## 4 Case Study
### Obtain the Decision Matrix and Its Normalization  
1. Convert evaluation information into a cloud  
Suppose the linguistic evaluation term set is \(S=\{s_{0}\): poor, \(s_{1}\): fair, \(s_{2}\): moderate, \(s_{3}\): excellent, \(s_{4}\): outstanding}, where the universe is [0, 1]. According to Equation (4), five evaluation clouds can be generated, as shown in Table 4.
2. Calculate the expert weight  
In the case study, six experts form the expert group. The evaluation criteria [39] for the RRS include effectiveness (\(Z_{1}\)), technical feasibility (\(Z_{2}\)), economically reasonable (\(Z_{3}\)), and quick response (\(Z_{4}\)). According to the linguistic evaluation term set \(S\), the initial evaluation language values of each expert with respect to every criterion are collected, as shown in Table 5. In Table 5, poor, fair, moderate, excellent, and outstanding are represented by P, F, M, E, and O, respectively. Based on the transformation of linguistic evaluation variables and cloud models (Table 4), evaluation information shown in Table 5 is converted into cloud models. Then, combined with Equation (6), the AAC can be calculated, as shown in Table 6.  
According to Equations (5) and (7), the similarity between the evaluation cloud of the single expert and the AAC of the expert group is calculated and further normalized by Equation (8). The expert weights are obtained: \begin{table}
\begin{tabular}{c c c} \hline \hline
**Linguistic Variables** & **Cloud Models** & **Digital Features of Clouds** \\ \hline Poor (P) & \(s_{0}\) & (0, 0.083, 0.001) \\ Fair (F) & \(s_{1}\) & (0.25, 0.083, 0.001) \\ Moderate (M) & \(s_{2}\) & (0.5, 0.083, 0.001) \\ Excellent (E) & \(s_{3}\) & (0.75, 0.083, 0.001) \\ Outstanding (O) & \(s_{4}\) & (1, 0.083, 0.001) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Transformation of linguistic evaluation variables and cloud models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{3}{c}{**Number**} \\ \cline{2-4}  & \(\mathbf{O_{1}}\) & \(\mathbf{O_{2}}\) & \(\mathbf{O_{3}}\) & \(\mathbf{O_{4}}\) \\ \hline Horizontal drainage pipes & \(\surd\) & & \\ \hline Radiant wells & & \(\surd\) & & \\ \hline Implementation of seepage control measures & \(\surd\) & & \(\surd\) & \(\surd\) \\ \hline Development of a safety management system for drainage facilities & & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Risk reduction schemes. \[v_{ij}^{1}=\left[ \begin{array}{ccccc}0.148&0.167&0.152&0.164\\ 0.178&0.167&0.183&0.163\\ 0.173&0.178&0.166&0.164\\ 0.167&0.167&0.164&0.163\end{array} \right] \tag{16}\]  
\[v_{ij}^{2}=\left[ \begin{array}{ccccc}0.176&0.167&0.152&0.169\\ 0.178&0.167&0.183&0.170\\ 0.184&0.178&0.166&0.169\\ 0.167&0.167&0.169&0.170\end{array} \right] \tag{17}\]  
\[v_{ij}^{3}=\left[ \begin{array}{ccccc}0.176&0.166&0.200&0.164\\ 0.178&0.166&0.156&0.170\\ 0.184&0.178&0.167&0.164\\ 0.166&0.166&0.164&0.170\end{array} \right] \tag{18}\]  
\[v_{ij}^{4}=\left[ \begin{array}{ccccc}0.176&0.166&0.200&0.169\\ 0.110&0.166&0.183&0.163\\ 0.184&0.110&0.167&0.169\\ 0.166&0.166&0.169&0.163\end{array} \right] \tag{19}\]  
\[v_{ij}^{5}=\left[ \begin{array}{ccccc}0.176&0.167&0.148&0.169\\ 0.178&0.167&0.156&0.170\\ 0.145&0.178&0.167&0.169\\ 0.167&0.167&0.169&0.170\end{array} \right] \tag{20}\]  
\[v_{ij}^{6}=\left[ \begin{array}{ccccc}0.148&0.167&0.148&0.165\\ 0.178&0.167&0.139&0.164\\ 0.130&0.178&0.167&0.165\\ 0.167&0.167&0.165&0.164\end{array} \right] \tag{21}\]