## 4 Case Study
### Solution of the Fuzzy Analytic Hierarchy Process Approach  
The FAHP approach combines the fuzzy set approach [11] and the typical AHP approach [3] to effectively navigate uncertain and fuzzy decision-making environments, providing more accurate and credible results. The FAHP approach could not handle the incomplete information provided by expert E4. Based on the data in Table 4, experts E1, E2, and E3 provided the aggregated information to establish the pairwise criteria comparison matrix. The calculation results are outlined in Table 6.  
According to Table 6, Equation (9) was used to defuzzify the TFN and to calculate the value of \(\lambda_{max}\) as 4.190. Equations (11) and (12) were used to calculate the values of CI and CR. The calculation process is as follows.  
\[\text{CI}=\frac{\lambda_{max-n}}{n-1}=\frac{4.190-4}{4-1}=0.063\]  
\[\text{CR}=\frac{\text{CI}}{\text{RI}}=\frac{0.063}{0.900}=0.070\]  
The CR value is \(<\)0.1 in the consistency test, which is considered acceptable. According to the data in Table 6, Equation (10) was used to calculate the weights of the four evaluation criteria (TM, UN, PF, and CS). The weight values are 0.335, 0.446, 0.139, and 0.080, respectively.  
Based on the data in Table 5, the four evaluation criteria weighted values and the aggregated value of the FAHP approach were calculated. The results are shown in Table 7.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Criteria** & **TM** & **UN** & **PF** & **CS** \\ \hline TM & (1.000, 1.000, 1.000) & (0.778, 0.883, 0.833) & (2.000, 2.333, 2.667) & (4.000, 5.000, 5.333) \\ UN & (1.333, 1.333, 1.667) & (1.000, 1.000, 1.000) & (3.333, 4.000, 4.667) & (4.000, 4.667, 5.667) \\ PF & (0.389, 0.444, 0.611) & (0.242, 0.306, 0.344) & (1.000, 1.000, 1.000) & (1.677, 1.677, 2.333) \\ CS & (0.194, 0.206, 0.261) & (0.178, 0.222, 0.261) & (0.444, 0.667, 0.667) & (1.000, 1.000, 1.000) \\ \hline \end{tabular}
\end{table}
Table 6: The pairwise comparison matrix of different criteria of the FAHP approach.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Platform**} & \multirow{2}{*}{**TM**} & \multirow{2}{*}{**UN**} & \multirow{2}{*}{**PF**} & \multirow{2}{*}{**CS**} & \multicolumn{2}{c}{**WSM Approach**} & \multicolumn{2}{c}{**WPM Approach**} \\ \cline{5-8}  & & & & & \(P_{i}^{1}\)**Value** & & **Rank** & \(P_{i}^{2}\)**Value** & **Rank** \\ \hline P13 & 2.667 & 4.333 & 2.667 & 1.667 & 2.833 & 19 & 2.677 & 21 \\ P14 & 3.667 & 5.000 & 5.000 & 2.333 & 4.000 & 11 & 3.824 & 11 \\ P15 & 2.667 & 2.667 & 4.000 & 2.000 & 2.833 & 19 & 2.746 & 19 \\ P16 & 1.667 & 2.333 & 5.333 & 3.667 & 3.250 & 16 & 2.953 & 16 \\ P17 & 4.667 & 3.333 & 5.000 & 3.667 & 4.167 & 9 & 4.109 & 7 \\ P18 & 2.000 & 2.000 & 2.000 & 2.000 & 2.000 & 25 & 2.000 & 25 \\ P19 & 1.667 & 2.000 & 5.000 & 2.333 & 2.750 & 22 & 2.497 & 23 \\ P20 & 6.000 & 4.000 & 4.667 & 5.333 & 5.000 & 5 & 4.944 & 5 \\ P21 & 4.333 & 4.333 & 3.000 & 2.667 & 3.583 & 14 & 3.501 & 13 \\ P22 & 4.667 & 6.000 & 5.000 & 1.667 & 4.333 & 6 & 3.908 & 9 \\ P23 & 4.667 & 7.000 & 4.000 & 1.667 & 4.333 & 6 & 3.842 & 10 \\ P24 & 6.000 & 6.000 & 4.667 & 5.000 & 5.417 & 3 & 5.384 & 3 \\ P25 & 1.333 & 2.333 & 2.000 & 1.667 & 1.833 & 26 & 1.795 & 26 \\ P26 & 2.667 & 2.667 & 2.333 & 4.333 & 3.000 & 17 & 2.912 & 17 \\ \hline \end{tabular}
\end{table}
Table 5: _Cont._