## 3 Methodology
### Composited Group Decision-Making Approach  
#### 3.2.1 Super-Efficiency Slack-Based Model (Super-SBM)  
In 1978, DEA was first introduced as a method to measure the relative efficiency of decision-making units (DMUs) [37]. DMUs can be companies, organizations, etc., that can take multiple inputs and convert them to different outputs. Over the years, the development of different models in DEA has evolved and is widely adopted by researchers in many fields around the world [38]. The first model is the CCR model (Charnes, Cooper and Rhodes), followed by the BBC model ([PERSON], Charnes and Cooper) [39]. In 2001, [PERSON] developed a slack-based performance measure (SBM) to evaluate the efficiency (\(\rho_{1}\)) of \(DMU_{k}\) in \(n\) DMUs with \(s\) output and \(m\) inputs, according to Equation (19) [40]:  
\[\begin{array}{c}min\ \rho_{1}=\frac{1-\frac{1}{n}\sum_{i=1}^{m}\frac{s_{i}^{-} }{s_{ik}}}{1+\frac{1  
\[\text{where}\ \sum_{k=1}^{K}\Psi_{k}=1\ \text{and}\ 0\leq\ \theta_{\widetilde{Q^{k}}}^{2}+ \mu_{\widetilde{Q^{k}}}^{2}+\pi_{\widetilde{Q^{k}}}^{2}\leq 1\]  
Step 2. Decision makers define evaluation criteria \((j=1\dots J)\) based on expertise, experience, and references. Then, decision makers provide pairwise comparisons in the form of linguistic terms about the influence among criteria. As shown in the scale presented in Table 3, pairwise comparisons are converted to SFNs. As a result, the individual SF direct-influence matrices are established. The individual SF direct-influence matrix of \(k\)th decision maker \((\widetilde{A}^{k})\) is represented as Equation (23). \[\widetilde{A}^{k}= \begin{bmatrix}\widetilde{a}_{11}^{k}&\widetilde{a}_{12}^{ k}&\cdots&\widetilde{a}_{1J}^{k}\\ \widetilde{a}_{21}^{k}&\widetilde{a}_{22}^{k}&\cdots&\widetilde{a}_{2J}^{k} \\ \vdots&\vdots&\ddots&\vdots\\ \widetilde{a}_{J1}^{k}&\widetilde{a}_{J2}^{k}&\cdots&\widetilde{a}_{JJ}^{k} \end{bmatrix} \text{with}\ \widetilde{a}_{jp}^{k}=\left(\theta_{\widetilde{x}_{jp}^{k}},\mu_{ \widetilde{x}_{jp}^{k}},\ \pi_{\widetilde{x}_{jp}^{k}}\right);j=1\dots J,p=1\dots J \tag{23}\]  
Step 3. To aggregate individual matrices, the spherical weight arithmetic mean is used with decision makers' weights \((\Psi_{k})\), as described in Equation (7). Hence, the SF direct-influence matrix \(\left(\widetilde{A}\right)\) is established, as represented in Equation (24). \[\widetilde{A}= \begin{bmatrix}\widetilde{a}_{11}&\widetilde{a}_{12}&\cdots& \widetilde{a}_{1J}\\ \widetilde{a}_{21}&\widetilde{a}_{22}&\cdots&\widetilde{a}_{2J}\\ \vdots&\vdots&\ddots&\vdots\\ \widetilde{a}_{11}&\widetilde{a}_{J2}&\cdots&\widetilde{a}_{JJ}\end{bmatrix}  \text{with}\ \widetilde{a}_{jp}=\left(\theta_{\widetilde{a}_{jp}},\mu_{ \widetilde{a}_{jp}^{k}},\ \pi_{\widetilde{a}_{jp}}\right);j=1\dots J,p=1\dots J \tag{24}\]  
Step 4. To construct the SF initial direct-influence submatrices, the SF direct influence matrix is separated into three submatrices corresponding to the three parameters of spherical fuzzy, as represented in Equation (25). Then, the submatrices are normalized according to Equations (26)-(28). \[A^{\theta}= \begin{bmatrix}\theta_{\widetilde{a}_{11}}&\theta_{\widetilde{a}_ {12}}&\cdots&\theta_{\widetilde{a}_{1J}}\\ \theta_{\widetilde{a}_{21}}&\theta_{\widetilde{a}_{22}}&\cdots&\theta_{ \widetilde{a}_{2J}}\\ \vdots&\vdots&\ddots&\vdots\\ \theta_{\widetilde{a}_{J1}}&\theta_{\widetilde{a}_{J2}}&\cdots&\theta_{ \widetilde{a}_{JJ}}\end{bmatrix} ,A^{\pi}= \begin{bmatrix}\mu_{\widetilde{a}_{11}} &\mu_{\widetilde{a}_{12}}&\cdots&\mu_{\widetilde{a}_{1J}}\\ \mu_{\widetilde{a}_{21}}&\mu_{\widetilde{a}_{22}}&\cdots&\mu_{\widetilde{a}_{ 2J}}\\ \vdots&\vdots&\ddots&\vdots\\ \pi_{\widetilde{a}_{11}}&\pi_{\widetilde{a}_{22}}&\cdots&\pi_{\widetilde{a}_{ 2J}}\end{bmatrix} ,A^{\pi}=