## 2 Materials and Methods
### Determine the Weight of Each Indicator  
There are two main methods to provide weights to indicators: subjective and objective. The subjective approach [46] emphasized the subjective judgment and decision-makers intention and assigned weights on subjective information of decision-makers, such as expert investigation method, analytic hierarchy process (AHP). The results of the subjective approach conform to the subjective wishes of decision-makers, ignoring the information inherent in the data. However, there is no unified standard for the evaluation index system of UI, so the weight calculated by the method of personal preference tends to errors. The objective approach [47] calculated indicator weights on objective mathematical theories, fully reflecting the information in the data. The weight information originating from the indicator itself was determined by the roles of indicators in decision-making. With information entropy as the core, the entropy method was an objective weighting method to determine the index weights by considering the relationship between the degree changes of indicators and information, and it is widely used in ecological resilience [48; 49], urban resilience [50], and risk assessment [51]. The smaller the entropy, the greater the utilization information provided by this parameter. So, entropy could measure the relative  
Figure 1: PSR Model. importance of various factors. In fact, under the same evaluation index system, more unstable indicators should be given higher weight to attract the government's attention to improve the resilience level of backward cities, consistent with the principle of entropy weight method. The smaller the variation amplitude of the index, the less information contained in the index, the smaller the effect on the comprehensive evaluation, and the lower the weight value. Therefore, it was assumed that the weights of different indicators are different, and the greater the dispersion degree, the greater the weight of indicators. The entropy weight method was then applied to determine each index weight in this paper. Step 1: establishing matrix \(X\). Assuming that the evaluation region is divided into \(n\) sub-regions, and \(m\) means the number of evaluation indicators. So, the dataset (\(X\)) associated with the evaluation area is expressed as follows:  
\[X=\left( \begin{array}{cccc}x_{11}&x_{12}&\cdots&x_{1m}\\ x_{21}&x_{22}&\cdots&x_{2m}\\ \vdots&\vdots&\vdots&\vdots\\ x_{n1}&x_{n2}&\cdots&x_{mm}\end{array} \right), \tag{1}\]  
where, \(i=1,2,\ldots,n\) and \(j=1,2,\ldots,m\), and \(x_{ij}\) refers to the value of area \(i\) relative to indicator \(j\). Step 2: normalize the raw data. Since units of measurement of each index are various, it projects the original data to the standardized dimensionless values in the interval [0, 1] by the maximum-minimum method, shown in formula (2)-(3). Where \(r_{ij}\) is the normalized value. The closer \(r_{ij}\) approaches 1, the higher the resilience, while \(r_{ij}\) closer to 0 means lower resilience. Notably, this projection is based on the positive or negative contribution of indicators to the overall resilience of UI. The positive indicators generate positive contributions to enhance resilience, while negative indicators generate negative contributions to inhibit resilience. The process is as follows:  
For positive indicator:  
\[r_{ij}^{+}=(x_{ij}-\min\{x_{j}\})/(\max\{x_{j}\}-\min\{x_{j}\}), \tag{2}\]  
While, for negative indicator:  
\[r_{ij}^{-}=(\max\{x_{j}\}-x_{ij})/(\max\{x_{j}\}-\min\{x_{j}\}), \tag{3}\]  
where \(\max\{x_{j}\}\) and \(\min\{x_{j}\}\) indicate the maximum and minimum values of the index among all evaluation objects, respectively. Step 3: the entropy of each indicator (\(H_{j}\)) is calculated. \[H_{j}=-\sum_{i=1}^{n}\left(r_{ij}/\sum_{i=1}^{n}r_{ij}\right)\ln\left(r_{ij}/ \sum_{i=1}^{n}r_{ij}\right)/\ln(m), \tag{4}\]  
Step 4: the weight of evaluation indicators (\(\omega_{j}\)) is calculated.