## 4 Case Study
### Comparative Analysis of Decision-Making Methods  
To test the accuracy and superiority of the proposed decision-making method, the proposed method is compared with the method proposed by [PERSON] et al. [43].  
The method proposed by [PERSON] et al. [43] is applied to the case study TSF presented in this paper; the ranking result is \(O_{4}=O_{2}>O_{3}>O_{1}\). The ranking result is different from the case generated, but the optimal RRS within both results is scheme \(O_{4}\). Therefore, the correctness of the proposed approach can be proven. However, the ranking order of schemes \(O_{2}\) and \(O_{4}\) are the same, which means that scheme \(O_{2}\) is also optimal. Indeed, scheme \(O_{2}\) does not take management measures into account compared with scheme \(O_{4}\). As for this, the proposed method is compared with the method proposed by [PERSON] et al. [43]. Several advantages of the proposed method are shown as follows:  
Figure 5: The radar plot of sensitivity analysis results for coefficient \(\theta\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**RRS** & \multicolumn{4}{c}{\(\tau_{i}\)} & \multicolumn{2}{c}{**Rank**} \\ \cline{2-6} \(O_{i}\) & \(O_{1}\) & \(O_{2}\) & \(O_{3}\) & \(O_{4}\) & \\ \hline \(\theta=0.2\) & 0 & 1 & 0.462 & 0.999 & \(O_{2}>O_{4}>O_{3}>O_{1}\) \\ \(\theta=0.4\) & 0 & 0.995 & 0.454 & 1 & \(O_{4}>O_{2}>O_{3}>O_{1}\) \\ \(\theta=0.6\) & 0 & 0.988 & 0.445 & 1 & \(O_{4}>O_{2}>O_{3}>O_{1}\) \\ \(\theta=0.8\) & 0 & 0.980 & 0.435 & 1 & \(O_{4}>O_{2}>O_{3}>O_{1}\) \\ \(\theta=1\) & 0 & 0.972 & 0.425 & 1 & \(O_{4}>O_{2}>O_{3}>O_{1}\) \\ \(\theta=2\) & 0 & 0.919 & 0.357 & 1 & \(O_{4}>O_{2}>O_{3}>O_{1}\) \\ \(\theta=3\) & 0 & 0.832 & 0.246 & 1 & \(O_{4}>O_{2}>O_{3}>O_{1}\) \\ \(\theta=4\) & 0 & 0.666 & 0.033 & 1 & \(O_{4}>O_{2}>O_{3}>O_{1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Overall dominance degrees and ranking orders of RRSs with various values of \(\theta\).  
1. For the same scheme concerning different evaluation criteria, different experts may hold different risk attitudes and appetites due to various experiences in their fields. The comprehensive weighted cloud is used to integrate the evaluation information of the experts in this paper. However, the method of [PERSON] et al. [43] ignores the differences generated from the expert group.
2. The linguistic variables provided by experts are transformed into a cloud model. The cloud model can present and consider the fuzziness, uncertainty, and randomness of qualitative concepts; as a result, the loss of the evaluation information is effectively reduced. Consequently, the ranking results can be more reasonable. But, [PERSON] et al. [43] used Fermatean fuzzy sets to quantify linguistic variables, which may lead to information deviation and inaccurate and unfavorable ranking results.
3. The TODIM method used in this paper considers the DMs' psychological behavior, in which the discrimination degree in ranking results is relatively higher. The Fermatean fuzzy TOPSIS method proposed by [PERSON] et al. [43] fails to take into account the psychological behavior of DMs, which is not in accordance with reality.  
To summarize, the ranking result obtained by the proposed method, \(O_{4}>O_{2}>O_{3}>O_{1}\), is more accurate and credible than the ranking result of [PERSON] et al. [43].