## 2 Materials and Methods
### TOPSIS Evaluation Methodology  
The TOPSIS method is a comprehensive rating method based on raw data and is suitable for the comparative analysis of multiple evaluation objects. The basic idea of the method is to calculate the distance between the evaluation results of multiple objects to be evaluated and the idealized target. Then, the ranking is performed according to the distance. This method can be used for both rating evaluation and program preference and effect evaluation [50; 51; 52; 53]. The algorithm steps are as follows:  
Step 1: Original matrix orthogonalizationThe initial evaluation matrix is established based on the evaluation indices and the raw data obtained from the evaluation objects, as shown in Equation (24):  
\[X=\left(x_{ij}\right)_{m\times n}= \begin{bmatrix}x_{11}&\cdots&x_{1n}\\ \vdots&\ddots&\vdots\\ x_{m1}&\cdots&x_{mm}\end{bmatrix}  \tag{24}\]  
where \(X\) denotes the initial evaluation matrix, \(x_{ij}\) denotes the original data of the \(j\)th index of the \(i\)th evaluation object, \(m\) denotes the number of evaluation objects, and \(n\) denotes the number of evaluation indices. The so-called normalization of the original matrix is the unified conversion of all indicator types into extremely large indicators, and the four most common types of indicators are shown in Table 2.  
1. Conversion of very small indicators to very large indicators, which is expressed as: \[x^{\prime}_{ij}=\underset{1\leq i\leq m}{max}\left\{x_{ij}\right\}-x_{ij}\] (25) If all elements are positive, the following formula can also be used for calculation: \[x^{\prime}_{ij}=\frac{1}{x_{ij}}\] (26) where \(x^{\prime}_{ij}\) denotes the value of the indicator after forwarding. 2. Conversion of intermediate indicators to very large indicators, which is expressed as: \[\left\{ \begin{aligned} M=\underset{1\leq i\leq m}{max}\left\{|x_{ij}-x _{best}|\right\}\\ x^{\prime}_{ij}=1-\frac{|x_{ij}-x_{best}|}{M}\end{aligned} \right.\] (27) where \(x_{best}\) represents the best value within the metric. 3. Conversion of interval-type indicators to very large indicators, which is expressed as: \[\left\{\begin{aligned} M=\underset{1\leq i\leq m}{max}\left\{a- \underset{1\leq i\leq m}{min}\left\{x_{ij}\right\},\underset{1\leq i\leq m}{ max}\left\{x_{ij}\right\}-b\right\}\\ x^{\prime}_{ij}= \begin{cases}1-\frac{a-x_{ij}}{M},x<a\\ 1,a\leq x\leq b\\ 1-\frac{x_{ij}-b}{M},x>b\end{cases} \right.\] (28) where \(a\) denotes the upper limit of the optimal interval, and \(b\) denotes the lower limit of the optimal interval. Step 2: Normalization of the forwarding matrix \begin{table}
\begin{tabular}{c c} \hline \hline
**Indicator Name** & **Indicator Characteristics** \\ \hline Extremely large (efficiency-based) indicators & The bigger (more), the better \\ Extremely small (cost-type) indicators & The smaller (less), the better \\ Intermediate indicators & The closer to a certain value, the better \\ Interval-type indicators & It is best to fall in a certain range \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Types and characteristics of indicators. To remove the effect of the magnitude, the matrix that completes the normalization is normalized as shown in Equation (29) and the matrix \(Y\) is obtained. \[y_{ij}=\frac{x^{\prime}_{ij}}{\sqrt{\sum_{i=1}^{m}{x^{\prime}_{ij}}^{2}}} \tag{29}\]  
\[Y=\left(y_{ij}\right)_{m\times n}= \begin{bmatrix}y_{11}&\cdots&y_{1n}\\ \vdots&\ddots&\vdots\\ y_{m1}&\cdots&y_{mn}\end{bmatrix}  \tag{30}\]  
Step 3: Construct a weighted judgment matrix  
\[S=YU= \begin{bmatrix}y_{11}&\cdots&y_{1n}\\ \vdots&\ddots&\vdots\\ y_{m1}&\cdots&y_{mm}\end{bmatrix}\begin{bmatrix}u_{1}&\cdots&0\\ \vdots&\ddots&\vdots\\ 0&\cdots&u_{n}\end{bmatrix} = \begin{bmatrix}s_{11}&\cdots&s_{1n}\\ \vdots&\ddots&\vdots\\ s_{m1}&\cdots&s_{mm}\end{bmatrix}  \tag{31}\]  
where \(S\) denotes the weighted judgment matrix, \(U\) denotes the evaluation index weight matrix, \(u_{ij}\) denotes the combination weight of index, and \(s_{ij}\) denotes the \(j\)th-index weighted value of the \(i\)th evaluation object.