Green Supplier Selection Using Fuzzy AHP, Fuzzy TOSIS, and Fuzzy WASPAS: A Case Study of the Moroccan Automotive Industry

Abstract

The green supplier selection presents numerous challenges, from initial assessment to final selection, which specialists in this field of supplier management often encounter. Among the techniques that aim to meet these challenges that are continually progressing is the creation and development of high-quality decision-making tools. In this study, the assessment of suppliers hinges on both traditional and environmental factors. A framework of multi-criteria decision-making (MCDM) is announced in order to appraise green supplier selection. This framework integrates Fuzzy Analytical Hierarchy Process (AHP) combined with two additional methods: WASPAS (“Weighted Aggregated Sum-Product Assessment”) and TOPSIS (“Technique for Order Preference by Similarity to Ideal Solution”). At the outset, there were five environmental criteria for green supplier selection: “Health and Safety”, “Sustainable Product Design”, “ISO 14001 Certification”, “Investment Recovery”, and “Green Packaging”, along with three conventional criteria including quality, price, and delivery, were pinpointed through a review of literature and expert input to facilitate the MCDM approach. As part of demonstrating the pertinency of the recommended framework, a practical case study of the automotive industry in Morocco is discussed. The results demonstrate that the utilized Fuzzy hybrid methods yield consistent rankings for green suppliers. Additionally, among the four green suppliers, number three obtained the best ranking, which indicates the robustness and performance of the chosen models. Furthermore, this study offers a unified platform for selecting green suppliers under a Fuzzy environment. Therefore, the chosen strategy and its analysis provide relevant data and information to decision-makers for the choice and selection of suppliers. It can also provide and help procurement departments and decision-makers to choose and select the efficient ecological supplier in the global market supply chain.

1. Introduction

The role of supplier selection is crucial in various industries and businesses [1]. It involves the manner of detecting, evaluating, and choosing the most suitable suppliers or vendors to provide goods or services that meet the organization’s requirements [2]. The selection of suppliers is an important aspect of supply chain management that has a direct bearing on an organization’s overall performance and success [3]. The integration of environmental issues into supply chain practices has become increasingly important due to growing concerns about sustainability, climate change, and environmental degradation [4]. This integration involves incorporating environmental considerations into various aspects of supply chain management to minimize environmental impact, enhance resource efficiency, and promote sustainable business practices. Planning, carrying out, and overseeing every step of the flow of goods and services—from locating raw materials to delivering the finished product to the final consumer—is the scope of supply chain management, or SCM [2,4,5,6,7,8,9,10,11]. In order to maximize effectiveness, save expenses, and improve customer satisfaction, coordinating and integrating operations across many roles and organizations is required [12]. Organizations usually integrate several programs and regulatory reviews into their supply chain management procedures to address these issues. According to [13], these programs are meant to guarantee increased efficiency and improve supplier performance.

The challenge of selecting the best green supplier based on a thorough evaluation of suppliers’ environmental performance has attracted international attention. Environmental performance, as used in practice, includes ecological processes in design, manufacturing, and transactions, in addition to environmental accomplishments. As a result, a panel of decision specialists should be assembled to make decisions, a variety of criteria should be taken into account, and the environmental performance of selected suppliers should be assessed. The solution of green supplier selection (GSS) issues has drawn the attention of numerous academics and professionals. The most well-known classification of models that solve GSS problems, which comes after literature reviews on the methodological categories of the problems, splits the models into three categories: multi-criteria decision-making (MCDM), artificial intelligence (AI), and mathematical programming (MP) [8]. An established methodological category called multi-criteria decision-making (MCDM) can help decision-makers (DMs) find a suitable solution that satisfies several conflicting criteria. MCDM models are the most widely utilized methodological category in the research that have already been conducted because selecting a GSS problem may be thought of as a conventional MCDM problem [14]. In order to evaluate the criteria, researchers created appropriate evaluative criteria, modeled the optimal weights for the pertinent criteria, asked decision experts to evaluate the criteria, and used MCDM approaches. Ref. [15] suggested using the (AHP) to measure the criterion for prioritization. The discrete-event modeling approach incorporates the AHP-derived weights and ranks patients based on waiting time, patient suffering, and health condition on a regular basis. In order to evaluate flood vulnerability in coastal cities, this study created an analytical network process (ANP) that was integrated into a geographic information system (GIS; shortened as ANP-GIS) [16]. This study suggests a Fuzzy TOPSIS-based framework for a Brazilian electronics company to choose environmentally friendly suppliers [17]. Ref. [18] used the ViseKriterijum-ska Optimizacija I Kompromisno Resenj (VIKOR) technique for ranking the threat-agent categories according to the experts’ assessment of risk. Ref. [19] working on Tramcar selection for environmentally friendly urban transportation via a modified WASPAS method based on Heronian operators. AHP and TOPSIS are the two most often used MCDM models for GSS problems; they have been taken up both separately and in combination to create integrated methods. The AHP method is notable for its capacity to manage qualitative and quantitative data and present results according to the criteria at every tier. In comparison to other MCDM techniques, TOPSIS has special qualities and benefits. By considering the largest distance from an identified negative ideal solution (NIS) and the smallest distance from an identified positive ideal solution (PIS), it is a popular and successful method for solving MCDM problems. This method may effectively express the overall influence of multiple factors, avoid subjectivity, and do away with the requirement for the objective function and passing exam. For GSS challenges, integrated techniques that combine AHP and TOPSIS have therefore been extensively used. In this context, AHP and WASPAS are rarely employed. Weighted Aggregated Sum-Product Assessment, or WASPAS, is a multi-criteria decision-making (MCDM) technique that attempts to assess and rank several options according to a number of criteria. This approach combines the weighted sum (Sum) and product (Product) aggregation of criteria. The benefit of the WASPAS method is its capacity to offer a thorough assessment of alternatives by taking into account both the advantages and disadvantages of each criterion while allowing for flexibility in the distribution of weights among criteria and the averaging of performances. Because of this, it can be a helpful tool when making decisions involving trade-offs between conflicting goals. The challenges of GSS in practice are characterized by complexity, uncertainty, and dynamicity because of the complexity of the closed-loop chain structure of the green supply chain, environmental effects, dynamic operations, uncertain external environment, and diversity in DMs’ cognitive styles and thinking models. We highlight some of the pertinent reasons for this study and point out certain shortcomings in the current integrated MCDM techniques for GSS issues.

Initially, the existing GSS problem criteria primarily include the direct addition of specific environmental components to conventional criteria, perhaps leading to an incomplete assessment of suppliers’ sustainable performance. Ref. [14] evaluated the accomplishments of sustainable suppliers by using traditional criteria price, delivery time, online ranking, rejection rate, and flexibility. In order to evaluate the accomplishments of green suppliers to the plastics industry, based on the GSCM literature, examines the activities and performances of the GSCM and takes into account the relationship between performance outcomes and green supply chain practices, such as environmental management, green purchasing, supplier and customer environmental collaboration, product recovery, reverse logistics, and design for the environment. Ref. [20] included green image and design as an environmental representation when evaluating possible suppliers’ green performance for an agricultural tool and machinery firm. Thus, it’s possible that the literature currently in publication on the criteria for evaluating green suppliers does not accurately represent green performance across the whole operating process. Looking at it this way, our study’s primary goal is to restore a set of standards for evaluating a candidate’s performance in terms of economics (“investment recovery”), the environment (“sustainable product design, green packaging, and ISO 14001 certification”), and society (“health and security”). To do this, we’ve added traditional components (“cost, quality, and distribution”) while making sure that green considerations are integrated into every step of the design, production, and management processes.

Secondly, the MCDM techniques for GSS problems that are currently available have not often used Fuzzy sets theory. Owing to the DMs’ limited experiences and cognitive abilities as well as the imprecise nature of preferences, a precise numerical representation may not accurately reflect their assessments of the relevant criterion. Relatively few Fuzzy forms have been employed with MCDM combinations [21], despite the fact that Fuzzy information has been used to indicate DMs’ imprecise assessments of the importance of pertinent criteria and candidate ratings for GSS difficulties. Using Fuzzy set theory in MCDM techniques has the following benefits: modeling uncertainty, since data are frequently imprecise or incomplete, Fuzzy logic enables the modeling of the uncertainty and vagueness that are prevalent in many real-life scenarios; flexibility in knowledge representation, compared to classical binary logic, Fuzzy sets provide a more subtle way to represent knowledge and expert opinions, more accurately representing the complexity of human judgments and preferences; and managing subjectivity, by taking into account varying levels of certainty or uncertainty in assessments and preferences, Fuzzy logic allows for the successful integration of differing viewpoints from various decision-makers.

Third, it is uncommon to compare two combinations of MCDM models, such as AHP-TOPSIS and AHP-WASPAS. In light of this, the third reason for our research is to compare the Fuzzy AHP-Fuzzy TOPSIS and Fuzzy AHP-Fuzzy WASPAS in order to fully assess how well each method performs in a particular setting. This makes it possible to identify the approach that will work best in resolving a particular multi-criteria decision-making scenario. It is feasible to assess the conclusions’ robustness and lower the likelihood of bias or analytical errors by contrasting the outcomes of various model combinations. Comparing various MCDM modeling techniques encourages the creation of new, more efficient techniques and sparks research in this area, which advances a process of continual progress. In conclusion, comparing various MCDM model combinations enables the acquisition of more accurate and insightful results, a deeper comprehension of the subtleties of multi-criteria decision-making issues, and the identification of optimal approaches for resolving these issues successfully.

The following goals have been determined for the case study that is being presented based on a thorough analysis of the literature:

• Restore a set of standards for evaluating a candidate’s performance in terms of economics (“investment recovery”), the environment (“sustainable product design, green packaging, and ISO 14001 certification”), and society (“health and security”). To do this, we’ve added traditional components (“cost, quality, and distribution”).
• Using Fuzzy set theory in MCDM techniques to indicate DMs’ imprecise assessments of the importance of pertinent criteria and candidate ratings for GSS difficulties.
• The Fuzzy Analytic Hierarchy Process (AHP) extended version is utilized to compute the weights of the criteria.
• The Fuzzy TOPSIS and the Fuzzy WASPAS are used to rank and choose the best possible supplier.
• The comparison of the two combinations the Fuzzy AHP-Fuzzy TOPSIS and Fuzzy AHP-Fuzzy WASPAS are realized in discussion and conclusion in order to fully assess how well each method performs in a particular setting.
• Make management recommendations based on the study’s conclusions.

The remainder of this paper unfolds as follows: Section 2 provides an extensive review of the literature. Then the Section 3 delves into the various models employed for the case study undertaken in this research. In Section 4, the result of our work is presented, offering a detailed technical explanation of the selected methodologies. The Implications for managers of this research are discussed in Section 5. Furthermore, Section 6 thoroughly discusses the results, along with providing insights into future research directions.

2. Literature Review

Thoroughly evaluating and strategically choosing the appropriate criteria and models is absolutely crucial in ensuring that we effectively meet and exceed our objectives. This careful selection process lays the foundation for our success, guiding our efforts towards optimal outcomes and performance.

2.1. Criteria Selection

As per [22], the literature from 1966 to 1990 predominantly emphasized scope, price (C1), quality (C2), and distribution (C3) as the key criteria in supplier selection (SS) [23]. However, there was a notable absence of consideration for environmental criteria in the selection of green suppliers (GSS). The main feature of the current GSS problem criteria is the direct addition of particular environmental elements to traditional criteria, which could result in an inadequate evaluation of suppliers’ sustainable performance. Ref. [14] combined environmental concerns with economic factors (cost, quality, stability, and flexibility) to assess the achievements of sustainable suppliers for a European manufacturer. integrated environmental criteria—such as green production, green packaging and labeling, and environmental management—to relevant economic criteria, in order to assess the achievements of green suppliers to the plastics industry. When assessing potential suppliers’ green performance for an agricultural tool and machinery company, ref. [20] added green image and design as an environmental representation in addition to delivery, production, quality, and other traditional criteria.

Thus, it’s probable that green performance across the entire operating process is not accurately represented in the literature that is now available in publications regarding the criteria for evaluating green providers. To put it another way, our study restores a set of criteria for assessing a candidate’s performance in terms of society (“health and security”), the environment (“sustainable product design, green packaging, and ISO 14001 certification”), and economics (“investment recovery”). To these criteria, we add traditional elements (“cost, quality, and distribution”), ensuring that green considerations are incorporated into every stage of the design, production, and management processes.

Table 1. Green supplier criteria.

Criteria	Code	Sub-Criteria	Sources
Sustainable product design	C5	Designing products and services that use less energy and material	[24,25,26]
		Designing products and services to recover materials, reuse waste, and recycle waste	[27,28,29,30]
		Design of products/services to prevent or minimize use of potentially hazardous products and/or their manufacturing process	[27,28,29,30,31,32,33,34,35,36,37,38,39,40]
Green packaging	C8	Ensures that the materials in the packaging are recyclable.	[27,28,29,30,31,32,33,34,35,36,37,38,39,40]
		Ensures that the packaging may be reused.	[31,32,33,37,39,40]
		Reduces the amount of materials used in the packaging	[31,32,33,37]
		Minimizes the use of potentially harmful components in the packaging	[31,32,33,37]
Investment recovery	C7	Investment recovery(selling) of surplus materials/inventory	[27,28,29,30,31,32,33,34,35,36,37,38,39,40]
		selling of scrap and waste materials	[27,28,29,30,31,32,33,34,35,36,37,38,39,40]
		selling excess capital equipment	[27,28,29,30,31,32,33,34,35,36,37,38,39,40]
ISO 14001 certification	C6	Minimize negative environmental impacts on organizations	[41,42,43,44]
		Reduce the use of resource and waste	[38,39,40,41,42,43,44,45,46]
		Work indirectly by influencing all supply chain stakeholders to choose more environmentally sustainable activities	[43,44,47,48]
Health and security	C4	Monitoring of production safety	[31,32,33,49,50]
		Health and safety education training	[29,38,41,44,51]

presents a compilation of identified criteria derived from literature reviews [9] and expert interviews, providing a concise overview of various evaluation criteria for GSS examined by researchers across various domains.

In the provided case study on green supplier selection, criterion C1 is categorized as a cost criterion, while the rest are regarded as benefit criteria throughout the analysis process.

2.2. Model Selection

Ref. [8] classifies models that address GSS challenges into three main categories: multi-criteria decision-making, artificial intelligence, and mathematical programming. MCDM, is a well-respected methodological approach that assists decision-makers (DMs) in identifying workable solutions that satisfy several competing criteria. The subcategories of MCDM methods are as follows: (1) multi-attribute techniques such as AHP and ANP); (2) compromise techniques such as Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Elimination and Choice Expressing the Reality (ELECTRE), and Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE); and (3) ranking techniques using the Qualitative Method with Flexible Multiple Criteria (QUALIFLEX). MCDM models are widely used in current research because choosing a GSS problem is consistent with the structure of a normal MCDM problem.

Multi-criteria decision-making (MCDM) is a well-established methodological category that assists decision-makers (DMs) in identifying a workable solution that meets many competing criteria. Since choosing a GSS problem can be considered as a traditional MCDM problem, MCDM models are the most frequently used methodological category in the research that has previously been done [14]. Researchers developed suitable evaluative criteria, modeled the ideal weights for the relevant criteria, solicited feedback from decision experts, and applied MCDM techniques to assess the criteria. The AHP was proposed by [15] as a means of measuring the prioritization criterion. The AHP-derived weights are incorporated into the discrete-event modeling approach, which regularly scores patients according to their health, waiting time, and level of suffering. This study developed an analytical network process (ANP) that was incorporated into a geographic information system (GIS; abbreviated as ANP-GIS) to assess flood vulnerability in coastal cities [16]. For a Brazilian electronics business to select ecologically friendly suppliers, this study proposes a Fuzzy TOPSIS-based framework [17]. The ViseKriterijum-ska Optimizacija I Kompromisno Resenj (VIKOR) technique was developed by [18] to rank the threat-agent categories based on the risk assessment of the experts. Ref. [19] using a modified WASPAS approach based on Heronian operators to pick tramcars for environmentally sustainable urban transportation. Despite the complexity of GSS problems, integrated approaches, particularly combining AHP and TOPSIS, AHP and TOPSIS stand out as the two most frequently utilized MCDM models for GSS problems, being employed both independently and in conjunction to develop integrated methodologies. AHP is distinguished by its ability to handle both qualitative and quantitative data and to present outcomes based on criteria at each level [15]. In contrast, TOPSIS possesses unique qualities and advantages compared to other MCDM techniques. By considering the greatest distance from an identified negative ideal solution (NIS) and the smallest distance from an identified positive ideal solution (PIS), it has emerged as a popular and effective approach for addressing MCDM problems. This method can effectively capture the overall impact of multiple factors, mitigate subjectivity, and eliminate the need for an objective function and passing test. Consequently, integrated approaches combining AHP and TOPSIS have been widely adopted for GSS challenges.

However, methods like AHP and WASPAS remain less common in this domain. WASPAS, also known as Weighted Aggregated Sum-Product Assessment, is a multi-criteria decision-making (MCDM) method designed to evaluate and rank alternatives based on multiple criteria. This method combines criteria aggregation using both weighted sum (Sum) and product (Product). The WASPAS method allows for a comprehensive evaluation of alternatives, considering both positive and negative aspects of each criterion, while providing flexibility in weight assignment and performance aggregation. This versatility makes it a valuable tool for decision-making when trade-offs between competing objectives are present.

The integration of Fuzzy Set Theory with multi-criteria decision-making (MCDM) models involves incorporating Fuzzy logic into decision-making processes that deal with multiple criteria or objectives. Fuzzy Set Theory allows for the representation of uncertainty and imprecision in decision-making, enabling decision-makers to handle ambiguous or vague information more effectively. By integrating Fuzzy logic with MCDM models, decision-makers can account for the inherent uncertainty in decision environments and make more robust and flexible decisions. This integration enhances the capability of MCDM models to address complex real-world problems where precise numerical data may be lacking or difficult to obtain. Overall, the integration of Fuzzy Set Theory with MCDM models provides a powerful framework for decision-making under uncertainty and ambiguity, leading to more informed and reliable decisions [6].

The decision to utilize the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was informed by our research findings. Through our investigation [8], we identified the three most prevalent models, AHP, TOPSIS, and DEA, in the context of green supplier selection.

Few research works have carried out comparative evaluations with more than two methods of decision-making. The Fuzzy-(TOPSIS, VIKOR, and GREY) methods were compared by [52], who also offered information on the time complexity of each method. Ref. [12] investigated four hybrid approaches and suggested a material selection model: Fuzzy AHP with DEA, Fuzzy AHP with DEMATEL, and Fuzzy AHP with MABAC. We use integrated Fuzzy techniques in this study, including Fuzzy AHP with TOPSIS and Fuzzy AHP with WASPAS. This strategy should make comparison analysis easier, validate the data we obtained, and give us insightful information that will help us decide which model is best for our theme [53].

3. Methodology

In this section, we present the models used to achieve our objectives. The Figure 1 presents the flow chart of the green supplier selection process.

3.1. Fuzzy Set Theory

Refs. [5,53] introduced the concept of Fuzzy Set Theory (FST), which has been widely applied by decision-makers (DMs) to tackle complex decision-making problems involving multiple alternatives and criteria in a productive, consistent, and systematic manner [54]. Because supplier selection characteristics are inherently ambiguous, Fuzzy set theory (FST) has become a widely used technique to convert ambiguous preferences into a rigorously mathematical framework. Through managing imperfect data and ambiguity, FST seeks to determine which supplier is best suited overall.

Definition 1.

A triangle membership function defines a Fuzzy number expressed as a triangular Fuzzy number, denoted by the ($l_a,m_b, u_c$), where [$l_a-lower, m_b-middle, u_c-upper$]. This graphical representation, depicted in the accompanying Figure 2, illustrates the extent of membership (${\dot{u}}_{\tilde{n}}$) and is interpreted as:

$$\left({\dot{u}}_{\tilde{n}}\right)=\left\{\begin{array}{c}\frac{\mathsf{Ƒ} - l_a}{m_b - l_a}; for l_a\le \mathsf{Ƒ}\le m_b\\ \frac{\mathsf{Ƒ} - u_c}{u_c - m_b}; for m_b\le \mathsf{Ƒ}\le u_c\\ 0; otherwise\end{array}\right.$$

Definition 2.

The mathematical equations of the two Fuzzy triangular functions ${\widetilde{\mathsf{Ƒ}}}_1=\left(l_{a1},m_{b1},u_{c1}\right)$ and ${\widetilde{\mathsf{Ƒ}}}_2=\left(l_{a2},m_{b2},u_{c2}\right)$ are as follows:

Addition of two Fuzzy triangular functions

$${\widetilde{\mathrm{Ƒ}}}_1+{\widetilde{\mathrm{Ƒ}}}_2=\left(l_{a1},m_{b1},u_{c1}\right)+\left(l_{a2},m_{b2},u_{c2}\right)=\left[\right(l_{a1}+l_{a2}),(m_{b1}+m_{b2}),(u_{c1}+u_{c2}\left)\right],$$

Subtraction of two Fuzzy triangular functions

$${\widetilde{\mathrm{Ƒ}}}_1-{\widetilde{\mathrm{Ƒ}}}_2=\left(l_{a1},m_{b1},u_{c1}\right)-\left(l_{a2},m_{b2},u_{c2}\right)=\left[\right(l_{a1}-l_{a2}),(m_{b1}-m_{b2}),(u_{c1}-u_{c2}\left)\right],$$

Multiplication of two Fuzzy triangular functions

$${\widetilde{\mathrm{Ƒ}}}_1\ast {\widetilde{\mathrm{Ƒ}}}_2=\left(l_{a1},m_{b1},u_{c1}\right)\ast \left(l_{a2},m_{b2},u_{c2}\right)=\left[\right(l_{a1}\ast l_{a2}),(m_{b1}\ast m_{b2}),(u_{c1}\ast u_{c2}\left)\right],$$

Division of two Fuzzy triangular functions

$${\widetilde{\mathrm{Ƒ}}}_1/{\widetilde{\mathrm{Ƒ}}}_2=\left(l_{a1},m_{b1},u_{c1}\right)/\left(l_{a2},m_{b2},u_{c2}\right)=\left[\right(l_{a1}/l_{a2}),(m_{b1}/m_{b2}),(u_{c1}/u_{c2}\left)\right].$$

Definition 3.

The distance between two Fuzzy triangular functions ${\widetilde{\mathsf{Ƒ}}}_1=\left(l_{a1},m_{b1},u_{c1}\right)$ and ${\widetilde{\mathsf{Ƒ}}}_2=\left(l_{a2},m_{b2},u_{c2}\right)$ is determined by the ‘Vertex Method’ [55].

$$d({\widetilde{\mathrm{Ƒ}}}_1,{\widetilde{\mathrm{Ƒ}}}_2)=\sqrt{\frac{1}{3}\left[{(l_{a1}-l_{a2})}^2+{(m_{b1}-m_{b2})}^2+{(u_{c1}-u_{c2})}^2\right]}$$

Definition 4.

The expression of de-fuzzing of Fuzzy function $\widetilde{\stackrel{~}{\mathsf{Ƒ}}}=\left(l_a,m_b,u_c\right)$

De-fuzzing ${\tilde{\mathcal{L}}}_i=\frac{1}{3}\left[\left(u_c-l_a\right)+\left(m_b-l_a\right)\right]+l_a$

De-fuzzing ${\tilde{\mathcal{L}}}_i=\frac{1}{2}\left[\lambda u_c+m_b+(1-\lambda )·l_a\right]$

Within the Analytic Hierarchy Process (AHP), a pairwise comparison matrix is created to aggregate the criteria under consideration for weight determination. We have chosen three decision-makers with the most experience in the automotive company where we conducted the case study in the following areas: decision-maker 1, supply chain management responsible with 8 years of experience; decision-maker 2, quality management system responsible with 10 years of experience; and decision-maker 3, logistics responsible with 11 years of experience.

Table 2. Language variables.

language Variables	TFN’s
Very poor (VP)	(0,0,1)
Poor (P)	(0,1,3)
Medium poor (MP)	(1,3,5)
Fair (F)	(3,5,7)
Medium good (MG)	(5,7,9)
Good (G)	(7,9,10)
Very good (VG)	(9,10,10)

shows how the linguistic variables chosen for this study are converted into triangular Fuzzy numbers. The decision-makers provide evaluations of the suppliers in linguistic terms based on different criteria using a questionnaire (see Figure 3) that contains multiple-choice weights for each criterion relative to each supplier, as indicated in

Table 3. Supplier evaluation by the first decision-maker.

	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(5.00,7.00,9.00)	(1.00,3.00,5.00)	(3.00,5.00,7.00)	(1.00,3.00,5.00)	(1.00,3.00,5.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)
Supplier 2	(1.00,3.00,5.00)	(3.00,5.00,7.00)	(1.00,3.00,5.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)	(7.00,9.00,10.00)	(5.00,7.00,9.00)
Supplier 3	(1.00,3.00,5.00)	(7.00,9.00,10.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(7.00,9.00,10.00)	(3.00,5.00,7.00)	(7.00,9.00,10.00)
Supplier 4	(7.00,9.00,10.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)

,

Table 4. Supplier evaluation by the second decision-maker.

	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(7.00,9.00,10.00)	(1.00,3.00,5.00)	(3.00,5.00,7.00)	(1.00,3.00,5.00)	(1.00,3.00,5.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)
Supplier 2	(1.00,3.00,5.00)	(5.00,7.00,9.00)	(1.00,3.00,5.00)	(3.00,5.00,7.00)	(7.00,9.00,10.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)
Supplier 3	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)	(7.00,9.00,10.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)
Supplier 4	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(1.00,3.00,5.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)

and

Table 5. Supplier evaluation by the third decision-maker.

	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)	(1.00,3.00,5.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)
Supplier 2	(1.00,3.00,5.00)	(7.00,9.00,10.00)	(3.00,5.00,7.00)	(1.00,3.00,5.00)	(7.00,9.00,10.00)	(1.00,3.00,5.00)	(7.00,9.00,10.00)	(5.00,7.00,9.00)
Supplier 3	(1.00,3.00,5.00)	(7.00,9.00,10.00)	(5.00,7.00,9.00)	(7.00,9.00,10.00)	(3.00,5.00,7.00)	(7.00,9.00,10.00)	(3.00,5.00,7.00)	(3.00,5.00,7.00)
Supplier 4	(7.00,9.00,10.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(1.00,3.00,5.00)	(1.00,3.00,5.00)	(1.00,3.00,5.00)

. Next, the information from Table 2, Table 3, Table 4 and Table 5 is combined with Table data to create the integrated Fuzzy decision matrix, or $\tilde{y}$. Equation (x) synthesizes the Fuzzy rating values to create each element of the $\tilde{y}$ matrix,

$${\tilde{y}}_{ij}=\frac{1}{k}\left[{{\tilde{y}}_{ij}}^1+{{\tilde{y}}_{ij}}^2+...+{{\tilde{y}}_{ij}}^n\right]$$

where, k = expert’s number; n = supplier’s number, m = criteria’s number and i = (1, 2, …, n), j = (1, 2, …, m).

The integrated Fuzzy decision matrix is represented in Equation (x):

$$\tilde{y}=\left[\begin{array}{ccc}{\tilde{y}}_{11}& \cdots & {\tilde{y}}_{1n}\\ ⋮& \ddots & ⋮\\ {\tilde{y}}_{m1}& \cdots & {\tilde{y}}_{mn}\end{array}\right]$$

The integrated Fuzzy decision matrix, or $\tilde{y}$, is produced at the end of this procedure and is shown in

Table 6. [TOPSIS] Integrated Matrix.

	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(5.00,7.66,10.00)	(1.00,4.33,9.00)	(3.00,5.00,7.00)	(1.00,4.33,9.00)	(1.00,3.00,5.00)	(5.00,7.00,9.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)
Supplier 2	(1.00,3.00,5.00)	(3.00,7.00,10.00)	(1.00,3.66,7.00)	(1.00,4.33,7.00)	(3.00,7.66,10.00)	(1.00,4.33,7.00)	(3.00,7.66,10.00)	(3.00,6.33,9.00)
Supplier 3	(1.00,4.33,9.00)	(3.00,7.66,10.00)	(5.00,7.00,9.00)	(3.00,7.00,10.00)	(3.00,5.00,7.00)	(7.00,9.00,10.00)	(3.00,5.00,7.00)	(3.00,7.00,10.00)
Supplier 4	(5.00,8.33,10.00)	(5.00,7.00,9.00)	(1.00,4.33,7.00)	(5.00,7.00,9.00)	(3.00,6.33,9.00)	(1.00,4.33,9.00)	(1.00,4.33,7.00)	(1.00,4.33,7.00)

. The TOPSIS process uses this matrix as the foundation for supplier rating.

3.2. Outlining the Fuzzy AHP Technique

This work combines the widely used Fuzzy Set Theory (FST) with the expanded AHP method to estimate the weights of evaluation criteria. The Fuzzy AHP, an improved variant of the AHP approach, successfully addresses the inherent vagueness in human judgments, a problem that the original AHP method struggles to handle. The application of AHP to the Green Supplier Selection (GSS) problem is shown in Figure 4.

The triangular Fuzzy number (TFN) can be expressed as follows:

$${\widetilde{\mathrm{Ƒ}}}_i^j=\left(l_{aj},m_{bj},u_{cj}\right)$$

where $j=\left(1,2,...,m\right)$.

There are four steps that make up the overall procedure.

Step 1: Use expression (1) to calculate the “Fuzzy synthetic extent” Z_i for the ith criterion.

$$Z_i={\sum }_{j=1}^n{\widetilde{{\mathrm{Ƒ}}_i}}^j{\left({\sum }_{i=1}^n{\sum }_{i=1}^m{\widetilde{{\mathrm{Ƒ}}_i}}^j\right)}^{-1}$$

(1)

Step 2: Based on the parameters given in Equation (2), ascertain the likelihood that Z_b ≥ Z_a.

$$V\left(Z_b\ge Z_a\right)=\left\{\begin{array}{c}1 if m_{b1}\ge m_{b2}\\ 0 if l_{a1}\ge u_{c2}\\ \frac{(l_{a2} - u_{c1})}{(m_{b1} - u_{c1}) - (m_{a2} - l_{a2})}; otherwise\end{array}\right.$$

(2)

Step 3: According to expression (3), the degree of possibility for a convex Fuzzy number should be more than ‘k’ convex Fuzzy number Z_i, where (i = 1, 2, …, k):

$$V(Z_i\ge Z_1,Z_2,...,Z_k)=minV\left(Z_b\ge Z_a\right)=w\left(Z_i\right)$$

$$d^{″}\left(A_i\right)=minV\left(Z_i\ge Z_k\right),where k\ne i;and(k=\mathrm{1,2},..,n)$$

(3)

Expression (4) can be utilized for illustrating the value of the weight vector, as seen in Figure 5 below:

$$W^{″}={\left(d^{″}\left(A_1\right),d^{″}\left(A_2\right),...,d^{″}\left(A_n\right),\right)}^T$$

(4)

Step 4. We obtain the normalized weight vectors by going through the normalization process, which is specified by Equation (5):

$$W={\left(d\left(A_1\right),d\left(A_2\right),...,d\left(A_n\right),\right)}^T$$

(5)

3.3. Outlining the Fuzzy TOPSIS Technique

Ref. [56] presented the multi-criteria decision-making (MCDM) TOPSIS approach for the first time. The core principle behind TOPSIS is centered on the concept of “relative closeness to the ideal solution”. Essentially, the chosen options should be the ones that are the furthest from the negative ideal solution (NIS) and the shortest geometric distance from the positive ideal solution (PIS). The following steps outline the TOPSIS procedure:

Step 1: The Fuzzy normalized decision matrix, or $\tilde{R}$ normalized, is represented as follows:

$$\tilde{R} \mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}=\left[{\tilde{r}}_{ij}\right]m·n$$

(6)

As explained in Equation (6), the $\tilde{R}$ normalized is generated.

Using Equations (7) and (8), the normalizing process is carried out on a Fuzzy choice matrix ($\tilde{y}$):

$${\tilde{r}}_{ij}=\left(\frac{l_{aij}}{u_{cj}^{\mathrm{*}}},\frac{m_{bij}}{u_{cj}^{\mathrm{*}}},\frac{u_{cij}}{u_{cj}^{\mathrm{*}}}\right),j \mathsf{ϵ} B$$

(7)

$${\tilde{r}}_{ij}=\left(\frac{l_{aj}^{-}}{u_{cij}},\frac{l_{aj}^{-}}{m_{bij}},\frac{l_{aj}^{-}}{l_{aij}}\right),j \mathsf{ϵ} C$$

(8)

where $u_{cj}^{\mathrm{*}}=max u_{cij}$, $j \mathsf{ϵ} B$; $l_{aj}^{-}=min l_{aij}$, $j \mathsf{ϵ} C$.

The collections of benefit criteria are represented by B and the sets of cost criteria by C.

Step 2: By multiplying a Fuzzy normalized decision matrix (($\tilde{R}$ normalized) by the computed weights of the criterion (${\tilde{W}}_{ij}$).), the weighted decision matrix (U_ij) is obtained

U = [U_ij]_mn

(9)

where i = (1, 2, 3 …, m) and ${\tilde{W}}_i$ denote the weight of the jth criterion, and j = (1, 2, 3 …, n).

Step 3: The Fuzzy ideal solutions, positive (PIS, P⁺), and negative (NIS, N⁻), are computed as follows:

$$P^{+}=\left(P_1^{+},P_2^{+},...,P_n^{+}\right)$$

$$N^{-}=\left(N_1^{-},N_2^{-},...,N_n^{-}\right)$$

where $P_i^{+}=\left\{\left(\mathrm{1,1},1\right)\right\}$; $N_i^{-}=\left\{\left(\mathrm{0,0},0\right)\right\}$ ; $j=\left(1,2,...,n\right)$.

Step 4: The following formula is used to get each alternate distance from (PIS, P⁺) and (NIS, N⁻):

$$d_i^{+}={\sum }_{j=1}^n{d}_P\left(P_{ij},P_j^{+}\right),i=1,2,...,m$$

(10)

$$d_i^{-}={\sum }_{j=1}^n{d}_N\left(N_{ij},N_j^{-}\right),i=1,2,...,m$$

(11)

Step 5: The proximity coefficient (C_i) for each choice is derived as follows after taking into account the distance values that were calculated in step 4:

$$C_i=\frac{\left(d_i^{+}\right)}{\left(d_i^{+}\right)+\left(d_i^{-}\right)}$$

(12)

Step 6: The best option is ultimately chosen based on the closest value of the proximity coefficient (C_i) after judging the C_i quantities for every choice. Stated otherwise, the greatest option by the maximum C_i value is chosen as the one (A_i) that is closer to the (P⁺) and farther from the (N⁻) than the other options.

3.4. Outlining the Fuzzy WASPAS Technique

The Weighted Aggregated Sum-Product Assessment (WASPAS) approach was first presented by (Zavadskas et al., 2012) [57], and it was then modified to become WASPAS-IFIV. The construction site selection problem was subsequently addressed by [58] with the introduction of an integrated model integrating WASPAS and Fuzzy Set Theory (FST).

The foundation of WASPAS is two aggregated models:

Weighted-Sum Model (WSM): Using a weighted sum of attribute values, this method calculates the overall score of alternatives (A_i).

Weighted-Product Model (WPM): This idea was created to deal with alternatives (A_i) that have low attribute values. It determines the score of each alternative by multiplying the attribute’s important weight (${\tilde{W}}_i$) by the scale rating of each attribute.

The following are the procedures for using Fuzzy WASPAS:

Step 1: Create the matrix ($\tilde{y}$).

Step 2: The representation of the “Normalized Fuzzy decision matrix” ($\tilde{R}$ normalized) is as follows:

$$\tilde{R} \mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}=\left[{\tilde{r}}_{ij}\right]m·n$$

where Bα stands for benefit criteria and Cα for cost criteria.

The normalizing procedure for the Fuzzy decision matrix ($\tilde{y}$) is carried out in order to produce the normalized Fuzzy decision matrix ($\tilde{R}$ normalized), Equations (2) and (3).

Step 3: (i) Determine the WSM’s Weighted Decision Matrix, or ${\widehat{X}}_q$.

$${\widehat{X}}_q=\left[\begin{array}{ccc}{\widehat{X}}_{11}& \cdots & {\widehat{X}}_{1n}\\ ⋮& \ddots & ⋮\\ {\widehat{X}}_{1m}& \cdots & {\widehat{X}}_{mn}\end{array}\right];{\widehat{X}}_{ij}={\tilde{r}}_{ij}\times {\tilde{W}}_i;j=(1,2,...,n) and i=(1,2,...,m)$$

(13)

(ii) Determine the WPM of the “Weighted Normalized Fuzzy Decision Matrix” ${\widehat{X}}_p$.

$${\widehat{X}}_p=\left[\begin{array}{ccc}{\widehat{X}}_{11}& \cdots & {\widehat{X}}_{1n}\\ ⋮& \ddots & ⋮\\ {\widehat{X}}_{1m}& \cdots & {\widehat{X}}_{mn}\end{array}\right];{\widehat{X}}_{ij}={\tilde{r}}_{ij}^{{\tilde{W}}_i};$$

(14)

Step 4: Determine the optimality function’s values.

(i) Using the WSM approach, for every option:

$${\tilde{L}}_i={\sum }_{j=1}^n{\widehat{X}}_{ij};i=1,2,...,m$$

(15)

(ii) Using the WPM approach, for every alternative:

$${\tilde{P}}_i={\prod }_{j=1}^n{\widehat{X}}_{ij};i=1,2,...,m$$

(16)

The Fuzzy performance measurements for each alternative are represented by the Fuzzy integers ${\tilde{L}}_i$ and ${\tilde{P}}_i$.

The “center of area” approach is the most straightforward and useful for de-fuzzification.

$$L_{i\left[defuzzification\right]}=\frac{1}{3}\left(L_{ia}+L_{ib}+L_{ic}\right)$$

(17)

$$P_{i\left[defuzzification\right]}=\frac{1}{3}\left(P_{ia}+P_{ib}+P_{ic}\right)$$

(18)

Step 5: The following formula can be used to get the integrated utility function (IUF) for an alternative (A_i):

$$K_I=\lambda {\sum }_{j=1}^n{L}_I+(1-\lambda ){\sum }_{j=1}^n{P}_I; \lambda =0,..,1; 0\le K_I\le 1$$

(19)

The value in Equation (19) is computed based on the supposition that the “total of WPM scores” and the “total of all alternatives WSM scores” must coincide:

$$\lambda =\frac{\sum _{i=1}^n{P}_i}{\sum _{i=1}^m{L}_i+\sum _{i=1}^m{P}_i}$$

(20)

Step 6: Determine which alternative (A_i) has the greatest computed “K_I” value and rank them in order of preference.

4. Result and Case Study

In this section, we conduct a thorough investigation using two innovative techniques—the Fuzzy AHP-Fuzzy TOPSIS and Fuzzy AHP-Fuzzy WASPAS—within the working environment of a well-known Moroccan automaker that was specifically chosen for this research. The choice to only use supplier data from this organization guarantees a targeted and contextually relevant analysis.

The first step in our methodological journey is to determine the relative value of each criterion using the Fuzzy AHP technique. This is an important phase since it sets the stage for the other assessments and rankings. Fuzzy AHP allows us to account for the linguistic ambiguities and intrinsic uncertainties that are frequently present in decision-making processes, which strengthens the analytical framework.

We use both the Fuzzy TOPSIS and Fuzzy WASPAS approaches to assess the performance of suppliers against each criterion, building on the insights obtained from Fuzzy AHP. We can determine which suppliers most closely match the specified criteria by using Fuzzy TOPSIS, which considers both the positive and negative elements of the suppliers’ performance. In a similar vein, Fuzzy WASPAS provides a holistic evaluation by combining the suppliers’ weighted scores and taking into account the interactions between different criteria.

Our goal is to offer practical insights into supplier selection and ranking in the context of the automotive sector by utilizing these cutting-edge analytical tools. Our comparison study utilizing the Fuzzy TOPSIS and Fuzzy WASPAS approaches will provide stakeholders with a sophisticated view of supplier performance, empowering them to take well-informed decisions that improve supply chain resilience and operational excellence.

4.1. Calculating Weight with Fuzzy AHP

Step 1: Using the method described in Section 3.2, the integrated pairwise comparison matrix of criteria (for each decision-maker) is produced and displayed in Table 5. Table 6 displays the weight and normalized value of each criterion following the computation of the data in step (4).

4.2. Resolution for Fuzzy TOPSIS

A similar normalization process is used by the Fuzzy TOPSIS and Fuzzy WASPAS techniques. Using Equations (6) and (7), the normalized Fuzzy decision matrix (R normalized) is built.

Table 7. Integrated comparison matrix of criteria.

	C1	C2	C3	C4	C5	C6	C7	C8	Fuzzy Geometroc Mean Value ri	Fuzzy Weights Wi	Weights	Rank
C1	(1.00,1.00,1.00)	(1.00,1.00,1.00)	(7.00,9.00,10.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(7.00,9.00,10.00)	(7.00,9.00,10.00)	(3.79,4.72,5.4)	(0.22,0.32,0.46)	0.333	2
C2	(1.00,1.00,1.00)	(1.00,1.00,1.00)	(7.00,9.00,10.00)	(5.00,7.00,9.00)	(7.00,9.00,10.00)	(5.00,7.00,9.00)	(7.00,9.00,10.00)	(7.00,9.00,10.00)	(3.95,4.87,5.47)	(0.23,0.33,0.46)	0.34	1
C3	(0.10,0.11,0.14)	(0.10,0.11,0.14)	(1.00,1.00,1.00)	(3.00,5.00,7.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(1.44,1.86,2.35)	(0.083,0.12,0.2)	0.134	5
C4	(0.11,0.14,0.20)	(0.11,0.14,0.20)	(0.14,0.20,0.33)	(1.00,1.00,1.00)	(5.00,7.00,9.00)	(5.00,7.00,9.00)	(7.00,9.00,10.00)	(9.00,10.00,10.00)	(1.13,1.43,1.79)	(0.065,0.097,0.15)	0.312	3
C5	(0.11,0.14,0.20)	(0.10,0.11,0.14)	(0.11,0.14,0.20)	(0.11,0.14,0.20)	(1.00,1.00,1.00)	(5.00,7.00,9.00)	(7.00,9.00,10.00)	(7.00,9.00,10.00)	(0.65,0.8,1.00)	(0.037,0.054,0,085)	0.176	4
C6	(0.11,0.14,0.20)	(0.11,0.14,0.20)	(0.11,0.14,0.20)	(0.11,0.14,0.20)	(0.11,0.14,0.20)	(1.00,1.00,1.00)	(5.00,7.00,9.00)	(7.00,9.00,10.00)	(0.39,0.49,0.64)	(0.022,0.033,0.054)	0.109	6
C7	(0.10,0.11,0.14)	(0.10,0.11,0.14)	(0.11,0.14,0.20)	(0.10,0.11,0.14)	(0.10,0.11,0.14)	(0.11,0.14,0.20)	(1.00,1.00,1.00)	(5.00,7.00,9.00)	(0.24,0.26,0.33)	(0.014,0.017,0.028)	0.059	7
C8	(0.10,0.11,0.14)	(0.10,0.11,0.14)	(0.11,0.14,0.20)	(0.10,0.10,0.11)	(0.10,0.11,0.14)	(0.10,0.11,0.14)	(0.11,0.14,0.20)	(1.00,1.00,1.00)	(0.13,0.15, 0.19)	(0.00754,0.01,0.016)	0.024	8

provides the full normalized decision matrix.

Using Equation (9), the weighted normalized matrix (U_ij = r_ij·W_i) is constructed once the values of each element in the normalized matrix have been determined.

Table 8. The normalized value for each criterion.

	Normalized Weights
C1	0.221
C2	0.228
C3	0.090
C4	0.209
C5	0.118
C6	0.073
C7	0.039
C8	0.016

shows the matrix that is weighted and normalized.

Table 9. The normalized Fuzzy decision matrix.

	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(0.10,0.13,0.20)	(0.10,0.43,0.9)	(0.33,0.55,0.77)	(0.10,0.43,0.90)	(0.10,0.30,0.50)	(0.50,0.70,0.90)	(0.30,0.50,0.70)	(0.50,0.70,0.90)
Supplier 2	(0.20,0.33,1.00)	(0.30,0.70,1.00)	(0.11,0.40,0.77)	(0.10,0.43,0.70)	(0.30,0.76,1.00)	(0.10,0.43,0.70)	(0.30,0.76,1.00)	(0.30,0.63,0.90)
Supplier 3	(0.11,0.23,1.00)	(0.30,0.76,1.00)	(0.55,0.77,1.00)	(0.30, 0.70, 1.00)	(0.30,0.50,0.70)	(0.70,0.90,1.00)	(0.30,0.50,0.70)	(0.30,0.70,1.00)
Supplier 4	(0.10,0.12,0.20)	(0.50,0.70,0.90)	(0.11,0.48,0.77)	(0.50,0.70,0.90)	(0.30,0.63,0.9)	(0.10,0.43,0.90)	(0.10,0.43,0.70)	(0.10,0.43,0.70)

shows the distance measures of the possibilities from the Positive (D_i⁺) and Negative Ideal Solution (D_i⁻) using Equations (10) and (11).

The integrated Fuzzy AHP and Fuzzy TOPSIS results, using the C_i values for each alternative as shown in Table 9, indicate that Supplier 3 has the highest coefficient index value and is ranked highest, followed by Supplier 2. Supplier 4 is ranked lowest, whereas Supplier 1 is ranked third.

4.3. Resolution for Fuzzy WASPAS

Table 4 illustrates that the Fuzzy combined decision matrix is the same for the Fuzzy TOPSIS and Fuzzy WASPAS approaches. Next, the weighted normalized decision matrix is created for the Weighted-Product Model (WPM) and the Weighted-Sum Model (WSM). Notably, as determined from Equation (13) and displayed in

Table 10. The weighted normalized matrix.

	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(0.022,0.041,0.092)	(0.023,0.141,0.414)	(0.027,0.066,0.154)	(0.065,0.041,0.135)	(0.037,0.0162,0.042)	(0.011,0.0231,0.048)	(0.004,0.008,0.019)	(0.0037,0.07,0.014)
Supplier 2	(0.044,0.105,0.460)	(0.069,0.231,0.460)	(0.009,0.048,0.154)	(0.065,0.041,0.105)	(0.011,0.041,0.085)	(0.002,0.0141,0.037)	(0.004,0.012,0.028)	(0.0022,0.0063,0.014)
Supplier 3	(0.024,0.033,0.460)	(0.069,0.250,0.460)	(0.045,0.092,0.200)	(0.019,0.067,0.150)	(0.011,0.027,0.059)	(0.015,0.029,0.054)	(0.004,0.008,0.019)	(0.0022,0.0043,0.016)
Supplier 4	(0.022,0.038,0.092)	(0.115,0.231,0.414)	(0.009,0.057,0.154)	(0.032,0.067,0.135)	(0.011,0.034,0.076)	(0.002,0.014,0.048)	(0.001,0.007,0.019)	(0.00075,0.0043,0.011)

, the weighted normalized decision matrix generated for ç is similar to WSM (Xq).

Table 11. [TOPSIS] Result.

Alternatives	Di+	Di−	CCi	Rank
Supplier 1	0.553	0.224	0.288288	3
Supplier 2	0.158	0.418	0.725694	2
Supplier 3	0.065	0.342	0.840294	1
Supplier 4	0.329	0.1	0.233100	4

shows the computation of each element’s value in the weighted normalized Fuzzy decision matrix for the Weighted Product Model (WPM).

Equations (15) and (16) are used to calculate the optimality function value for the Weighted-Sum Model (WSM) and the Weighted-Product Model (WPM).

Equations (17) and (18) are used to defuzzify the obtained result. Using Equation (19), one may calculate λ = 0.44 as the value of the Integrated Utility Function (IUF) for an alternative (A_i) in the Fuzzy WASPAS approach. It is possible to compute the value of K_i given several options.

Table 12. [WASPAS] The weighted normalized matrix for WSM.

Alternatives	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(0.022,0.041,0.092)	(0.023,0.141,0.414)	(0.027,0.066,0.154)	(0.065,0.041,0.135)	(0.037,0.0162,0.042)	(0.011,0.0231,0.048)	(0.004,0.008,0.019)	(0.0037,0.07,0.014)
Supplier 2	(0.044,0.105,0.460)	(0.069,0.231,0.460)	(0.009,0.048,0.154)	(0.065,0.041,0.105)	(0.011,0.041,0.085)	(0.002,0.0141,0.037)	(0.004,0.012,0.028)	(0.0022,0.0063,0.014)
Supplier 3	(0.024,0.033,0.460)	(0.069,0.250,0.460)	(0.045,0.092,0.200)	(0.019,0.067,0.150)	(0.011,0.027,0.059)	(0.015,0.029,0.054)	(0.004,0.008,0.019)	(0.0022,0.0043,0.016)
Supplier 4	(0.022,0.038,0.092)	(0.115,0.231,0.414)	(0.009,0.057,0.154)	(0.032,0.067,0.135)	(0.011,0.034,0.076)	(0.002,0.014,0.048)	(0.001,0.007,0.019)	(0.0007,0.0043,0.011)

displays the obtained ki values. The alternative’s top rank is determined by the maximum K_I value. Supplier 3 has the highest K_i score in Table 12, followed by Supplier 2. Accordingly, the following is the ranking order determined using the hybrid Fuzzy AHP and Fuzzy WASPAS method: Suppliers 3 > 2 > 4 > 1 are the suppliers.

4.4. Sensitivity Examination

Sensitivity examination (SE) is a technique used in decision-making situations to evaluate the effects of changing the weights of the criteria. Changes in the order in which the options are prioritized can happen as a result of analyzing different circumstances. Results are resilient if they remain unchanged when criteria’s relative importance is changed, but they become sensitive otherwise. When determining the relative importance of many elements is unclear, SE can offer decision-makers important information. Furthermore, switching the weights of one criterion with another makes it possible to ascertain whether this swap changes the order in which the options are prioritized [25].

The examination of results obtained from both Fuzzy models [AHP, TOPSIS] and Fuzzy models [AHP, WASPAS] reveals a noteworthy resemblance in the outcomes of the two approaches. In the Fuzzy AHP/TOPSIS model, Supplier 3 is ranked as the top choice, followed by Supplier 2 as the second choice, Supplier 1 as the third choice, and Supplier 4 as the least preferred option. Conversely, in the Fuzzy AHP/WASPAS model, Supplier 4 is ranked as the third choice, with Supplier 1 being the least favored option (see

Table 13. [WASPAS] Weighted Normalized Matrix for WPM.

Alternatives	C1	C2	C3	C4	C5	C6	C7	C8
Supplier 1	(0.602,0.520,0.476	(0.588,0.756,0.952)	(0.912,0.930,0.949)	(0.860,0.921,0.984)	(0.918,0.937,0.942)	(0.984,0.988,0.994)	(0.983,0.988,0.990)	(0.994,0.996,0.998)
Supplier 2	(0.701,0.701,1.000)	(0.758,0.888,1,000)	(0.832,0.895,0.949)	(0.860,0.921,0.947	(0.956,0.985,1.000)	(0.950,0.972,0.980)	(0.983,0.995,1.000)	(0.990,0.995,0.998)
Supplier 3	(0.615,0.624,1.000)	(0.758,0.913,1,000)	(0.951,0.969,1.000)	(0.924,0.965,1.000)	(0.956,0.963,0.970)	(0.992,0.996,1.000)	(0.983,0.988,0.990)	(0.990,0.996,1.000)
Supplier 4	(0.602,0.507,0.476)	(0.852,0.888,0.952)	(0.832,0.915,0.949)	(0.955,0.965,0.984)	(0.956,0.975,0.991)	(0.950,0.972,0.994)	(0.968,0.985,0.990)	(0.982,0.991,0.994)

and

Table 14. [WASPAS] Result.

Alternatives	Li	Pi	Ki	Rank
Supplier 1	0.505	0.314	0.398	4
Supplier 2	0.613	0.566	0.586	2
Supplier 3	0.705	0.613	0.653	1
Supplier 4	0.531	0.376	0.444	3

).

Based on the radar chart presented in Figure 6 and

Table 15. Rank Fuzzy [AHP, TOPSIS] and [AHP, WASPAS].

Alternatives	Rank Fuzzy [AHP, TOPSIS] CCi	Rank Fuzzy [AHP, WASPAS] Ki
Supplier 1	0.288 (3)	0.398 (4)
Supplier 2	0.725 (2)	0.586 (2)
Supplier 3	0.840 (1)	0.653 (1)
Supplier 4	0.233 (4)	0.444 (3)

, it is evident that Supplier 3 has achieved the highest score among the alternatives. Following closely behind is Supplier 2. Then Supplier 4 and finally Supplier 1. Although Supplier 1’s score is slightly higher than Supplier 4’s in the Fuzzy [AHP, TOPSIS] model. As the alteration of criterion importance does not affect the precedence of alternatives, it can be inferred that the obtained results demonstrate robustness.

5. Implications for Managers

With a focus on tackling the intricacies of Green Supply Chain Management (G-SCM), the case study provides a thorough and methodical approach to Green Supplier Selection (GSS). This technique gives managers the tools they need to carefully assess their suppliers and make sure that only those that follow eco-friendly practices are added to the supply chain. It does this by giving managers an organized framework. This helps the company save a lot of money and conserve resources in addition to encouraging environmental responsibility.

This approach’s capacity to successfully handle the different obstacles faced in the process of producing eco-friendly products is one of its main advantages. The framework offers a strong basis for supplier evaluation by clearly outlining actionable criteria that are derived from insights obtained from industry experts and a thorough review of the literature. This raises the legitimacy and dependability of the evaluation process by guaranteeing that selections are based on actual data and industry best practices.

Additionally, the system gives managers the adaptability they need to meet changing legal needs and environmental standards. Managers can determine areas that may require revisions and assess the strength of their evaluations with the help of sensitivity analysis. This iterative process improves supplier assessments’ accuracy while also encouraging ongoing development of the company’s sustainability programs. All things considered, the creation of this GSS framework is a big step toward incorporating sustainability concerns into the supplier selection procedure. Through the alignment of supplier practices with environmental objectives, organizations can effectively manage risks and gain a competitive edge in the increasingly eco-aware modern marketplace.

6. Discussion and Conclusions

It is becoming more and more important to include environmental considerations when choosing providers who practice environmental responsibility. Decision-makers (DMs) and managers now have invaluable support in addressing the many issues encountered in procurement procedures within supply chain management, thanks to the development of new supplier selection models and analytical tools.

The necessity to give ecologically sustainable practices top priority when choosing suppliers is recognized by this changing landscape. Demand for suppliers who adhere to environmental standards is rising as companies work to reduce their environmental impact. As a result, cutting-edge strategies and sophisticated analytics are being created to expedite the supplier selection procedure and enable decision-makers to make well-informed decisions that support their sustainability objectives.

Organizations can reduce environmental hazards and improve their standing as ethical corporations by integrating environmental factors into their supplier selection processes. This proactive strategy promotes long-term sustainability throughout the supply chain in addition to encouraging environmental responsibility.

This study provides a detailed account of how a Fuzzy ranking algorithm was implemented to find environmentally conscious suppliers in the Moroccan automotive industry. The study emphasizes the validity and effectiveness of the integrated framework suggested through a case study focused on the dynamics of the Moroccan automotive sector. The selection of the evaluation criteria was done with great care, considering the advice of industry professionals as well as relevant literature to make sure that traditional and environmental factors were covered thoroughly. After a rigorous procedure, eight crucial criteria that covered different aspects of operational excellence and sustainability emerged as critical elements. Making use of stakeholders’ knowledge, a pairwise comparison matrix was painstakingly created to determine the relative importance of each criterion, providing the foundation for well-informed decision-making.

The process of determining weights involved the application of the Fuzzy AHP method, which allowed for the systematic assessment of criteria importance. The evaluation criteria considered encompassed various facets crucial to supplier selection, including cost, quality, delivery efficiency, health and safety standards, sustainable product design, ISO 14001 certification, investment recovery, and green packaging. These criteria served as the foundational inputs for the subsequent phases of supplier selection, conducted through the Fuzzy TOPSIS and Fuzzy WASPAS methodologies, both integrated with Fuzzy AHP.

To ensure the robustness of the selection system, sensitivity analysis was carried out, as depicted in Figure 6. The outcomes of this analysis indicated that among the alternative suppliers, Supplier 3 secured the highest score, closely followed by Supplier 2. Subsequently, Suppliers 4 and 1 were ranked accordingly. Although there was a marginal difference in the scores between Supplier 1 and Supplier 4 in the Fuzzy [AHP, TOPSIS] model and Fuzzy [AHP, WASPAS], the alteration in criterion importance did not affect the overall precedence of alternatives. This observation underscores the robustness of the results obtained. The comparison between the two-combination Fuzzy [AHP, TOPSIS] model and Fuzzy [AHP, WASPAS] show that the two approaches present the same results.

Consequently, the descending ranking of green suppliers was established as follows: Supplier 3 > Supplier 2 > Supplier 4 > Supplier 1. This hierarchical arrangement provides a clear delineation of supplier performance based on the comprehensive evaluation criteria considered in the study.

Similar normalization techniques are followed in the case study presentation to guarantee uniformity in the handling of the data. Even with differences in normalization, these processes have very little effect on the final ranking; this is especially true for Fuzzy TOPSIS and Fuzzy AHP approaches. As such, this work provides a solid basis or coherent framework for the use of Green Supplier Selection (GSS) in an uncertain environment, opening the door for additional research in this important field to expand the body of knowledge.

Decision-makers typically convey their opinions verbally rather than numerically, which adds subjectivity to the suggested integrated models. However, the authors have presented strategies to reduce subjectivity in circumstances involving decision-making. This methodology could be modified for more thorough study to account for a dynamic and unpredictable environment by adding other variables that impact change. This method improves the model’s resilience and makes it more applicable in real-world situations where uncertainty is common.

To verify the general validity of the findings, this research might be extended to certain supply chain scenarios in sectors including electronics, textiles, food, gas, and petroleum. Subsequent investigations may also examine the application of diverse decision-making instruments, like VIKOR, PROMETHEE, and GRA. A drawback of the suggested model is that it ignores subsystems related to criteria, which may reduce complexity. Despite significant efforts, choosing environmentally friendly suppliers is still a significant barrier in the environmental space. Further investigation should be conducted into the model’s ordering process for possible green suppliers. In future research, we plan also to delve into the exploration of how weight variations affect the outcomes and how the model can adapt to diverse supply chain environments. Additionally, we aim to investigate the integration of Pythagorean Fuzzy AHP with mathematical programming models such as DEA and compare its performance with that of artificial intelligence models such as genetic algorithms or neural network models. Then we will also be working on exploring in more detail how to quantify and evaluate each criterion, as well as how to integrate green supplier evaluations into the decision-making process.