*4.2. Fuzzy AHP-TOPSIS Methodology*

The analytic hierarchy process (AHP) was introduced by Saaty in 1990 [22]. Both numerical and subjective aspects were taken into account in the decision-making procedure. Given that AHP uses a discreet scale of 1 to 9, this technique is usually criticized because it does not include uncertainty during the decision-making procedure. The fuzzy-AHP approach has also been utilized in other disciplines to tackle multicriteria challenges. This method was used by Haq and Kannan [23] to choose the best supplier in a delivery chain. This was utilized by Huang et al. [24] for R&D shortlisting. For the selection of the most appropriate method of bridge building, Pan [25] employed this technique. For a staff-selection process, Güngör et al. [26] used this methodology. The fuzzy set theory, as developed by Zadeh, is a generalized variant of the classical set theory. It is an affiliate and assigns a grade of 1 to 10. In this paper, different types of EVs were classified using TOPSIS on the basis of characteristics [27].

In order to deal with uncertain numerical values in reality, Zadeh [34] invented fuzzy numbers. A fuzzy number is an amount for which a single-valued figure is not accurate, but imprecise. Classification of fuzzy numbers is a significant decision-making technique. Fuzzy decisions represent the effectiveness of different alternative models in the modeling of real-world situations by using fuzzy variables. Generally, a fuzzy-based approach is any system in which the variables vary over fuzzy values rather than real figures. These fuzzy values could reflect linguistic terms like "very small", "moderate", and so on, depending on how they are perceived in a specific scenario [35]. The defuzzification process is the technique of extracting a single value using the aggregated outcome of fuzzy numbers. This is used to convert the findings of fuzzy rules into a crisp output. In another word, defuzzification is accomplished through the use of a decision-making mechanism that determines the best crisp output from a fuzzy set.

A number of fuzzy criteria are used for a finite series of alternatives; i.e., the values of the alternatives are fuzzy figures. An additional process maps each m-tuple of fuzzy values into one fuzzy value, which is the alternative as per the entire set of criteria.

Let *A* = % *Ai <sup>i</sup>* = 1, . . . , *n* & be a finite group of possibilities for decision making, and let *K* = % *Kj <sup>j</sup>* = 1, . . . , *m* & be a finite group of fuzzy criteria, through which activity is regarded to be desirable. The estimates of the alternatives are fuzzy values. It must decide on this set of alternatives as a ranking challenge or decision problem. It is a two-stage technique:

(i) Compliance with all criteria aggregating judgments (fuzzy-numbers);

(ii) Ranking alternative decision making in relation to aggregating judgments.

In this research, two alternatives, the negative ideal solution (d−i) and positive ideal solution (d+i) were investigated. Further closeness coefficients (CCi) were calculated. We denoted CC−i as the degree of satisfaction in the i-th alternative and CC+i as the degree of gap in the i-th alternative. From a fuzzy collection of possible choices, we could evaluate which, as well as how, gaps must be closed in order to achieve ambitious goals and attain the ultimate findings. Closeness coefficients were used to rate all of the alternatives. Furthermore, CCi demonstrated the alternative closest to d+i and farthest from d−i. TOPSIS was determined by the choice of the ultimate solution or EVs that went beyond the perfect negative solution and were nearest to the ideal solution for the positive. The positive and the negative ideal solutions correspondingly had the highest advantages and lowest advantages. The final evaluations of the EVs were based on relative proximity to the optimal solution [28]. Figure 9 shows the integrated fuzzy AHP-TOPSIS methodology for the evaluation of different EVs.

**Figure 9.** The fuzzy AHP TOPSIS methodology for the evaluation of different EVs.
