## 4 Results and Discussion
### Risk Assessment Results of Toxic Gas Leak
\begin{table}
\begin{tabular}{l l c c c c} \hline \hline \multirow{2}{*}{**First-Level Indices \(V_{i}\)**} & \multirow{2}{*}{**Secondary Indices \(u_{ij}\)**} & \multicolumn{5}{c}{**Membership \(r_{ij}\)**} \\ \cline{3-6}  & & **Excellent** & **Good** & **Moderate** & **Defective** & **Poor** \\ \hline \multirow{4}{*}{Blast furnace safety performance} & Three-way valve effectiveness & 0.8 & 0.1 & 0.1 & 0 & 0 \\  & Gas water seal height & 0.7 & 0.2 & 0.1 & 0 & 0 \\  & Corrosion degree of gas tank & 1 & 0 & 0 & 0 & 0 \\  & Aging degree of gas tank & 0.9 & 0 & 0.1 & 0 & 0 \\ \hline \multirow{4}{*}{Protective facility} & CO monitoring alarm device & 1 & 0 & 0 & 0 & 0 \\  & Mechanical ventilation device & 0.8 & 0.1 & 0.1 & 0 & 0 \\  & CO concentration detector & 0.8 & 0.2 & 0 & 0 & 0 \\  & Low pressure alarm means & 0.9 & 0 & 0.1 & 0 & 0 \\ \hline \multirow{4}{*}{Evacuation and dilution facilities} & Emergency evacuation route & 0.7 & 0.1 & 0.2 & 0 & 0 \\  & Evacuation channel settings & 0.7 & 0.2 & 0.1 & 0 & 0 \\ \cline{1-1}  & DCS system & 0.8 & 0.1 & 0.1 & 0 & 0 \\ \cline{1-1}  & Nitrogen sealing device & 0.9 & 0.1 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{Poisonous gas management} & Management System & 0.8 & 0.2 & 0 & 0 & 0 \\ \cline{1-1}  & Monitoring duty & 0.9 & 0.1 & 0 & 0 & 0 \\ \cline{1-1}  & Emergency plan & 0.9 & 0 & 0.1 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fuzzy membership matrix of toxic gas leak risk. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**First-Level Indices** & **Secondary Indices** & **Importance Order** & **Importance Ratio \(x_{ij}\)** \\ \hline \multirow{4}{*}{Blast furnace safety performance} & Three-way valve effectiveness & 4 & - \\  & Gas water seal height & 3 & 1.2 \\  & Corrosion degree of gas tank & 1 & 1.2 \\  & Aging degree of gas tank & 2 & 1.4 \\ \hline \multirow{4}{*}{Protective facility} & CO monitoring alarm device & 1 & 1.2 \\  & Mechanical ventilation device & 2 & 1.0 \\  & CO concentration detector & 4 & - \\ \cline{1-1}  & Low pressure alarm means & 3 & 1.2 \\ \hline \multirow{4}{*}{Evacuation and dilution facilities} & Emergency evacuation route & 4 & - \\ \cline{1-1}  & Evacuation channel settings & 3 & 1.4 \\ \cline{1-1}  & DCS system & 2 & 1.2 \\ \cline{1-1}  & Nitrogen sealing device & 1 & 1.0 \\ \hline \multirow{4}{*}{Poisonous gas management} & Management System & 1 & 1.0 \\ \cline{1-1}  & Monitoring duty & 2 & 1.0 \\ \cline{1-1}  & Emergency plan & 3 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Importance gradation of the toxic gas leak risk. By using the weight information, the risk of a toxic gas leak can be evaluated through the fuzzy comprehensive evaluation method. The evaluation index weight \(w_{i}\) and the fuzzy membership matrix \(R_{i}\) were substituted into the evaluation method of the RAS in Section 2.3. Then, the evaluation vector was obtained. First, it was necessary to calculate the membership matrix based on Table 3 before obtaining the evaluation vector. Taking the first-level index \(V_{1}\) (blast furnace safety performance) as an example, the weight vector of \(W_{1}\) was (0.2996, 0.2078, 0.2958, 0.1967). Based on the fuzzy membership matrix \(R_{1}\) and the weights of \(V_{1}\), the evaluation value of \(F_{1}\) was calculated using Equation (13):  
\[F_{1}=W_{1}\times R_{1}= \begin{bmatrix}0.2996\\ 0.2078\\ 0.2958\\ 0.1967\end{bmatrix} ^{T}\times \begin{bmatrix}0.8&0.1&0.1&0&0\\ 0.7&0.2&0.1&0&0\\ 1&0&0&0&0\\ 0.9&0&0.1&0&0\end{bmatrix} = \begin{bmatrix}0.8581\\ 0.0715\\ 0.0704\\ 0\\ 0\end{bmatrix} ^{T}.\]  
Similarly, the first-level comprehensive evaluation vectors for other indices were obtained. The evaluation vectors for all indices are provided in Table 5.  
Based on the principle of maximum membership, \(F_{1}\) =max \(\{f_{i}\}\) = 0.8581, and thus, the blast furnace safety performance of the steel plant was found to be \"excellent,\" being the highest in rank [34].