## 2 Materials and Methods
### Importance Analysis of Fuzzy TOPSIS-Based Alternatives  
In Section 2.1, we used the relative importance analysis methodology using a pairwise comparison-based Fuzzy AHP technique for the evaluation criteria. However, for the alternative evaluation, when the number of alternatives that participants need to respond to is large, the pairwise comparison evaluation can result in more questionnaire items, and thus, more insincere responses. As this study evaluates more than 20 alternatives, a pairwise comparison between each item is impossible. Consequently, we attempted to evaluate the alternatives using an absolute evaluation instead of a relative importance evaluation. For absolute evaluation, a classic AHP method can be utilized. However, the TOPSIS technique can also be applied as Fuzzy theory can be applied, as shown in Section 2.1, and rational choices can be induced by simultaneously considering the best and worst alternatives [73; 74; 75; 76]. In particular, the TOPSIS technique can simultaneously display the best and worst alternatives as real values, and it is possible to measure the performance of all alternatives from a multicriteria perspective. It also has the advantages of rational logic and calculation simplicity [77]. This study uses fuzzy language to solve the uncertainty problem of subjective and ambiguous linguistic information. Based on this, we used the Fuzzy TOPSIS technique, which combines the TOPSIS method to provide more accurate criterion weighting by considering the best and worst alternatives. The widely used TOPSIS method, proposed by [PERSON] and [PERSON], elects alternatives closest to the Positive Ideal Solution (PIS), and farthest from the Negative Ideal Solution (NIS) [78]. As this technique can induce rational choices by simultaneously considering the best and worst alternatives, it is facile to calculate evaluations of all alternatives from a multi-attribute perspective [73; 74; 75; 76]. The fuzzy scale is a 5-point scale utilized in the Fuzzy-AHP analysis. The fuzzification of alternatives per evaluation criterion aggregated from multiple evaluators is calculated in Equation (5), and the fuzzy weights are calculated in Equation (6) [79]. \[a_{ij}=min_{k}\Big{(}a_{ij}^{k}\Big{)},\;b_{ij}=\frac{1}{k}{\sum_{k=1}^{k}{b_{ ij}^{k}}},\;c_{ij}=max_{k}\Big{(}c_{ij}^{k}\Big{)} \tag{5}\]  
\[w_{j1}=min_{k}\Big{(}w_{j1}^{k}\Big{)},\;w_{j2}=\frac{1}{k}{\sum_{k=1}^{k}{w_{ j2}^{k}}},\;w_{j3}=max_{k}\Big{(}w_{j3}^{k}\Big{)} \tag{6}\]  
Then, the normalized fuzzy decision matrix \(\widetilde{R}=\Big{[}\widetilde{r_{ij}}\Big{]}\) (Equations (7) and (8)), and the fuzzy decision matrix \(\widetilde{V}=\Big{[}\widetilde{v_{ij}}\Big{]}\), \(v_{ij}=\widetilde{r_{ij}}\times w_{j}\) with the evaluation criteria weights (TFN) derived by Equation (4), can be calculated [79]. \[\widetilde{r_{ij}}=\Bigg{(}\frac{a_{ij}^{-}}{c_{ij}^{*}},\;\frac{b_{ij}}{c_{ j}^{*}},\;\frac{c_{ij}}{c_{j}^{*}}\Bigg{)}\;\text{and}\;c_{j}^{*}=max_{i} \big{(}c_{ij}\big{)}\;(benefit\;criteria) \tag{7}\]  
\[\widetilde{r_{ij}}=\Bigg{(}\frac{a_{j}^{-}}{c_{ij}},\;\frac{a_{j}^{-}}{b_{ij} },\;\frac{a_{j}^{-}}{a_{ij}}\Bigg{)}\;\text{and}\;c_{j}^{-}=min_{i}\big{(}a_{ ij}\big{)}\;(cost\;criteria) \tag{8}\]  
Next, the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) can be calculated as shown in Equations (9) and (10), respectively [79]. \[A^{*}=(\widetilde{v_{1}}^{\sim*},\;\widetilde{v_{2}}^{\sim*}\ldots,\;\widetilde {v_{n}}^{\sim*}),\;\text{where}\;\widetilde{v_{j}}^{\sim*}=max_{i}\big{(}v_{i \geqslant 3}\big{)} \tag{9}\]  
\[A^{-}=\big{(}\widetilde{v_{1}}^{\sim-},\;\widetilde{v_{2}}^{\sim-}\ldots,\; \widetilde{v_{n}}^{\sim-}\big{)},\;\text{where}\;\widetilde{v_{j}}^{\sim-}=min_ {i}\big{(}v_{i\geqslant 1}\big{)} \tag{10}\]  
Two TFN distance calculation methods suggested by [PERSON] were utilized to measure the FPIS and FNIS distances per alternative [80].