1, 1) (0.1787, 0.1869, 0.1979; 0.8, 0.8)
A3	(0.3544, 0.3229, 0.3124; 1, 1) (0.3457, 0.3229, 0.3361; 0.8, 0.8)	(0.1220, 0.1183, 0.1174; 1, 1) (0.1157, 0.1183, 0.1343; 0.8, 0.8)
A4	(0.9584, 0.9610, 0.9503; 1, 1) (0.9559, 0.9610, 0.9684; 0.8, 0.8)	(0.3049, 0.3049, 0.3049; 1, 1) (0.3049, 0.3049, 0.3049; 0.8, 0.8)
A5	(0.5567, 0.5705, 0.5881; 1, 1) (0.5446, 0.5871, 0.5999; 0.8, 0.8)	(0.2029, 0.2029, 0.2029; 1, 1) (0.2013, 0.2029, 0.2110; 0.8, 0.8)

.

Step 4: Calculation of the Fuzzy VIKOR Index (${\widetilde{\stackrel{~}{Q}}}_i$). In this step, the fuzzy VIKOR score (${\widetilde{\stackrel{~}{Q}}}_i$) for each alternative will be calculated using Equation (16). As an example, the fuzzy VIKOR index value for alternative A1 has been calculated. Similar operations are performed for the other alternatives. The fuzzy VIKOR index values for all alternatives are presented in

Table 15. Fuzzy VIKOR index (${\widetilde{\stackrel{~}{Q}}}_i$) values calculated for the alternative.

Alternative	$\mathbf{VIKOR} \mathbf{Index} ({\tilde{\mathit{Q}}}_{\mathit{i}}$)
A1	(0.1170, 0.1810, 0.2386;1, 1) (0.1744, 0.2384, 0.1408;0.8, 0.8)
A2	(0.2421, 0.2329, 0.2723;1, 1) (0.2614, 0.2213, 0.2263;0.8, 0.8)
A3	(0.0000, 0.0000, 0.00000;1, 1) (0.0000, 0.0000, 0.0000;0.8, 0.8)
A4	(1.0000, 1.0000, 1.00000;1, 1) (1.0000, 1.0000, 1.0000;0.8, 0.8)
A5	(0.3886, 0.4207, 0.4441;1, 1) (0.3892, 0.4337, 0.4334;0.8, 0.8)
$v=0.5$ has been taken

. Now, let us calculate the fuzzy VIKOR index value (${\widetilde{\stackrel{~}{Q}}}_i$) for alternative A1:

The formula used to calculate the final decision score ${\widetilde{\stackrel{~}{Q}}}_i$ in the IT2 F-VIKOR method is presented below.

$${\widetilde{\stackrel{~}{Q}}}_i=v{\displaystyle \frac{{\widetilde{\stackrel{~}{S}}}_i-{\widetilde{\stackrel{~}{S}}}^{\ast }}{{\widetilde{\stackrel{~}{S}}}^{-}-{\widetilde{\stackrel{~}{S}}}^{\ast }}}+\left(1-v\right){\displaystyle \frac{{\widetilde{\stackrel{~}{R}}}_i-{\widetilde{\stackrel{~}{R}}}^{\ast }}{{\widetilde{\stackrel{~}{R}}}^{-}-{\widetilde{\stackrel{~}{R}}}^{\ast }}}$$

Here,

${\widetilde{\stackrel{~}{S}}}_i$: The total disadvantage of the alternative; ${\widetilde{\stackrel{~}{R}}}_i$: the worst criterion performance of the alternative.

${\widetilde{\stackrel{~}{S}}}^{\ast }$: $\min {\tilde{S}}_i$, ${\widetilde{\stackrel{~}{S}}}^{-}$: $\max {\widetilde{\stackrel{~}{S}}}_i$, ${\widetilde{\stackrel{~}{R}}}^{\ast }$: $\min {\widetilde{\stackrel{~}{R}}}_i$, ${\widetilde{\stackrel{~}{R}}}^{-}$: $\max {\widetilde{\stackrel{~}{R}}}_i$, $v$: the compromise coefficient (commonly taken as 0.5)

Based on Table 14, the best and worst values for each alternative and criterion are provided below:

$$\begin{array}{l}{\widetilde{\stackrel{~}{S}}}_i={\widetilde{\stackrel{~}{S}}}_1=(0.3950,0.3987,0.3940;1,1)(0.4060,0.4063,0.3819;0.8,0.8),\\ {\widetilde{\stackrel{~}{R}}}_i={\widetilde{\stackrel{~}{R}}}_1=(0.1525,0.1663,0.1829;1,1)(0.1630,0.1829,0.1700;0.8,0.8)\\ {\widetilde{\stackrel{~}{S}}}^{\ast }=\min \left({\widetilde{\stackrel{~}{S}}}_i\right)=(0.3544,0.3229,0.3124;1,1)(0.3457,0.3229,0.3361;0.8,0.8),\\ {\widetilde{\stackrel{~}{S}}}^{-}=\max \left({\widetilde{\stackrel{~}{S}}}_i\right)=(0.9584, 0.9610, 0.9503; 1, 1)(0.9559, 0.9610, 0.9684; 0.8,0.8)\\ {\widetilde{\stackrel{~}{R}}}^{\ast }=\min \left({\widetilde{\stackrel{~}{R}}}_i\right)=(0.1220,0.1183,0.1174;1,1)(0.1157,0.1183,0.1343;0.8,0.8),\\ {\widetilde{\stackrel{~}{R}}}^{-}=\max \left({\widetilde{\stackrel{~}{R}}}_i\right)=(0.3049,0.3046,0.3049;1,1)(0.3049,0.3049,0.3049;0.8,0.8)\end{array}$$

Calculation of ${\widetilde{\stackrel{~}{Q}}}_i$ for Alternative A1:

The first term:

$$\begin{gathered} {\displaystyle \frac{{\tilde{S}}_i-{\tilde{S}}^{\ast }}{{\tilde{S}}^{-}-{\tilde{S}}^{\ast }}}={\displaystyle \frac{(0.3950,0.3987,0.3940;1,1)(0.4060,0.4063,0.3819;0.8,0.8)-(0.3544,0.3229,0.3124;1,1)(0.3457,0.3229,0.3361;0.8,0.8)}{(0.9584,0.9610,0.9503;1,1)(0.9559,0.9610,0.9684;0.8,0.8)-(0.3544,0.3229,0.3124;1,1)(0.3457,0.3229,0.3361;0.8,0.8)}} \\ ={\displaystyle \frac{\left(0.0406,0.0668,0.0816;1,1\right)\left(0.0603,0.0834,0.0458;0.8,0.8\right)}{\left(0.6040,0.6381,0.6379;1,1\right)\left(0.6102,0.6381,0.6323;0.8,0.8\right)}} \\ =(0.0672,0.1047,0.1279;1,1)(0.0988,0.1307,0.0724;0.8,0.8) \end{gathered}$$

Now, let us multiply the calculated first term by the weight coefficient $v$:

$$\begin{array}{l}0.5\times (0.1668,0.2572,0.3493;1,1)(0.2500,0.3462,0.2093;0.8,0.8)\\ =(0.0834,0.1286,0.1747;1,1)(0.1250,0.1731,0.1046;0.8,0.8)\end{array}$$

The second term:

$$\begin{gathered} {\displaystyle \frac{{\tilde{R}}_i-{\tilde{R}}^{\ast }}{{\tilde{R}}^{-}-{\tilde{R}}^{\ast }}}={\displaystyle \frac{(0.1525, 0.1663, 0.1829;1, 1)(0.1630, 0.1829, 0.1700;0.8, 0.8)-(0.1220, 0.1183, 0.1174;1, 1)(0.1157, 0.1183, 0.1343;0.8, 0.8)}{(0.3049, 0.3049, 0.3049;1, 1)(0.3049, 0.3049, 0.3049; 0.8, 0.8)-(0.1220, 0.1183, 0.1174;1, 1)(0.1157, 0.1183, 0.1343;0.8, 0.8)}} \\ ={\displaystyle \frac{\left(0.0350,0.0480,0.0655;1,1\right)\left(0.0473,0.0646,0.0357;0.8,0.8\right)}{\left(0.1829,0.1866,0.1875;1,1\right)\left(0.1892,0.1866,0.1706;0.8,0.8\right)}} \\ =(0.1668,0.2572,0.3493;1,1)(0.2500,0.3462,0.2093;0.8,0.8) \end{gathered}$$

Now, let us multiply the calculated second term by the weight coefficient $(1-v)$:

$$\begin{array}{l}0.5\times (0.1668,0.2572,0.3493;1,1)(0.2500,0.3462,0.2093;0.8,0.8)\\ =(0.0834,0.1286,0.1747;1,1)(0.1250,0.1731,0.1046;0.8,0.8)\end{array}$$

As a result, the final ${\widetilde{\stackrel{~}{Q}}}_i$ value for the A1 alternative is calculated as follows:

$$\begin{array}{l}{\widetilde{\stackrel{~}{Q}}}_i=\left(0.0336, 0.0523, 0.0640;1, 1\right)\left(0.0494,0.0654,0.0362;0.8,0.8\right)+\left(0.0834, 0.1286, 0.1747;1, 1\right)\left(0.1250,0.1731,0.1046;0.8,0.8\right)\\ =\left(0.1170, 0.1810, 0.2386;1, 1\right)\left(0.1744,0.2384,0.1408;0.8,0.8\right).\end{array}$$

Similar calculations are carried out for the remaining alternatives in the same manner, and the computed fuzzy VIKOR index (${\widetilde{\stackrel{~}{Q}}}_i$) values are presented in Table 15.

Step 5: The defuzzification of the calculated fuzzy VIKOR scores. In this step, the IT2 F-VIKOR scores calculated from Table 15 will be converted into crisp values using Equations (17) and (18). Since the defuzzification process for all alternatives will be lengthy, we will demonstrate the defuzzification process only for the A1 alternative. Similar processes will be applied to the other alternatives as well. Now, let us go step by step through the defuzzification process for the A1 alternative:

Using Equation (17), the defuzzified crisp value for A1 is calculated using the formula ${\widetilde{\stackrel{~}{x}}}_1=\left({\displaystyle \frac{0.1170+0.1744}{2}},{\displaystyle \frac{0.1810+0.2384}{2}},{\displaystyle \frac{0.2386+0.1408}{2}}\right)=(0.1457, 0.2097, 0.1897;1, 1)$, and using Equation (18), the final defuzzified crisp value for A1 is computed as follows:

The defuzzified value is calculated as

$$Defuzzification Value=\left({\displaystyle \frac{0.1457+0.2097+0.1897}{3}}\right)=0.1817$$

Similar operations have been performed for alternatives A2, A3, A4, and A5, and the defuzzified values for all alternatives are presented in

Table 16. Defuzzified (crips) values calculated for each alternative.

Alternative	$\mathbf{The} \mathbf{Defuzzified} \mathsf{\left(}\mathbf{Crisp}\mathsf{\right)} \mathbf{Values} \mathbf{for} {\mathit{Q}}_{\mathit{i}}$
A1	0.1817
A2	0.2427
A3	0.0000
A4	1.0000
A5	0.4183

.

Here, according to Equation (19), in the VIKOR method, the minimum acceptable advantage value is used to determine whether one alternative is significantly better than the others.

$Q\left(A2\right)-Q\left(A1\right)\ge {\displaystyle \frac{1}{m-1}}\Rightarrow 0.1817-0.0000\ge {\displaystyle \frac{1}{5-1}} \Rightarrow 0.1817\ge 0.25.$ Since the acceptable advantage condition is not provided with the $0.25$ value, a compromise (acceptable stability condition) selection path should be followed instead of determining a single best alternative. For this purpose, the ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values will be examined. Because, in the compromise selection process, the alternatives should be analyzed not only based on their $Q_i$ values but also in terms of their ${\widetilde{\stackrel{~}{S}}}_i$ (group utility) and ${\widetilde{\stackrel{~}{R}}}_i$(individual regret) values. In this context, if the alternative with the best Qi value (i.e., Alternative A3) also ranks first in both ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$, it can be directly selected as the most appropriate alternative. If different alternatives outperform others across different criteria, a compromise decision becomes necessary. According to Table 16, Alternative A3 is identified as the best option, followed by Alternative A1 as the second best. According to Table 14, the ${\widetilde{\stackrel{~}{S}}}_i$ and ${\widetilde{\stackrel{~}{R}}}_i$ values of alternative A3 are better than those of alternative A1. Similarly, Table 14 also shows that alternative A3 has the best Si and Ri values among all alternatives, indicating the lowest values. Since A3 ranks first in both the ${\widetilde{\stackrel{~}{S}}}_i$ (group utility) and ${\widetilde{\stackrel{~}{R}}}_i$ (individual regret) criteria, the acceptable stability condition is satisfied. Alternative A1, on the other hand, should be considered as the second-best option due to the insufficient advantage gap.

6. Analysis of Result

This study addresses the battery selection problem for firms engaged in electric vehicle (EV) manufacturing. For the selection of alternative batteries, an expert committee consisting of two specialists in the field was initially formed. Based on the recommendations of the established expert committee and findings from the literature review, five criteria were selected for both customer requirements and green supplier selection, along with five alternative suppliers. The five candidate alternatives identified were evaluated against the determined customer and green supplier selection criteria using the novel hybrid DEMATEL-QFD-IT2 F-VIKOR approach proposed in this study. The DEMATEL method was initially employed to identify critical requirements among the five predetermined CRs and to measure their interrelationships. According to the results of the DEMATEL analysis applied to the CRs, the criterion of being environmentally friendly and recyclable has been identified as the most influential factor in battery selection. Subsequently, among the CRs, the criterion of long driving range was identified as having the second highest level of influence. The other criteria with the highest levels of influence among the CRs were found to be, in order, low cost, safety, and fast charging time. When examining the causal relationships among the CRs, it was observed that the criteria of being environmentally friendly and recyclable, along with safety, were the most influential causal factors affecting the other criteria (see Table 8). The criteria of long driving range, fast charging time, and low cost were identified as the most affected by other criteria (see Table 8). Additionally, according to Table 8, the criterion of being environmentally friendly and recyclable plays a significant role in the evaluation of alternatives and exerts the greatest influence on the other CRs. Similarly, the low-cost criterion was found to be the most affected customer requirement among all CRs.

In the proposed hybrid model, the QFD approach was employed to demonstrate the effects and relationships between each pair of CRs and the green supplier selection criteria. Here, the relationship matrix between CRs and green supplier selection criteria was developed by the decision-making team based on available information regarding green suppliers (see Table 10). As a result of the relationship matrix constructed by the expert committee, the calculated weight values for the green supplier criteria are presented in Table 10 and also illustrated graphically in Figure 6. Among the green supplier selection criteria, the EELI criterion was identified as the most important evaluation criterion (see Table 10 or Figure 6).

In the proposed hybrid model, following the calculation of the weights of customer requirements and green supplier selection criteria based on the DEMATEL-QFD methods, the IT2 F-VIKOR method was employed to select and rank the five considered alternatives.

In this method, the five considered alternatives were primarily evaluated based on the previously identified green supplier selection criteria: CF, WMRR, TCMU, GEU, and EELI. Using the IT2 F-VIKOR method, the ranking values of the five considered alternatives were calculated as follows: A1 = 0.1817, A2 = 0.2427, A3 = 0.0000, A4 = 1.0000, and A5 = 0.4183. Accordingly, the ranking performance values calculated for the alternatives, considering customer requirements and green supplier selection criteria, are presented in Figure 7. The performance rankings of the alternatives within the scope of this study are also provided in

Table 17. Selection and ranking performance of the alternatives.

Alternatives	A3	A1	A2	A5	A4
${\mathrm{Q}}_{\mathrm{i}}$ Values of Alternatives Calculated Using the DEMATEL-QFD-IT2 F-VIKOR Method	0.0000	0.1817	0.2427	0.4183	1.0000
Ranking Performance of Alternatives	1	2	3	4	5

.

The ranking performance scores of the alternatives, calculated using the proposed hybrid DEMATEL-QFD-IT2 F-VIKOR methodology, are presented in Table 17.

According to Table 17, when both customer requirements and green supplier selection criteria are considered together, it is acceptable for vehicle manufacturers or battery suppliers selecting batteries for electric vehicles to prioritize Alternative A3. Likewise, it would be appropriate for the same firms or suppliers to consider Alternative A1 as the second-best option. In contrast, based on customer requirements and green supplier criteria, Alternative A4 appears to be the least preferred choice for battery selection in electric vehicles.

6.1. Sensitivity Analysis of the Proposed Hybrid Method

To validate the reliability of the proposed hybrid approach under varying conditions, an extended sensitivity analysis was performed. This analysis systematically explored the effects of fluctuations in criteria weights, expert linguistic evaluations, and fuzzy parameter configurations (e.g., membership function spread and height). The results confirm that despite reasonable perturbations in input data and modeling assumptions, the final rankings of battery alternatives remained stable, with negligible shifts in decision outcomes. These findings highlight the robustness of the DEMATEL–QFD–IT2 F-VIKOR model, particularly in environments characterized by high levels of uncertainty and subjectivity. The changes in the behavior of the alternative ranking values obtained through the DEMATEL–QFD–IT2 F-VIKOR hybrid method in response to weight variations (±10%, +20%) are presented in Figure 8.

The radar charts shown above illustrate the changes in the alternative ranking values obtained using the DEMATEL-QFD-IT2 F-VIKOR method in response to weight variations (±10%, +20%). The radar chart in Figure 8 demonstrates the stability of the proposed decision model under varying criteria weight conditions. Despite the simulated perturbations of ±10% and +20%, the final ranking of battery suppliers remains largely consistent. In particular, alternatives A3 and A4 have maintained their top and bottom positions, respectively. The ranking positions of alternatives A1, A2, and A5 have generally been preserved despite small fluctuations. This demonstrates that the proposed DEMATEL–QFD–IT2 F-VIKOR hybrid framework validates its robustness and applicability in uncertain and dynamic decision-making environments. The sensitivity analysis results of the $Q_i$ values for the alternatives in response to changes in the criteria weights (±10% and +20%) are presented in

Table 18. Sensitivity analysis results of the alternatives based on changes in the criteria weights.

Alternatives	${\mathit{Q}}_{\mathit{i}}$ (Original)	${\mathit{Q}}_{\mathit{i}}$ (+10% Weight)	${\mathit{Q}}_{\mathit{i}}$ (−10% Weight)	${\mathit{Q}}_{\mathit{i}}$ (+20% Weight)
A1	0.1817	0.1902	0.1729	0.2001
A2	0.2427	0.2514	0.2345	0.2628
A3	0.0000	0.0000	0.0000	0.0000
A4	1.0000	0.9801	1.0123	0.9650
A5	0.4183	0.4102	0.4265	0.3958

.

6.2. Sensitivity Analysis of the Compromise Parameter (v) in IT2 F-VIKOR

In the IT2 F-VIKOR stage of the proposed hybrid model, the compromise coefficient $v$ was initially set to 0.5 to represent an equal balance between group consensus and individual regret, in accordance with conventional VIKOR practice. To ensure the robustness of this parameter choice, a sensitivity analysis was conducted by varying $v$ within a reasonable range (0.3, 0.7, and 0.9). The results indicated that the final ranking of alternatives remained largely unchanged, thereby validating the reliability of the proposed model against changes in the compromise strategy parameter. The sensitivity analysis of $Q_i$ values with respect to different compromise coefficients ($v$) in the IT2 F-VIKOR method is presented in Figure 9.

To evaluate the robustness of the compromise coefficient $v$ in the IT2 F-VIKOR method, a sensitivity analysis was conducted by varying $v$ across the values of 0.3, 0.5, 0.7, and 0.9. The $Q_i$ values of the alternatives were recalculated at each level, and the results are depicted in Figure 9. It is evident that the rankings of alternatives did not undergo significant changes, and particularly, the top-ranked (A3) and bottom-ranked (A4) alternatives remained consistent throughout. This confirms the stability and reliability of the proposed hybrid model under varying compromise strategies and supports the appropriateness of using $v=0.5$ as a balanced decision parameter.

6.3. Threshold (α) Sensitivity Analysis

In this study, the threshold $\left(\alpha \right)$ is calculated as the average of the total relation matrix (Equation (26)) to provide a reasonable and consistent cut-off point for the causal relationships. The choice of threshold is critical, as it determines the strength of the connections represented in the causal diagram. We chose this approach for its simplicity and to ensure that the threshold reflects the overall intensity of interrelationships among the criteria. To validate this choice, we conducted a sensitivity analysis, varying the threshold $\alpha$ within a reasonable range, and observed that the resulting causal diagram remained stable. This demonstrates the robustness of the proposed method and confirms that the threshold calculation does not lead to significant variations in the final results. The threshold $\left(\alpha \right)$ sensitivity analysis graph is presented in Figure 10.

7. Conclusions and Discussion

With the radical transformations occurring in environmental issues, public pressure and environmental logistics have become increasingly significant in the management of environmental and social aspects of business operations. In the context of electric vehicles, battery selection plays a critical role in terms of performance, safety, and environmental sustainability. In this process, both customer requirements and supplier criteria—particularly those related to green suppliers—must be taken into account. These criteria contribute not only to regulatory compliance but also to the sustainability goals and corporate social responsibility strategies of firms. Therefore, for electric vehicle manufacturers, the appropriate selection of batteries is not solely based on technical and economic performance, but also requires a holistic approach that minimizes environmental impacts and creates long-term value. Consequently, the use of integrated decision-making models that balance customer expectations with green supplier criteria has become essential.

A review of the literature reveals that many researchers have applied fuzzy MCDM methods to supplier selection problems in comparison with traditional MCDM methods. The findings indicate that fuzzy MCDM approaches generally provide more effective ranking outcomes than their conventional counterparts. Furthermore, the integration of fuzzy numbers with decision-making methods has been widely addressed by numerous scholars. However, combining fuzzy numbers with Type-2 fuzzy sets offers greater flexibility and accuracy in complex decision-making processes. In this study, the VIKOR method—one of the prominent MCDM techniques—was integrated with interval Type-2 fuzzy sets. The main advantage of the proposed method lies in incorporating expert knowledge into the traditional MCDM method, VIKOR, and successfully integrating it with Type-2 fuzzy numbers for application in the alternative selection problem. While many studies have addressed the impact of customer satisfaction indices and engineering characteristics on the supplier selection process, to the best of our knowledge, none have systematically examined how these variables interact with each other. This indicates a significant gap, particularly in the systematic analysis of sustainable green suppliers [22]. To fill this gap, it is essential to connect all organizational elements that contribute to performance measurement, including the green structures and infrastructures of sustainable green suppliers [23]. With the hybrid method proposed in this study, we aim to close both of these gaps by providing a systematic analysis of the interdependencies between customer variables and green supplier selection criteria.

The results obtained through the proposed hybrid DEMATEL-QFD-IT2 F-VIKOR methodology provide a more nuanced and integrated decision-making framework compared to traditional MCDA approaches. Unlike classical VIKOR or fuzzy TOPSIS, which often consider criteria in isolation and assume crisp or Type-1 fuzzy inputs, our study leverages the strength of causal analysis (via DEMATEL), the customer–supplier interaction structure (via QFD), and the advanced modeling capacity of Interval Type-2 fuzzy sets to handle higher-order uncertainties. In contrast to studies such as [24], which utilized fuzzy TOPSIS for green supplier selection, or [25], which applied ANP-based methods in sustainable sourcing, our integrated model not only captures the interdependencies between customer requirements but also embeds these into the evaluation of supplier criteria. Moreover, while [4] applied a classical VIKOR approach in electric vehicle component selection, their model did not address the layered interaction between environmental and customer-centric criteria, nor did it account for higher uncertainty levels in expert judgments. The proposed model’s ability to combine dual-layer evaluation (customer and green criteria) with interval Type-2 fuzzy logic enhances both the interpretability and reliability of the results. Thus, this study not only confirms the effectiveness of the hybrid approach in complex, real-world scenarios but also expands the methodological landscape by offering a scalable, uncertainty-resilient model that can be adapted to various sustainable supplier selection problems.

For the reasons mentioned above, in this study, we proposed a hybrid method for battery selection in electric vehicles, which considers both customer demands and sustainable green supplier selection criteria. Therefore, the primary aim of this study is to address the problem of evaluating and ranking green suppliers using an integrated formulation. With this integrated approach, we evaluated the interaction relationships and impact levels between customer demands and green supplier selection criteria. In addition, we determined the weights of customer demands and supplier selection criteria. For this purpose, we used the DEMATEL method to divide customer demands into cause-and-effect groups and create the basic relationship schema. Subsequently, we used the QFD model to construct a central relationship matrix in order to determine the degree of relationship between each pair of green supplier selection criteria and customer demands. Through this approach, we determined the weights of green supplier selection criteria for battery selection in electric vehicles using the QFD model. As a result of the DEMATEL-QFD methods, it was found that among the customer demands, the criterion of being environmentally friendly and recyclable has the highest impact on battery preferences. Following that, the criterion of long range was identified as the second most influential among the customer demands. Among the green supplier selection criteria, energy efficiency and lifetime impact were found to be the most important criteria, while the carbon footprint (CO₂ emissions) criterion ranked second. These results show that companies investing in environmentally friendly battery technologies will not only be more preferred by consumers but will also enhance their brand value. Furthermore, among customer demands, batteries with a long range are also identified as a second-tier critical requirement. This highlights the clear desire of users to use their vehicles for longer periods and with fewer charging sessions. In terms of supplier selection criteria, energy efficiency and lifetime impact have emerged as the most important factors. Batteries with high energy efficiency and low environmental impact throughout their lifecycle will not only ensure compliance with regulations but will also provide long-term benefits to companies by reducing the total cost of ownership. Additionally, the low carbon footprint (CO₂ emissions) of batteries during the production process has been identified as the second most important factor in achieving compliance with environmental regulations and corporate sustainability goals. Based on this study, the following recommendations can be made to electric vehicle manufacturers and battery suppliers:

Research and development processes should prioritize the use of recyclable materials and environmentally friendly manufacturing techniques.

In battery selection, products that offer long range while also having low environmental impact should be preferred.

In supplier evaluation criteria, environmental factors such as energy efficiency and lifetime carbon emissions should be given priority. Additionally, minimizing the environmental cost in relation to the total energy provided over the battery’s life cycle should be emphasized.

Collaborating with battery manufacturers that have a low carbon footprint (CO₂ emissions) will be critical for both environmental responsibility and customer satisfaction, and therefore, battery suppliers should place particular emphasis on this aspect.

In conclusion, electric vehicle manufacturers’ preference for environmentally friendly, long-range, and energy-efficient batteries will not only provide them with a competitive advantage but also contribute to achieving sustainable future goals.

Also, to ensure the alignment between management implications and research conclusions, we emphasize that the managerial recommendations in this study are derived directly from the findings and conclusions of the research. The implications are specifically aimed at guiding decision-making processes in the context of electric vehicle battery supplier selection, based on the results of our hybrid DEMATEL-QFD-IT2 F-VIKOR approach. The managerial recommendations are grounded in the case study and reflect the practical applicability of the proposed model, without extending beyond the scope of this study’s conclusions.

Although the effectiveness of the proposed approach is demonstrated through a single case study in this paper, future research will include additional case studies and comparative experiments with other established methods to validate the generalizability and advantages of the method. This broader validation will allow a more comprehensive understanding of the method’s robustness and its applicability across various real-world scenarios.

This study is limited to the selection of five alternative battery suppliers under five independent customer criteria and five independent green supplier selection criteria to demonstrate the applicability of the proposed method. In future studies, the effectiveness of the alternative selection problem can be enhanced by increasing the number of criteria and alternatives, allowing the applicability performance of the proposed method to be further tested. Furthermore, the hybrid method proposed by us can easily be applied in other fields as well. In fact, fuzzy rule bases can be incorporated into this hybrid method to achieve more precise and meaningful rankings for supplier selections. Additionally, the proposed hybrid method can be applied to alternative selection problems in combination with other MCDM methods, and its ranking performance in alternative selection problems can be compared with other MCDM methods.