## 3 Proposed Model
### Prepare the defuzzified aggregated pairwise comparison matrices. * Develop fuzzy pairwise comparison matrices for each expert. In accordance with Table 2, the questionnaire results of each expert should be converted into triangular fuzzy numbers. For instance, the fuzzy pairwise comparison matrix of criteria for expert \(k\) is as follows: \[\mathbf{\tilde{W}}_{\mathbf{C}}^{k}= \begin{array}{cccc}\text{C1}&\text{C2}& \cdots&\text{CN}\\ \text{C2}&\begin{bmatrix}1&\tilde{a}_{12}^{k}&\cdots&\tilde{a}_{1N}^{k}\\ \tilde{a}_{21}^{k}&1&\cdots&\tilde{a}_{2N}^{k}\\ \vdots&\vdots&\tilde{a}_{ij}^{k}&\vdots\\ \text{CN}&\begin{bmatrix}\tilde{a}_{N1}^{k}&\tilde{a}_{N2}^{k}&\cdots&1\\ \end{bmatrix}\end{array} ,i=1,2,\ldots,N;j=1,2,\ldots,N\] (6) where \(\tilde{a}_{ij}^{k}\) is the pairwise comparison value between criterion \(i\) and \(j\) determined by expert \(k\). * Prepare fuzzy aggregated pairwise comparison matrices. Expert opinions are synthesized using the geometric mean method. For \(K\) experts, the geometric mean of the pairwise comparison values between criteria \(i\) and \(j\) is as follows: \[\tilde{f}_{ij}=(\tilde{a}_{ij}^{k}\otimes\cdots\otimes\tilde{a}_{ij}^{K})^{1/ k}=(l_{ij},m_{ij},u_{ij}),\,i=1,2,\ldots,N;j=1,2,\ldots,N\] (7) The fuzzy aggregated pairwise comparison matrix for the criteria is as follows: \[\mathbf{\tilde{W}}_{\mathbf{C}}=\begin{array}{cccc}\text{C1}&\text{C2}& \cdots&\text{CN}\\ \text{C1}& \begin{bmatrix}1&\tilde{f}_{12}&\cdots&\tilde{f}_{1N}\\ \tilde{f}_{21}&1&\cdots&\tilde{f}_{2N}\\ \vdots&\vdots&\tilde{f}_{ij}&\vdots\\ \tilde{f}_{N1}&\tilde{f}_{N2}&\cdots&1\end{bmatrix} ,i=1,2,\ldots,N;j=1,2, \ldots,N\] (8)
* Compute the defuzzified aggregated pairwise comparison matrices. Transform the fuzzy aggregated pairwise comparison matrices into defuzzified aggregated pairwise comparison matrices using the center of gravity method. \[f_{ij}=\frac{l_{ij}+m_{ij}+u_{ij}}{3},\,i=1,2,\ldots,N;j=1,2,\ldots,N\] (9) \begin{table}
\begin{tabular}{c c c} \hline
**Fuzzy Number** & **Linguistic Variable** & **Triangular Fuzzy Number** \\ \hline \(\tilde{1}\) & Equally important & \((1,1,1)\) \\ \(\tilde{3}\) & Moderately important & \((1,3,5)\) \\ \(\tilde{5}\) & Important & \((3,5,7)\) \\ \(\tilde{7}\) & Very important & \((5,7,9)\) \\ \(\tilde{9}\) & Extremely important & \((9,9,9)\) \\ \hline \end{tabular}
\end{table} 
Table 2: Fuzzy numbers for relative importance. \[\mathbf{W_{C}}= \begin{array}{ccccc}\text{C1}&\text{C2}&\cdots&\text{CN}\\ \text{C1}&1&f_{12}&\cdots&f_{1N}\\ \text{C2}&1/f_{12}&1&\cdots&f_{2N}\\ \vdots&\vdots&\vdots&f_{ij}&\vdots\\ \text{CN}&1/f_{1N}&1/f_{2N}&\cdots&1\end{array} ,i=1,2,\ldots,N;j=1,2,\ldots,N \tag{10}\]
* Obtain the importance vector of the criteria, importance vector of the sub-criteria, interdependence among the criteria, and interdependence among the sub-criteria. For instance, the importance vector for the defuzzified aggregated pairwise comparison for the criteria is as follows [49; 50]: \[\mathbf{W_{C}}\times\mathbf{w_{C}}=\lambda_{\text{max}}\times\mathbf{w_{C}}\] (11) where \(\mathbf{W_{C}}\) is the defuzzified aggregated comparison matrix for the criteria, \(w_{C}\) is the eigenvector, and \(\lambda_{\text{max}}\) is the largest eigenvalue of \(\mathbf{W_{C}}\). * Check the consistency of each defuzzified aggregated pairwise comparison matrix. The Consistency Index (CI) and Consistency Ratio (CR) for the defuzzified aggregated comparison matrix for the criteria are calculated using the following [49; 50]: \[\text{CI}_{C}=\frac{\lambda_{\text{max}}-N}{N-1}\] (12) \[\text{CR}_{C}=\frac{\text{CI}_{C}}{\text{RI}}\] (13) where RI is a Random Index [49; 50]. If the consistency ratio is greater than 0.1, there is an inconsistency and experts will need to revise part of the questionnaire. In such cases, the calculations will need to be carried out again. * Calculate the weights of the sub-criteria, \(\mathbf{s}_{j}\)
* Develop an unweighted supermatrix.