# Resilience Analysis of Traffic Network under Emergencies: A Case Study of Bus Transit Network
## 3 Methodology
### Transport Network Index Evaluation Model Based on CRITIC-Entropy Weight  
This article uses a combination evaluation model to construct an indicator evaluation algorithm suitable for this study. The combination evaluation model is a method of weighting and combining multiple single evaluation models to integrate the advantages of single evaluation models. The data of the indicator system for monitoring and analyzing the operation status of the public transportation network in this article are all based on real quantitative data of the public transportation network operation, and there are no qualitative indicators that cannot be explained or calculated. Therefore, there is no need to use evaluation methods that combine qualitative and quantitative analysis, such as expert experience method or analytic hierarchy process. This study improved upon existing objective weighting methods, such as fuzzy comprehensive evaluation, entropy weighting, TOPSIS, and CRITIC (criteria importance through inter-criteria correlation), by combining entropy weighting with CRITIC to compensate for CRITIC's inability to consider the discreteness of attribute values. CRITIC emphasizes the comparability and conflict of indicators and calculates the objective weights of indicators based on these attributes, but it does not consider the discreteness of attribute values. In contrast, entropy represents the degree of disorder of a system, and the smaller the entropy value of an indicator value, the more information it contains and the higher  
Figure 5: Research approach. the weight, making it more capable of reflecting the operational characteristics of the bus network. The combination of entropy weighting and CRITIC in this study resulted in a CRITIC-entropy weighting model for selecting key indicators, as shown in Figure 6.  
The steps for using the entropy weight method to select key indicators are as follows: (1) Select \(n\) samples and \(m\) indicators within a time period affected by a sudden event. Then \(x_{ij}\) represents the value of the \(j\) indicator for the \(i\) sample \((i=1,2,\ldots,n;j=1,2,\ldots,m)\). (2) Homogenize the indicators: Homogenize the heterogeneous indicators to facilitate subsequent calculations. Since the calculation units of each indicator in the indicator system are not unified, using them directly will affect subsequent calculations. Therefore, before calculating the indicator weights, the data of each indicator needs to be standardized, unified, and homogenized. The absolute value of each indicator is used to solve the homogenization problem (i.e., \(x_{ij}=\left|x_{ij}\right|\)). In addition, the indicator system contains both positive indicators (max-type indicators) and negative indicators (min-type indicators), with different numerical meanings (higher values are better for positive indicators, while lower values are better for negative indicators). Therefore, different algorithms are used to standardize data for positive and negative indicators. The specific methods are as follows:  
\[\text{max-type indicators}:\ x_{ij}^{{}^{\prime}}=\frac{x_{ij}-min\{x_{1j}, \ldots,x_{nj}\}}{max\{x_{1j},\ldots,x_{nj}\}-min\{x_{1j},\ldots,x_{nj}\}} \tag{1}\]  
Figure 6: CRITIC–entropy weight method. \[\text{min-type indicators}:\ x_{ij}^{\ {}^{\prime}}=\frac{max\big{\{}x_{1j},\ldots,x_{nj} \big{\}}-x_{ij}}{max\big{\{}x_{1j},\ldots,x_{nj}\big{\}}-min\big{\{}x_{1j}, \ldots,x_{nj}\big{\}}} \tag{2}\]  
To simplify the expression, let \(x_{ij}=x_{ij}^{\ {}^{\prime}}\);  
(3) Calculate the weight \(p_{ij}\) of the \(i\) sample value under the \(j\) indicator:  
\[p_{ij}=\frac{x_{ij}}{\sum_{i=1}^{n}x_{ij}} \tag{3}\]  
(4) Calculate the entropy value \(e_{j}\) for the \(j\) indicator:  
\[e_{j}=-k\sum_{i=1}^{n}p_{ij}\ln\big{(}p_{ij}\big{)} \tag{4}\]  
Here, \(k=\frac{1}{\ln(n)}>0\) satisfies \(e_{j}>0\).