## 2 The Analytic Network Process
### Calculation of Weights in ANP Model  
Assuming an LNG storage tank leakage accident risk level as target element A, high-risk location, high-risk equipment, high-risk processes, high-risk personnel, and high-risk substances are respectively classified as B1, B2, B3, B4, and B5, and the secondary element is set to Cij (i = 1, 2,..., 5; j = 1, 2,... n). The judgment matrix is constructed using B1 to B5 as the criterion and Cij as the secondary criterion. R sets of expert scoring data S1,..., Sr obtained by expert scoring, and the overall standard deviation \(\sigma\)ij [19; 20] of the expert evaluations is calculated with Equation (1), see Equation (1). \[\sigma_{\bar{\mathrm{ij}}}=\sqrt{\frac{1}{\mathrm{r}-1}\sum_{k-1}^{\mathrm{r} }[\mathrm{b}_{\bar{\mathrm{ij}}}-\frac{1}{\mathrm{r}}\sum_{k-1}^{\mathrm{r}} \mathrm{b}_{\bar{\mathrm{ij}}}(k)]^{2}} \tag{1}\]  
All the \(\sigma_{\bar{\mathrm{ij}}}\) in the study are calculated to satisfy \(<\) 1, expert opinions are considered to be relatively uniform. The arithmetic mean of the expert ratings is used as the evaluation result of the group at this point. According to the correlation between different risk indicators, different risk factors are compared pairwise basis on a scale from 1 to 9. The comparison matrix between the two \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Age Group** & **Title** & **Working Years** & **Certificates** \\ \hline Expert 1 & 30–40 & Intermediate Engineer & 5 & Intermediate Certified Safety Engineer \\ Expert 2 & 40–45 & Intermediate Engineer & 8 & Intermediate Certified Safety Engineer; Safety evaluation engineer \\ Expert 3 & 45–50 & Deputy Senior Engineer & 15 & Intermediate Certified Safety Engineer \\ Expert 4 & 50–55 & Deputy Senior Engineer & 13 & Intermediate Certified Safety Engineer; Safety evaluation engineer \\ Expert 5 & 55–65 & Senior Engineer & 22 & Intermediate Certified Safety Engineer; Safety evaluation engineer \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relevant information of expert group. Figure 4: ANP structure model. indexes is constructed to obtain 5 first-level index judgment matrices and 52 second-level index judgment matrices, and consistency ratios CR of the calculated judgment matrices are used to conduct the consistency analysis to ensure that the CR of all judgment matrices are less than the acceptable level (0.1) [25]. Cluster for high-risk locations as an example, the results are shown in Table 3.  
The degree of association of first-level indicators is shown in Table 4.  
According to the judgment matrix of second-level indicators constructed above, the Super Decision software automatically generates the correlation degree of secondary indicators. Due to a large number of secondary indicators, in order to show the correlation between indicators more intuitively, the degree of association of second-level indicators is shown in Figure 5. The blocks in the figure gradually change from blue to yellow according to the increasing degree of association between the secondary indicators. The unweighted super matrix Aij is constructed from the ranking vector obtained by the characteristic root method,  
\[\text{Aij}= \begin{bmatrix}\text{a}_{11}&\text{a}_{12}&\cdots&\text{a}_{1n}\\ \text{a}_{21}&\text{a}_{22}&\cdots&\text{a}_{2n}\\ &&\vdots&\vdots\\ \text{a}_{51}&\text{a}_{52}&\cdots&\text{a}_{5n}\end{bmatrix}  \tag{2}\]  
The super matrix Aij was derived by a pairwise comparison of the elements, so the column vector is the sort vector degree to which the elements Ci1\(\sim\)Cin in the elements of the element set Bi are affected by the elements Ci1\(-\)Cin in the element set Bi. Specifically, if the elements in Bi are not affected by Bi, then aij = 0 [26]. The five calculated non-negative super matrices are normalized to obtain the weighted super matrix Wij. \[\text{Wij}= \begin{bmatrix}\text{W}_{11}&\text{W}_{12}&\cdots&\text{W}_{1n}\\ \text{W}_{21}&\text{W}_{22}&\cdots&\text{W}_{2n}\\ &&\vdots&\vdots\\ \text{W}_{51}&\text{W}_{52}&\cdots&\text{W}_{5n}\end{bmatrix}