## 5 The Integrated Evaluation Method  
The TOPSIS is a multi-attribute decision-making approach employed by many scholars. However, it has some limitations. One limitation is that the accuracy of Euclidean distances is affected by the correlation between indicators. Another limitation is that it cannot accurately reflect the similarity of data curves. The GRA approach can not only capture non-linear relationships between sequences but also determine the level of closeness between system indicators. Therefore, the simplicity of the calculation of the TOPSIS approach and the similarity of the GRA approach were integrated into the multi-attribute decision approach. Moreover, the experience and knowledge of decision makers are seldom considered in the applications of the TOPSIS approach. Given these, this paper introduces Criteria Importance through the Intercriteria Correlation (CRITIC) objective weighting method into the combination of the TOPSIS and GRA. Then, this approach was combined with the indicators to assess the candidate consolidation centers of the integrated transportation network. The specific evaluation process is shown below. 1. Construction of indicator matrix  
It is assumed that \(m\) indicators are employed to assess the importance of \(n\) nodes in the integrated transportation network. \(x_{ij}(i=1,\ 2,\ldots,n;j=1,\ 2,\ldots,\ m)\) is the indicator value of each node. Here, \(i\) and \(j\) indicate the \(i\)-th node and \(j\)-th indicator separately, and the initial indicator matrix \(\text{U}=\left(x_{ij}\right)_{n\times m}\) is shown in Equation (9):  
\[\text{U}= \begin{bmatrix}x_{11}&x_{12}&...&x_{1m}\\ x_{21}&x_{22}&...&x_{2m}\\ \vdots&\vdots&\ddots&\vdots\\ x_{n1}&x_{n2}&...&x_{nm}\end{bmatrix} . \tag{9}\]  
1. Construction of normalized indicator matrix  
Due to the presence of the evaluation indicators with different scales, the dimensionless indicator matrix \(F^{\prime}_{ij}=\left(x^{\prime}_{ij}\right)_{n\times m}\) is obtain by normalization. \[F^{\prime}_{ij}= \begin{bmatrix}x^{\prime}_{11}&x^{\prime}_{12}&...&x_{1m}\\ x_{21}&x_{22}&...&x_{2m}\\ \vdots&\vdots&\vdots&\vdots\\ x_{n1}&x_{n2}&...&x_{nm}\end{bmatrix} (i=1,2,...,n;j=1,2,...,m), \tag{10}\]where  
\[x_{ij}^{\prime}=\frac{x_{ij}}{\sum_{i=1}^{n}x_{ij}}(i=1,2,\ldots,n;j=1,2,\ldots,m). \tag{11}\]  
Step 3: Construction of indicator weight  
To avoid the influence of individual preferences of evaluators on indicator weights, the CRITIC method proposed in [37] was employed in this study, and the concrete process is shown below. 1. Calculate the difference between evaluation indicators  
The difference between evaluation indicators was calculated based on the normalized matrix constructed according to Equation (10). The CRITIC method uses the standard deviation to estimate the differential fluctuation between indicators \(i\) and \(j\), as shown in Equation (12):  
\[\left\{ \begin{aligned} \overline{x}_{j}=\frac{1}{n}\sum \limits_{i=1}^{n}x_{ij}^{\prime},\\ S_{j}=\sqrt{\frac{\sum_{i=1}^{n}\left(x_{ij}^{\prime}-\overline{x}_{j} \right)^{2}}{n-1}},\end{aligned} \right. \tag{12}\]  
where \(\overline{x}_{j}\) denotes the average value of indicator \(j\) (column) and \(S_{j}\) represents the standard deviation of indicator \(j\). When the standard deviation between \(j\) and \(i\) is larger, it means that the information contained by indicator \(j\) is larger, which indicates that the evaluation intensity of indicator \(j\) is higher. Therefore, it is necessary to assign greater weight to indicator \(j\). If the reverse is true, it is necessary to assign a smaller weight to indicator \(j\). 2. Calculate the conflict between evaluation indicators  
Similarly, the conflict between evaluation indicators was calculated based on the normalized matrix constructed according to Equation (10). The CRITIC method applies the correlation coefficient to estimate the conflict between indicator \(i\) and \(j\). The stronger the correlation is, the smaller the conflict is, indicating that there is more identical information between indicators.