## 3 Research Methods
### Methods  
#### 3.4.1 Entropy-Weighted TOPSIS Method  
The entropy-weighted method assigns weights based on the amount of information conveyed by the statistical data of the indices. The TOPSIS method assesses the relative strengths and weaknesses of existing schemes by evaluating the proximity of the evaluation objects to an idealized goal. The entropy-weighted TOPSIS method combines the entropy method of objective weighting with the technique for order preference by similarity to an ideal point method. It is not interfered with by subjective factors and reference sequence selection. It has the advantages of intuitive, simple operation, less information loss and so on [49]. Therefore, this study adopts this method to measure the supply-demand level of civil aviation passenger transport. The steps for performing the calculations are outlined below: Step 1: Standardize the original data matrix.  
Positive indicators:  
\[Y_{ij}=\frac{X_{ij}-minX_{j}}{maxX_{j}-minX_{j}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Target Layer** & **Criterion** & **Sub-Criterion** & **Indicator Layer** & **Property** \\ \hline \hline \multirow{7}{*}{Coupling} & \multirow{7}{*}{Supply level} & \multirow{7}{*}{Facilities system} & Number of airports (pcs) & + \\ \cline{3-4}  & & & Airport density (pcs/10000 km\({}^{2}\)) & + \\ \cline{3-4}  & & & Number of airports per million people & + \\ \cline{3-4}  & & & (pcs/ million people) & + \\ \cline{3-4}  & & & Number of runways (strip) & + \\ \cline{3-4}  & & & Airport terminal area (hectare) & + \\ \cline{3-4}  & & & Number of aviation employees (person/year) & + \\ \cline{3-4}  & & & Proportion of civil aviation employees (\%) & + \\ \cline{3-4}  & & & Passenger throughput (person-time) & + \\ \cline{3-4}  & & & Aircraft take-off and landing sorties (time) & + \\ \cline{3-4}  & & & Single-runway aircraft take-off and landing sorties (time/strip) & + \\ \cline{3-4}  & & & Passenger throughput per square kilometer (person/km\({}^{2}\)) & + \\ \cline{3-4}  & & & Annual growth rate of passenger throughput (\%) & + \\ \cline{3-4}  & & & Annual growth rate of aircraft take-off and landing sorties (\%) & + \\ \cline{3-4}  & & & Ratio of passenger throughput to resident population & + \\ \hline \hline \end{tabular} Note: ‘+’ represents the positive indicator. These indicators are positively correlated with the coordinated development of the system.  
\end{table}
Table 1: Evaluation index system of supply and demand of civil aviation passenger transport.  
Negative indicators:  
\[Y_{ij}=\frac{maxX_{j}-X_{ij}}{maxX_{j}-minX_{j}} \tag{2}\]  
Step 2: Calculate information entropy.  
\[E_{j}=-k\sum_{i=1}^{m}p_{ij}lnp_{ij} \tag{3}\]  
In the following formula : \(p_{ij}=\frac{\
u_{ij}}{\sum_{i=1}^{m}\
u_{ij}}\); \(k=\frac{1}{\ln m}\)  
Step 3: Calculate the weight of each index.  
\[W_{j}=\frac{1-E_{j}}{\sum_{j=1}^{n}\left(1-E_{j}\right)} \tag{4}\]  
Step 4: Construct a weighted decision matrix.  
\[R=\left(r_{ij}\right)_{m\times n^{\prime}}r_{ij}=w_{j}\times Y_{ij} \tag{5}\]  
Step 5: Calculate the positive ideal solution and negative ideal solution.  
\[R_{j}^{+}=max\left(r_{1j},\ r_{2j},\cdots r_{nj}\right), \tag{6}\]  
Step 6: Calculate the Euclidean distance between each scheme and the optimal solution and the worst solution.  
\[d_{i}^{+}=\sqrt{\sum_{j=1}^{n}\left(r_{ij}-R_{j}^{+}\right)^{2}},\ d_{i}^{-}= \sqrt{\sum_{j=1}^{n}\left(r_{ij}-R_{j}^{-}\right)^{2}} \tag{7}\]  
Step 7: Calculate the comprehensive evaluation index.  
\[U_{i}=\frac{d_{i}^{-}}{\left(d_{i}^{+}+d_{i}^{-}\right)},\ U_{i}\in[0,\ 1]. \tag{8}\]