## 4 EWM-TOPSIS-Gray Relational Degree Model
### TOPSIS-Gray Relational Mode  
The TOPSIS method is a ranking selection method that approximates the ideal solution, and it has been widely used in the comprehensive evaluation of indicators in some fields of study. The relative advantages and disadvantages of each program are determined by calculating the distance of each program from the positive ideal solution and the negative ideal solution. The positive ideal solution is the combination of the optimal value of each indicator, and the negative ideal solution is the combination of the worst value of each indicator. However, the single TOPSIS method has certain application defects, for this reason, the text adopts the EWM-TOPSIS-Gray correlation analysis method to comprehensively evaluate the level of situational awareness of the controllers under the condition of having remote towers and obtains the weights of each index through the entropy value method and integrates the basic idea of gray correlation analysis method on the basis of TOPSIS method. Based on the basic idea of TOPSIS method, the Euclidean distance and correlation degree between each scenario and the ideal scenario are considered, so as to measure the advantages and disadvantages of the scenarios in a comprehensive way [35]. The fundamental calculating stages are as follows:  
(1) Construct the weighted normalized matrix. Multiply the normalized matrix \(Y\) by the weight vector \(w_{j}\) to obtain the weighted normalized matrix \(Z\):  
\[Z=\left(z_{ij}\right)_{24\times 19}=\left(w_{j}y_{ij}\right)_{24\times 19} \tag{3}\]  
(2) Determine the positive and negative ideal solution sequences for each indicator:  
\[Z^{+}=\left\{\underset{1\leq i\leq 24}{\max}Z_{ij}\right\}=\left[z_{1}^{+},\,z_{2 }^{+},\cdots z_{19}^{+}\right] \tag{4}\]  
\[Z^{-}=\left\{\underset{1\leq i\leq 24}{\min}Z_{ij}\right\}=\left[z_{1}^{-},z_{2 }^{-},\cdots z_{19}^{-}\right] \tag{5}\]  
(3) Calculate the Euclidean distances of each indicator representing situational awareness level to the positive \(D_{i}^{+}\) and negative ideal solution sequences \(D_{i}^{-}\):  
\[D_{i}^{\pm}=\sqrt{\sum\limits_{j=1}^{n}\left(z_{ij}-z_{j}^{\pm}\right)^{2}} \tag{6}\]  
(4) Using the weighted normalized matrix \(Z\), calculate the gray correlation coefficients of the \(i\)th evaluation scheme with respect to the corresponding indicators of the positive and negative ideal solutions:  
\[\xi_{ij}^{\pm}=\frac{\underset{i}{\min}\underset{j}{\min}\left|z_{j}^{\pm}-z_ {ij}\right|+\rho\underset{i}{\max}\underset{j}{\max}\left|z_{j}^{\pm}-z_{ij} \right|}{\left|z_{j}^{\pm}-z_{ij}\right|+\rho\underset{i}{\max}\underset{j} {\max}\left|z_{j}^{\pm}-z_{ij}\right|} \tag{7}\]In the equations \(i=1,\,2,\cdots,\,24;\,j=1,\,2,\,\cdots,\,19\), \(\rho\) corresponds to the indicators, and the distinguishing function, \(\rho\), is typically set to 0.5 based on previous research [36]. Subsequently, the gray correlation degrees between each indicator parameter and the positive and negative ideal solutions are calculated, denoted as \(R_{i}^{+}\) and \(R_{i}^{-}\):  
\[R_{i}^{\pm}=\frac{1}{n}\sum_{j=1}^{n}\xi_{ij}^{\pm} \tag{8}\]  
(5) The Euclidean distances and gray correlation degrees from all evaluations are then subjected to a non-dimensionalization process:  
\[\beta_{i}=\frac{\theta_{i}}{\max\limits_{1\leq i\leq 24}(\theta_{i})} \tag{9}\]  
In the equations, let \(\theta_{i}\) represent the Euclidean distances, \(D_{i}^{+}\), \(D_{i}^{-}\), and of each evaluated sample to the ideal solution, as well as the gray correlation degrees, \(R_{i}^{+}\) and \(R_{i}^{-}\). \(\beta_{i}\) denotes the non-dimensionalized Euclidean distances and gray correlation degrees, which are represented as \(G_{i}^{+}\), \(G_{i}^{-}\) and \(S_{i}^{+}\), \(S_{i}^{-}\), respectively. A larger value of \(D_{i}^{-}\) and \(R_{i}^{+}\) indicates that the scheme is closer to the ideal solution, whereas an increase in \(D_{i}^{+}\) and \(R_{i}^{-}\) signifies that the scheme is farther from the ideal solution.