## 3 Methodology
### Spherical Fuzzy DEMATEL-EDAS Method  
To evaluate the interrelationships of factors in complex systems, the DEMATEL method was initially proposed by [PERSON] and [PERSON] [48]. A systematic review of MCDM studies found that the DEMATEL method is increasingly used in the role of weighting criteria. In terms of prioritizing alternatives, distance-based evaluation methods, such as TOPSIS or EDAS, are applied effectively with high frequency [8]. Moreover, fuzzy variations of MCDM methods are introduced and proposed more and more widely. Therefore, this study proposes a spherical fuzzy extension of the integration approach composed by DEMATEL and EDAS, named SF DEMATEL-EDAS, for the first time. The proposed approach includes the following steps:  
_Step 1: Identify experts and criteria_In this step, a group of experts \((k=1,\ 2,\ldots,K)\) with experience and a high level of expertise in the research field is selected. Then, the evaluation criteria \((j=1,\ 2,\ldots,J)\) are determined according to previous studies and expert contributions. _Step 2: Prioritize experts_  
The weights of experts are calculated because of the difference in their experience, knowledge, and expertise level. Let the expertise of the \(kth\) expert be expressed as a spherical fuzzy number (SFN) \(\widetilde{A}_{k}=(\alpha_{k},\ \beta_{k},\gamma_{k})\). The crisp weight of the \(kth\) expert can be calculated as Equation (23) [49]. \[ \begin{split}\theta_{k}&=\frac{1-\sqrt{\left(\left(1 -\alpha_{k}^{2}\right)+\beta_{k}^{2}+\gamma_{k}^{2}\right)/3}}{\sum_{k}\left(1 -\sqrt{\left(\left(1-\alpha_{k}^{2}\right)+\beta_{k}^{2}+\gamma_{k}^{2}\right) /3}\right)}\\ \text{where}\\ &\qquad\qquad\qquad\qquad\sum_{k=1}^{K}\theta_{k}=1\\ &\qquad\qquad\qquad\qquad\qquad\text{and}\\ 0\leq\ \alpha_{k}^{2}+\beta_{k}^{2}+\gamma_{k}^{2}\leq 1 \end{split}  \tag{23}\]  
_Step 3: Construct the individual direct influence matrices_  
The experts provide linguistic pairwise comparisons of the influence between the evaluation criteria. These linguistic pairwise comparisons were then converted to the respective SFNs as shown in Table 2[50]. The individual direct influence matrix of the \(kth\) expert is represented by \(U^{k}=\left[\widetilde{u}_{jl}^{k}\right]_{\gamma k\gamma}=\left[\left(\alpha _{jl}^{k},\beta_{jl}^{k},\gamma_{jl}^{k}\right)\right]_{\gamma k\gamma}\). _Step 4: Construct the aggregated direct influence matrix_  
The aggregated direct influence matrix is constructed by aggregating the matrices of the experts. This aggregation process applies the spherical weight arithmetic mean SWAM according to Equation (14). The aggregated direct influence matrix of the \(kth\) expert is represented by \(U^{s}=\left[\widetilde{u}_{jl}^{s}\right]_{\gamma k\gamma}=\left[\left(\alpha _{jl}^{s},\beta_{jl}^{s},\gamma_{jl}^{s}\right)\right]_{\gamma k\gamma}\). _Step 5: Construct the initial direct influence submatrices_  
To normalize the aggregated direct influence matrix, it is split into three submatrices corresponding to each parameter of the SFS. These submatrices are represented by \(U^{a}=\left[\alpha_{jl}^{s}\right]_{\gamma k\gamma}\), \(U^{\beta}=\left[\beta_{jl}^{s}\right]_{\gamma k\gamma}\) and \(U^{\gamma}=\left[\gamma_{jl}^{s}\right]_{\gamma k\gamma}\). Then, the normalized submatrices are calculated as Equations (24)-(26). \[V^{a}=s^{a}\times U^{a}\text{, where }s^{a}=min\left(\frac{1}{\max_{j}\sum_{l=1}^ {J}\alpha_{il}^{s}},\frac{1}{\max_{l}\sum_{j=1}^{J}\alpha_{il}^{s}}\right) \tag{24}\]  
\[V^{\beta}=s^{\beta}\times U^{\beta}\text{, where }s^{\beta}=min\left(\frac{1}{ \max_{j}\sum_{l=1}^{J}\beta_{il}^{s}},\frac{1}{\max_{l}\sum_{j=1}^{J}\beta_{il }^{s}}\right) \tag{25}\]  
\[V^{\gamma}=s^{\gamma}\times U^{\gamma}\text{, where }s^{\gamma}=min\left(\frac{1}{ \max_{j}\sum_{l=1}^{J}\gamma_{il}^{s}},\frac{1}{\max_{l}\sum_{j=1}^{J}\gamma_{ il}^{s}}\right) \tag{26}\]  
\begin{table}