## 5 The Integrated Evaluation Method
Correspondingly, the evaluation intensity of indicator \(j\) is weakened to some extent, and therefore, less corresponding weight is assigned to indicator \(j\). If the reverse is true, more weight is given. The equation for calculating the conflict \(R_{j}\) between indicator \(j\) and other indicators is shown in Equations (13) and (14):  
\[r_{jk}=\frac{\sum_{i=1}^{n}\left(x_{ij}^{\prime}-\overline{x}_{j}\right)\left( x_{ik}^{\prime}-\overline{x}_{k}\right)}{\sqrt{\sum_{i=1}^{n}\left(x_{ij}^{ \prime}-\overline{x}_{j}\right)^{2}\sum_{i=1}^{n}\left(x_{ik}^{\prime}- \overline{x}_{k}\right)^{2}}},(i=1,2,\ldots,n;j,k=1,2,\ldots,m), \tag{13}\]  
\[R_{j}=\sum_{k=1}^{m}\left(1-r_{jk}\right), \tag{14}\]  
where \(r_{jk}\) denotes the correlation coefficient of indicator \(j\) and \(k\). \(\overline{x}_{k}\) indicates the average value of indicator \(k\). 3. Calculate comprehensive information volume  
The difference and conflict between indicators were calculated using Equations (12)-(14), and the information volume contained in the indicators was calculated using Equation (15) according to the difference and conflict. \[I_{j}=S_{j}\sum_{i=1}^{n}\left(1-r_{jk}\right)=S_{j}\times R_{j}. \tag{15}\]  
Generally, the larger \(I_{j}\) is, the more the information contained in indicator \(j\), and the more important it is. In such cases, more weight should be assigned to the indicator. If the reverse is true, less weight should be assigned to the indicator. The CRITIC was employed to determine the objective weight of the indicators in accordance with the comprehensive information on the differences and conflicts. Therefore, according to Equation (16), the indicator information volume contained in the \(j\)-th indicator is calculated to determine the corresponding weight \(W_{j}\), and the equation of calculation is shown below:  
\[W_{j}=\frac{I_{j}}{\sum_{j=1}^{m}I_{j}}, \tag{16}\]  
where \(W_{j}\) is the weight of the indicator \(j\). Step 4: Calculate the weighted normalization matrix  
To effectively evaluate the influence of each indicator on the evaluation result, the normalized matrix constructed using Equation (10) and the weight of each indicator obtained from Equation (16) can be multiplied to obtain the weighted normalized matrix Z, as shown in Equation (17):  
\[\mathrm{H}=\big{(}\mathrm{h}_{ij}\big{)}_{n\times m}=F^{\prime}_{ij}\times W_ {j}, \tag{17}\]  
where \(z_{ij}\) represents the indicator value of the weighted normalized matrix, and \(F^{\prime}_{ij}\) indicates the dimensionless matrix. Step 5: Determine the ideal solutions  
According to the weighted normalization matrix, the maximum and minimum of the various indicators are determined as the positive ideal solutions and the negative ideal solutions, \(\mathrm{H}^{+}\) and \(\mathrm{H}^{-}\), respectively. \[\mathrm{H}^{+}=\big{(}\mathrm{h}_{1}^{+},\mathrm{h}_{2}^{+},\cdots,\mathrm{h} _{m}^{+}\big{)}=\max\big{(}\mathrm{h}_{ij},1\leq i\leq n;1\leq j\leq m\big{)}, \tag{18}\]  
\[\mathrm{H}^{-}=\big{(}\mathrm{h}_{1}^{-},\mathrm{h}_{2}^{-},\cdots,\mathrm{h} _{m}^{-}\big{)}=\min\big{(}\mathrm{h}_{ij},1\leq i\leq n;1\leq j\leq m\big{)}. \tag{19}\]  
Step 6: Calculate the Euclidean distance  
The weighted normalized matrix H was computed from Equation (17), and the positive ideal solution sets were obtained from Equation (18) and the negative ideal solution sets were obtained from Equation (19). Then, \(D_{i}^{+}\) is labeled as the Euclidean distance of indicator \(j\) from the positive ideal solution, as shown in Equation (20). \(D_{i}^{-}\) is labeled as the Euclidean distance of indicator \(j\) from the negative ideal solution, as shown in Equation (21).