## 4 Project Example Analysis
### Cloudification AHP Method to Determine the Subjective Weight of Risk Indicators  
According to the construction safety risk evaluation index system of the Yellow River bridge under study, the cloud model is used to improve the AHP method to carry out subjective weighting on each risk factor. In this paper, three experienced experts were invited to construct a comparison matrix of the relative importance of pairwise elements based on the improved cloud model scale, and the relative importance of the first-level and second-level indicators in the construction risk evaluation index system of the Yellow River bridge was analyzed. For comparison, the obtained comparison matrices are P1, P2, and P3. Due to space limitations, this article takes the first-level risk indicators and the second-level risk indicators under personnel risk B1 as examples. The results are summarized in Tables 5 and 6. We transformed the relative importance comparison matrix of the above risk indicators into a judgment matrix based on the cloud model scale and assembled the judgment matrix based on the cloud model scale constructed by three experts according to Formulas (6)-(8). The results are shown in Tables 7 and 8. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Risk**} & \multicolumn{3}{c}{**P1**} & \multicolumn{3}{c}{**P2**} & \multicolumn{3}{c}{**P3**} \\ \cline{2-13}  & **C1** & **C2** & **C3** & **C4** & **C1** & **C2** & **C3** & **C4** & **C1** & **C2** & **C3** & **C4** \\ \hline C1 & 1 & 3 & 2 & 1/2 & 1 & 3 & 3 & 1 & 1 & 4 & 2 & 1 \\ C2 & 1/3 & 1 & 1/3 & 1/4 & 1/3 & 1 & 2 & 1/3 & 1/4 & 1 & 1/4 & 1/2 \\ C3 & 1/2 & 3 & 1 & 1/3 & 1/3 & 1/2 & 1 & 1/4 & 1/2 & 4 & 1 & 1/3 \\ C4 & 2 & 4 & 3 & 1 & 1 & 3 & 4 & 1 & 1 & 2 & 3 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Relative importance comparison matrix of secondary indicators B1-C under personnel risk. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Risk**} & \multicolumn{3}{c}{**P1**} & \multicolumn{3}{c}{**P2**} & \multicolumn{3}{c}{**P3**} \\ \cline{2-13}  & **B1** & **B2** & **B3** & **B4** & **B1** & **B2** & **B3** & **B4** & **B1** & **B2** & **B3** & **B4** \\ \hline B1 & 1 & 1/4 & 1/3 & 1/2 & 1 & 1/4 & 1/4 & 1/3 & 1 & 1/3 & 1/2 & 1/2 \\ B2 & 4 & 1 & 2 & 3 & 4 & 1 & 3 & 4 & 3 & 1 & 2 & 3 \\ B3 & 3 & 1/2 & 1 & 3 & 4 & 1/3 & 1 & 4 & 2 & 1/2 & 1 & 3 \\ B4 & 2 & 1/3 & 1/3 & 1 & 3 & 1/4 & 1/4 & 1 & 2 & 1/3 & 1/3 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Relative importance comparison matrix of the first-level indicators A–B of the construction risk of the Yellow River Bridge. For the judgment matrix based on the scale of the cloud model assembled above, the multiplication operation and square root method of the cloud model are introduced, and the subjective weights of each first-level and second-level risk indicator are calculated by using Formulas (9)-(11) and in order to check the rationality of the above weight calculation, we use Formulas (12)-(14) to carry out the expected consistency test; the calculation results are shown in Tables 9 and 10. The expected consistency test in the calculation of the safety risk weight of the above-mentioned Yellow River bridge meets the requirements, and the comprehensive weights of each primary and secondary risk index can be obtained, as shown in Table 11. \begin{table}
\begin{tabular}{c c c} \hline
**Secondary Indicators** & **Subjective Weight \(\alpha(Ex_{i}^{0}.Ex_{i}^{0}.He_{i}^{0})\)** & **Judgment Matrix B1-C** \\  & & **Consistency Test** \\ \hline Personnel quality C1 & (0.331,0.334,0.334) & C.I. = 0.053 \\ Organizational completeness C2 & (0.115,0.118,0.118) & R.I. = 0.89 \\ Construction management efforts C3 & (0.158,0.154,0.154) & C.R. = 0.060 \textless{} 0.1 \\ Economic contract issues C4 & (0.396,0.393,0.393) & C.R. \\ \hline \end{tabular}
\end{table} 
Table 10: Subjective weight of secondary indicators under personnel risk B1.