## 4 Practical Example for EDM with Improved GA  
In this section, an emergency decision-making example is provided to show the application of the proposed method. How to make emergency decision quickly and efficiently is an important task of the decision support system. An earthquake occurred in cities, causing serious damage to A, B, C, D, and E districts. By analyzing the severity of the emergencies, DMs classify the emergency loss level into light (C\({}_{1}\)), moderate (C\({}_{2}\)), and severe (C\({}_{3}\)). The criteria of emergency loss levels are shown in Table 2. Each emergency loss level consists of different demand quantities of rescuers and materials, which are denoted by interval numbers. Specific requirements are shown in Table 3. At present, there are 170 rescuers and 350 kilograms of materials available for scheduling. \begin{table}
\begin{tabular}{c c c} \hline  & **Casualties** & **Property Loss** \\ \hline C1 & [0,5] & [0,50] \\ C2 & [6,15] & [50,100] \\ C3 & [16,30] & [100,200] \\ \hline \end{tabular}
\end{table} 
Table 2: Criteria of emergency loss levels. Figure 1: The flowchart of the entire steps for emergency decision making (EDM) with improved genetic algorithm (GA). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Area**} & \multicolumn{3}{c}{**Demand of Rescuers(X)**} & \multicolumn{3}{c}{**Demand of Materials(Y)**} \\ \cline{2-6}  & **Light** & **Moderate** & **Severe** & **Light** & **Moderate** & **Severe** \\ \hline A & [10,15] & [15,25] & [25,30] & [20,30] & [30,40] & [40,55] \\ B & [10,20] & [20,30] & [30,40] & [30,40] & [40,50] & [50,65] \\ C & [15,20] & [20,35] & [35,50] & [40,60] & [60,80] & [80,100] \\ D & [5,15] & [15,25] & [25,35] & [45,65] & [65,90] & [90,110] \\ E & [20,30] & [30,50] & [50,60] & [45,65] & [65,90] & [90,110] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Demand quantities of rescuers and materials. In what follows, the proposed method in this paper is employed to solve this example. **Step 1. ** Determine the weights of emergency loss levels. (i) Through Equations (5) to (8), the evaluation values of emergency loss levels are shown in Table 4.  
(ii) Through Equation (9), the weights of emergency loss levels are calculated as follows:  
\[\omega=(\omega_{1},\omega_{2},\omega_{3})=(0.0922,\;0.3052,\;0.6026).\]  
**Step 2. ** The area weights are determined by BWM. According to past experience, DMs determined area E as the best important area and area A as the worst important region. The judgment matrices of areas A and E are calculated through Equations (2) to (4). (i) Determine the preference of area E over all the other areas. The resulting best-to-others vector would be the following:  
\[\text{A}_{\text{B}}=(a_{\text{EA}},a_{\text{EB}},a_{\text{EC}},a_{\text{ED}}, )=(5,3,4,2).\]  
Through Equations (2) and (3), the judgment matrix for area E is shown in Table 5.  
(ii) Determine the preference of area E over all the other areas. The resulting best-to-others vector would be the following:  
\[A_{W}=(a_{AB},a_{AC},a_{AD},a_{AE})=(1,0.5,0.2,0.3333).\]  
Through Equations (2) and (3), the judgment matrix for area A is shown in Table 6.  
(iii) Through Equation (4), the final judgment matrix is shown in Table 7. Standardizing the above matrix by normalization, the areas weights are calculated as follows:  
\[\omega_{j}=(\;0.0887,\;0.1244,\;0.1295,\;0.3137,\;0.3437).\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Value** & **Casualties** & **Property Losses** \\ \hline C1 & \(-4.9454\) & \(-41.1344\) \\ C2 & \(-19.4366\) & \(-118.9654\) \\ C3 & \(-40.1294\) & \(-225.0962\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation values of emergency loss levels. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline _aij_ & **A** & **B** & **C** & **D** & **E** \\ \hline A & 1 & 0.6 & 0.8 & 0.4 & 0.2 \\ B & 1.67 & 1 & 1.32 & 0.66 & 0.3333 \\ C & 1.25 & 0.75 & 1 & 0.5 & 0.25 \\ D & 2.5 & 1.5 & 2 & 1 & 0.5 \\ E & 5 & 3 & 4 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table}