## 4 Case Study
### Comparison and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Score**} & \multicolumn{6}{c}{**Ranking**} \\ \hline
**Platform** & **WSM** & **WPM** & **FAHP** & **WASPAS** & **Proposed** & **WSM** & **WPM** & **FAHP** & **WASPAS** & **Proposed** \\  & **Approach** & **Approach** & **Approach** & **Approach** & **Approach** & **Approach** & **Approach** & **Approach** & **Approach** & **Approach** \\ \hline P1 & 2.833 & 2.702 & 3.265 & 0.445 & 0.468 & 19 & 20 & 17 & 20 & 18 \\ P2 & 4.250 & 4.173 & 4.570 & 0.673 & 0.687 & 8 & 6 & 9 & 6 & 8 \\ P3 & 5.667 & 5.651 & 5.808 & 0.909 & 0.915 & 1 & 1 & 1 & 1 & 2 \\ P4 & 2.917 & 2.748 & 3.106 & 0.449 & 0.478 & 18 & 18 & 18 & 18 & 17 \\ P5 & 5.500 & 5.405 & 5.709 & 0.872 & 0.907 & 2 & 2 & 3 & 2 & 3 \\ P6 & 3.833 & 3.453 & 4.716 & 0.579 & 0.670 & 12 & 14 & 8 & 13 & 9 \\ P7 & 3.667 & 3.642 & 3.808 & 0.586 & 0.570 & 13 & 12 & 14 & 12 & 14 \\ P8 & 2.750 & 2.677 & 2.421 & 0.441 & 0.395 & 22 & 22 & 23 & 21 & 22 \\ P9 & 2.333 & 2.159 & 2.867 & 0.357 & 0.435 & 24 & 24 & 19 & 24 & 19 \\ P10 & 3.417 & 3.279 & 3.780 & 0.541 & 0.536 & 15 & 15 & 15 & 15 & 15 \\ P11 & 5.083 & 5.030 & 4.953 & 0.813 & 0.728 & 4 & 4 & 6 & 4 & 7 \\ P12 & 4.083 & 4.058 & 3.998 & 0.656 & 0.572 & 10 & 8 & 13 & 8 & 13 \\ P13 & 2.833 & 2.677 & 3.330 & 0.437 & 0.489 & 19 & 21 & 16 & 22 & 16 \\ P14 & 4.000 & 3.824 & 4.340 & 0.622 & 0.614 & 11 & 11 & 10 & 11 & 11 \\ P15 & 2.833 & 2.746 & 2.799 & 0.446 & 0.413 & 19 & 19 & 20 & 19 & 20 \\ P16 & 3.250 & 2.953 & 2.634 & 0.500 & 0.387 & 16 & 16 & 22 & 16 & 23 \\ P17 & 4.167 & 4.109 & 4.038 & 0.667 & 0.575 & 9 & 7 & 11 & 7 & 12 \\ P18 & 2.000 & 2.000 & 2.000 & 0.323 & 0.322 & 25 & 25 & 25 & 25 & 25 \\ P19 & 2.750 & 2.497 & 2.332 & 0.420 & 0.344 & 22 & 23 & 24 & 23 & 24 \\ P20 & 5.000 & 4.944 & 4.869 & 0.807 & 0.768 & 5 & 5 & 7 & 5 & 5 \\ P21 & 3.583 & 3.501 & 4.015 & 0.568 & 0.616 & 14 & 13 & 12 & 14 & 10 \\ P22 & 4.333 & 3.908 & 5.068 & 0.652 & 0.758 & 6 & 9 & 5 & 9 & 6 \\ P23 & 4.333 & 3.842 & 5.375 & 0.645 & 0.821 & 6 & 10 & 4 & 10 & 4 \\ P24 & 5.417 & 5.384 & 5.735 & 0.870 & 0.920 & 3 & 3 & 2 & 3 & 1 \\ P25 & 1.833 & 1.795 & 1.899 & 0.290 & 0.276 & 26 & 26 & 26 & 26 & 26 \\ P26 & 3.000 & 2.912 & 2.754 & 0.483 & 0.412 & 17 & 17 & 21 & 17 & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The ranking results obtained by four different algorithm approaches. (1) Handling of quantitative and qualitative information simultaneously  
The WSM, WPM, and typical WASPAS approach lack the ability to handle qualitative information problems. Conversely, both the proposed approach and the FAHP approach utilize the computational properties of the AHP to effectively quantify experts' subjective ratings of the evaluation criteria for complex decision-making problems. (2) Processing fuzzy semantic messages provided by experts  
The WSM, WPM, and typical WASPAS approach are confined to handling crisp information and cannot handle expert-provided fuzzy semantic messages. Both the proposed approach and the FAHP approach can consider the interval value of the fuzzy semantic messages simultaneously, including lower bound, center bound, and upper bound information, to allow for more objective consideration of fuzzy expert-provided information. (3) Simultaneously considering the characteristics of two arithmetic models  
The WSM, WPM, and FAHP approach rely solely on a single arithmetic model to rank the possible construction industry Internet platforms. These approaches are susceptible to data-specific biases. Conversely, both the proposed approach and the typical WASPAS approach leveraged the combination of WSM and WPM values to perform a corresponding ranking evaluation of possible alternatives, providing a more robust decision suggestion. (4) Handling of incomplete information  
When the assessment information of expert-provided data contains some unclear information, the WSM, WPM, FAHP, and typical WASPAS approaches struggle to handle the ambiguity, disregarding some useful information.