# Operation Risk Assessment of Urban Dense Cable Passageway Based on Fuzzy-Analytic Hierarchy Process
## 4 Calculation Results and Analysis
\begin{pmatrix}0.4&0.3&0.1&0.2\\ 0.3&0.4&0.1&0.2\\ 0.2&0.3&0.3&0.2\\ 0.2&0.1&0.4&0.3\\ 0.5&0.3&0.1&0.1\\ 0.2&0.1&0.3&0.4\end{pmatrix}  \tag{33}\]  
\[R_{2}= \begin{pmatrix}0.1&0.3&0.4&0.2\\ 0.1&0.3&0.4&0.2\\ 0.1&0.2&0.2&0.5\\ 0.4&0.3&0.2&0.1\\ 0.2&0.4&0.3&0.1\\ 0.2&0.3&0.4&0.1\end{pmatrix}  \tag{34}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Standardized Layer** & **Indicator Layer** & **Low Risk** & **Average Risk** & **Medium Risk** & **High Risk** \\ \hline \multirow{6}{*}{Cable body risk parameters} & Overheating of cables & 0.4 & 0.3 & 0.1 & 0.2 \\  & Ageing of cables and accessories & 0.3 & 0.4 & 0.1 & 0.2 \\  & Overloaded operation & 0.2 & 0.3 & 0.3 & 0.2 \\  & Mechanical damage & 0.2 & 0.1 & 0.4 & 0.3 \\  & Grounding issues & 0.5 & 0.3 & 0.1 & 0.1 \\  & Chemical corrosion factors & 0.2 & 0.1 & 0.3 & 0.4 \\ \hline \multirow{6}{*}{Cable channel risk parameters} & Blocked or poorly ventilated passageways & 0.1 & 0.3 & 0.4 & 0.2 \\  & Cable channel overcapacity & 0.1 & 0.3 & 0.4 & 0.2 \\  & High and low voltage with channel laying & 0.1 & 0.2 & 0.2 & 0.5 \\  & Irregular cable laying & 0.4 & 0.3 & 0.2 & 0.1 \\  & Defective access facilities & 0.2 & 0.4 & 0.3 & 0.1 \\  & Fire hazard & 0.2 & 0.3 & 0.4 & 0.1 \\ \hline \multirow{6}{*}{Risk parameters for the environment outside the cableway} & Proximity to oil and gas pipelines & 0.3 & 0.4 & 0.2 & 0.1 \\  & Groundwater level and humidity & 0.1 & 0.1 & 0.3 & 0.5 \\ \cline{1-1}  & Risk of external damage & 0.1 & 0.2 & 0.3 & 0.4 \\ \cline{1-1}  & Improper maintenance & 0.5 & 0.2 & 0.2 & 0.1 \\ \cline{1-1}  & Transportation and building construction & 0.2 & 0.3 & 0.2 & 0.3 \\ \cline{1-1}  & Urban climatic conditions & 0.4 & 0.2 & 0.2 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Indicator scoring of the methodology for operational risk assessment of urban dense cable corridors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Judgment Matrix** & **Maximum Eigenvalue** & _CI_ & _CR_ & **Calibration Result** \\ \hline \(A_{1}\) & 3.0037 & 0.0018 & 0.0032 & Pass \\ \(A_{2}\) & 6.1225 & 0.0245 & 0.0198 & Pass \\ \(A_{3}\) & 6.3358 & 0.0672 & 0.0542 & Pass \\ \(A_{4}\) & 6.2546 & 0.0509 & 0.0411 & Pass \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum eigenvalue and consistency check results for each judgment matrix. \[R_{3}= \begin{pmatrix}0.3&0.4&0.2&0.1\\ 0.1&0.1&0.3&0.5\\ 0.1&0.2&0.3&0.4\\ 0.5&0.2&0.2&0.1\\ 0.2&0.3&0.2&0.3\\ 0.4&0.2&0.2&0.2\end{pmatrix}  \tag{35}\]  
Then, the vector of comprehensive judgment results for the indicator layer corresponding to the criterion layer is shown below. \[E_{1}=B_{1}^{\mathrm{T}}\cdot R=(0.2853,\ 0.2873,\ 0.2152,\ 0.2122) \tag{36}\]  
\[E_{2}=B_{2}^{\mathrm{T}}\cdot R=(0.1656,\ 0.2975,\ 0.3683,\ 0.1686) \tag{37}\]  
\[E_{3}=B_{3}^{\mathrm{T}}\cdot R=(0.2732,\ 0.2864,\ 0.2298,\ 0.2106) \tag{38}\]  
Then, we solve the fuzzy scheme judgment matrix for the indicator layer as shown below. \[Z=H^{\mathrm{T}}\cdot(E_{1}^{\prime},E_{2}^{\prime},E_{3}^{\prime})^{\mathrm{T }}=(0.5815,\ 0.3090,\ 0.1095)\cdot \begin{pmatrix}0.2853&0.2873&0.2152&0.2122\\ 0.1656&0.2975&0.3683&0.1686\\ 0.2732&0.2864&0.2298&0.2106\end{pmatrix} =(0.2470,\ 0.2904,\ 0.2641,\ 0.1985) \tag{39}\]  
The value \(q_{i}\) is assigned to the rubric \(v_{i}\), whereby it is assumed that \(q_{1}=100\), \(q_{2}=85\), \(q_{3}=75\), and \(q_{4}=60\), which in turn leads to the assessed value of the fuzzy-hierarchical analysis-based method of assessing the operational risk of urban dense cable corridors, as shown below. \[S_{\mathrm{total}}=\sum_{i=1}^{4}z_{i}q_{i}=81.10>75 \tag{40}\]  
From Equation (40), the assessment value of the urban dense cable channel operation risk assessment method based on fuzzy-hierarchical analysis is 81.10, which is greater than the program assessment threshold. Therefore, the proposed assessment method has a certain degree of feasibility. From Equations (19)-(21), the corresponding weight values of the 18 elements of the indicator layer can be obtained, as shown in Table 5.