# Fire Risk Assessment of Urban Utility Tunnels Based on Improved Cloud Model and Evidence Theory
## 4 Instance Verification
### Determining Membership Degree of Indicator Level Based on the Improved Cloud Model  
The cloud model solution process is mainly divided into two steps. (1) Calculate the cloud numerical characteristics parameters of indicators at different levels, generate cloud maps through the cloud forward generator, and obtain the level normal cloud model of evaluation indicators. (2) Substitute the quantitative data of indicators into the cloud model to obtain the membership degree of index level. Taking the indicator \"fire routine inspection \(C_{20}\)\" as an example, according to the five risk level intervals and the indicator risk assessment value divided in this paper, the level boundary is treated as a double constraint space \([C_{\min},C_{\max}]\). The cloud numerical features \((E_{x},E_{n},H_{e})\) after cloud entropy optimization based on traditional cloud entropy algorithm and Equations (1)-(4) are solved, respectively. The results are shown in Table 4.  
As can be seen from Table 4, under different risk levels, when the range of the hierarchical boundary \([C_{\min},C_{\max}]\) is the same, the entropy values obtained by the traditional algorithm \(E_{n}\) are constant. The entropy values calculated based on the \"\(3E_{n}\)\" rule are smaller, while the entropy values calculated based on the \"50% correlative degree\" rule are larger. Additionally, the cloud entropy algorithm is not only related to the hierarchical boundary interval but also considers the actual situation of the evaluation indicators. So, the entropy value \(E_{n}\) under different risk levels changes dynamically and is more reasonable. Based on the cloud numerical feature parameters of indicator \(C_{20}\), cloud maps were generated by the forward cloud generator to obtain the hierarchical normal cloud models of indicator \(C_{20}\) under three different algorithms, as shown in Figures 1-3. By comparing Figures 1-3, it can be seen that the hierarchical boundaries of the cloud map of the \"\(3E_{n}\)\" rule are relatively clear. In contrast, the \"50% correlative degree\" rule is relatively vague. The cloud map based on the cloud entropy optimization algorithm considers the hierarchical division's clarity and fuzziness. Therefore, the improved cloud model results are more realistic in reflecting the subordinate distribution of risk levels. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Indicator \(C_{20}\)**} & \multirow{2}{*}{**The \"3E\({}_{n}\)\" Rule**} & **The \"50\%** & **Cloud Entropy** \\  & & **Correlative Degree”** & **Optimization** \\  & & **Rule** & **Algorithm** \\ \hline I & (1, 0.3333, 0.03333) & (1, 0.8493, 0.08493) & (1, 0.5394, 0.05394) \\ II & (3, 0.3333, 0.03333) & (3, 0.8493, 0.08493) & (3, 0.4633, 0.04633) \\ III & (5, 0.3333, 0.03333) & (5, 0.8493, 0.08493) & (5, 0.5610, 0.05610) \\ IV & (7, 0.3333, 0.03333) & (7, 0.8493, 0.08493) & (7, 0.7642, 0.07642) \\ V & (9, 0.3333, 0.03333) & (9, 0.8493, 0.08493) & (9, 0.5535, 0.05535) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cloud digital characteristic parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Indicators**} & **Expert 1** & **Expert 2** & **Expert 3** & **Expert 4** & **Expert 5** & **Average Value** \\ \hline Personnel working status \(C_{17}\) & 2 & 2 & 3 & 3 & 2 & 2.4 \\ Fire control management system \(C_{18}\) & 1 & 2 & 1 & 3 & 2 & 1.8 \\ Fire education training \(C_{19}\) & 4 & 5 & 4 & 3 & 4 & 4.0 \\ Routine fire inspection \(C_{20}\) & 5 & 7 & 6 & 6 & 5 & 5.8 \\ Fire emergency planning \(C_{21}\) & 6 & 5 & 4 & 5 & 6 & 5.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(Cont.\)Figure 1: Hierarchical normal cloud model based on the \"\(3E_{n}\)\" rule. Figure 3: Hierarchical normal cloud model based on cloud entropy optimization. Figure 2: Hierarchical normal cloud model based on the \"50% correlative degree\" rule.