## 4 Case Study
### Solution of the Proposed Novel Fuzzy Analytic Hierarchy Process-Based Approach
\[\text{CI}=\frac{\lambda_{max-n}}{n-1}=\frac{4.202-4}{4-1}=0.067\]  
\[\text{CR}=\frac{\text{CI}}{\text{RI}}=\frac{0.067}{0.900}=0.075\]  
After confirming that the CR value was <0.1 in the consistency test, it was deemed acceptable. Based on the data in Table 9, Equation (8) was employed to calculate the weights of the four evaluation criteria (TM, UN, PF, and CS). The weighted values are 0.329, 0.453, 0.132, and 0.086, respectively. Step 7. Calculate the normalized value of the initial decision matrix. The initial decision matrix was normalized using Equation (11). Step 8. Calculate the value of WSM and WPM for different alternatives. According to the data in Step 7, Equations (13) and (14) were used to calculate the \(Q_{i}^{1}\) value and \(Q_{i}^{2}\) value, as shown in Table 10.  
According to the data in Step 9. Calculate the total relative importance of different alternatives. According to the data in Step 8, the value of \(\lambda\) was set to 0.5. Subsequently, Equation (15) was used to calculate the \(Q_{i}\) value, as expressed in Table 10.  
Step 10. Sort the \(Q_{i}\) value and provide decision-making suggestions. Sorting \(Q_{i}\) values from largest to smallest yields all possible alternative sorting results, as expressed in Table 10. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Platform** & **TM** & **UN** & **PF** & **CS** & \(Q_{i}^{1}\)**Value** & \(Q_{i}^{2}\)**Value** & \(Q_{i}\)**Value** & **Rank** \\ \hline P1 & 4.000 & 3.000 & 1.750 & 2.000 & 0.476 & 0.460 & 0.468 & 18 \\ P2 & 4.250 & 4.750 & 5.000 & 3.000 & 0.688 & 0.687 & 0.687 & 8 \\ P3 & 5.750 & 6.250 & 6.000 & 4.750 & 0.916 & 0.915 & 0.915 & 2 \\ P4 & 2.750 & 3.500 & 4.000 & 1.500 & 0.482 & 0.474 & 0.478 & 17 \\ P5 & 5.750 & 6.250 & 6.250 & 4.000 & 0.908 & 0.907 & 0.907 & 3 \\ P6 & 5.000 & 5.000 & 2.750 & 2.000 & 0.679 & 0.662 & 0.670 & 9 \\ P7 & 3.750 & 3.750 & 3.750 & 3.000 & 0.571 & 0.570 & 0.570 & 14 \\ P8 & 2.500 & 2.250 & 3.000 & 3.500 & 0.401 & 0.389 & 0.395 & 22 \\ P9 & 3.000 & 3.500 & 1.500 & 1.500 & 0.442 & 0.429 & 0.435 & 19 \\ P10 & 3.750 & 3.750 & 2.250 & 3.000 & 0.539 & 0.533 & 0.536 & 15 \\ P11 & 3.750 & 5.000 & 6.000 & 5.000 & 0.734 & 0.722 & 0.728 & 7 \\ P12 & 3.000 & 4.000 & 4.250 & 4.000 & 0.575 & 0.568 & 0.572 & 13 \\ P13 & 2.750 & 4.000 & 3.000 & 1.500 & 0.493 & 0.485 & 0.489 & 16 \\ P14 & 3.000 & 5.000 & 4.500 & 2.500 & 0.620 & 0.608 & 0.614 & 11 \\ P15 & 2.500 & 2.500 & 4.250 & 2.000 & 0.418 & 0.408 & 0.413 & 20 \\ P16 & 1.750 & 2.250 & 5.000 & 3.500 & 0.404 & 0.370 & 0.387 & 23 \\ P17 & 4.250 & 3.000 & 5.250 & 3.250 & 0.585 & 0.565 & 0.575 & 12 \\ P18 & 2.000 & 2.250 & 1.750 & 2.000 & 0.322 & 0.321 & 0.322 & 25 \\ P19 & 1.750 & 2.000 & 4.500 & 2.250 & 0.355 & 0.333 & 0.344 & 24 \\ P20 & 6.000 & 4.250 & 4.750 & 5.000 & 0.777 & 0.759 & 0.768 & 5 \\ P21 & 4.333 & 4.333 & 3.000 & 2.667 & 0.618 & 0.613 & 0.616 & 10 \\ P22 & 4.667 & 6.000 & 5.000 & 1.667 & 0.768 & 0.748 & 0.758 & 6 \\ P23 & 5.000 & 7.000 & 4.250 & 1.750 & 0.836 & 0.807 & 0.821 & 4 \\ P24 & 6.250 & 6.250 & 5.000 & 4.750 & 0.921 & 0.918 & 0.920 & 1 \\ P25 & 1.250 & 2.250 & 2.000 & 1.500 & 0.279 & 0.273 & 0.276 & 26 \\ P26 & 2.500 & 2.500 & 2.500 & 4.250 & 0.419 & 0.405 & 0.412 & 21 \\ \hline \end{tabular}
\end{table} 
Table 10: The \(Q_{i}^{1}\), \(Q_{i}^{2}\), and \(Q_{i}\) values of the proposed approach.