# Operation Risk Assessment of Urban Dense Cable Passageway Based on Fuzzy-Analytic Hierarchy Process
## 3 Operational Risk Assessment Methodology for Urban Dense Cable Corridors
The comprehensive judgment result vector is obtained from the indicator weight vector and fuzzy evaluation matrix as shown in Equation (13). \[E_{i}=B_{i}^{T}\cdot R_{i} \tag{13}\]  
where \(E_{i}\) is the vector of integrated judgment results for the indicator layer corresponding to the \(i\)-th criterion layer, and \(E_{i}\) is normalized. \[E_{i}^{\prime}=\left(e_{i1}^{\prime},e_{i2}^{\prime},\ldots e_{ik}^{\prime} \right)=\left(e_{i1}/T_{i^{\prime}},e_{i2}/T_{i^{\prime}},\ldots,e_{ik}/T_{i}\right) \tag{14}\]  
\[T_{i}=\sum_{j=1}^{k}e_{ij} \tag{15}\]  
Therefore, a fuzzy scheme judgment matrix for the indicator layer can be obtained, as shown in Equation (16). \[Z=\left(z_{1},z_{2},\ldots,z_{k}\right)=H^{\text{T}}\cdot\left(E_{1}^{\prime},E_{2}^{\prime},E_{3}^{\prime}\right)^{\text{T}} \tag{16}\]  
\[H=\left(h_{1},h_{2},h_{3}\right)^{\text{T}} \tag{17}\]  
where \(Z\) is the fuzzy scheme judgment matrix for the indicator layer. Assigning \(q_{i}\) to the rubric \(v_{i}\) transforms the composite judgment result vector into an assessment value. \[S_{\text{total}}=\sum_{i=1}^{k}z_{i}q_{i} \tag{18}\]  
where \(S_{\text{total}}\) is the percentile score of the fuzzy-hierarchical analysis-based operational risk assessment method for urban dense cable channels. When the value of \(S_{\text{total}}\) is greater than 70, it indicates that the proposed scheme is feasible; otherwise, the judgment matrix \(A\) and the fuzzy evaluation matrix \(R\) are reconstructed. Therefore, the corresponding weight values for each of the 18 elements of the indicator layer are shown below. \[Q_{1}=h_{1}B_{1} \tag{19}\]  
\[Q_{2}=h_{2}B_{2} \tag{20}\]  
\[Q_{3}=h_{3}B_{3} \tag{21}\]  
where \(Q_{1}\) is the weight corresponding to the six indicators in the cable body risk parameter, \(Q_{2}\) is the weight corresponding to the six indicators in the cable channel risk parameter, and \(Q_{3}\) is the weight corresponding to the six indicators in the cable channel external environment risk parameter. In the risk assessment of urban dense cable channel operation, 18 indicators of cable body risk parameters, cable channel risk parameters, and cable channel external environment risk parameters are monitored, and the two-point method is used for data statistics. When the indicator has no risk, it is recorded as 0, and when the indicator has risk, it is recorded as 1. The 18 indicators counted are multiplied with the corresponding weights and summed to obtain the score \(F\) of the risk assessment result of the operation of the urban dense cable channel. The specific judging criteria are as follows. 1. Risk assessment criteria for common lines: \[\left\{ \begin{aligned} 0\leq F\leq 0.2,&\text{ Low risk}\\ 0.2<F\leq 0.3,&\text{ Average risk}\\ 0.3<F\leq 0.5,&\text{ Medium risk}\\ 0.5<F\leq 1,&\text{ High risk}\\ \end{aligned} \right.\] (22)
2. Risk assessment criteria for critical lines: \[\left\{ \begin{aligned} 0\leq F\leq 0.2,&\text{ Low risk}\\ 0.2<F\leq 0.4,&\text{ Medium risk}\\ 0.4<F\leq 1,&\text{ High risk}\\ \end{aligned} \right.\] (23)  
For the risk assessment to put forward targeted maintenance recommendations based on the fuzzy-hierarchical analysis method of urban dense cable channel operation risk assessment, the flow chart is shown in Figure 3.