# Historical Eco-Environmental Quality Mapping in China with Multi-Source Data Fusion
## 2 Materials and Methods
### Assessment of China's EEQ
#### 2.3.2 Calculation of EEQ  
Different indicators possess distinct dimensions, and thus, it is necessary to convert each indicator into a dimensionless form prior to evaluating the EEQ. In this study, the extreme difference standardization method was employed to transform the eight indicators. These indicators were categorized into positive and negative based on their respective impacts on the EEQ. Positive indicators encompassed PRE (precipitation), NPP (net primary productivity), NDVI (normalized difference vegetation index), DEM (digital elevation model), and LUCC (land use and land cover change), all of which contribute to the enhancement of the ecological environment. Conversely, negative indicators, including TEMP (temperature), POP (population), and PET (potential evapotranspiration), denote factors that are ecologically detrimental. The standardized formulas employed are as follows.  
Positive Indicators:  
\[r_{s}^{+}=(I_{j}-I_{\text{min}})/(I_{\text{max}}-I_{\text{min}}) \tag{1}\]  
Negative indicators:  
\[r_{s}^{-}=(I_{\text{max}}-I_{j})/(I_{\text{max}}-I_{\text{min}}) \tag{2}\]  
where, \(r_{s}^{+}\) is the standardized value of the \(j\)th indicator; \(I_{j}\) is the initial value of the \(j\)th indicator; \(I_{\text{min}}\), \(I_{\text{max}}\) are the minimum and maximum values of the \(j\)th index.  
The indicator weighting model serves as a crucial aspect of the evaluation system, as the chosen model's merits and limitations can significantly influence the evaluation outcomes. Currently, subjective and objective methods are commonly employed for determining the weights. The subjective approach encompasses methods such as the gray relation method (GRM) [38] and the analytic hierarchy process (AHP) [39]. On the other hand, objective methods include the entropy method (EM) [40] and the principal component analysis (PCA) [41]. The subjective method exhibits notable limitations in its application and lacks robust theoretical support, whereas the objective method calculates weights based on the interrelations among indicators. To mitigate the subjective influence stemming from human factors, this study adopts the entropy value method to ascertain the weights of the eight indicators:  
\[w_{ij}=\frac{r_{ij}^{+}}{\sum_{i=1}^{n}r_{ij}^{+}}\text{ or }w_{ij}=\frac{r_{ij}^{ -}}{\sum_{i=1}^{n}r_{ij}^{-}} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{2}{c}{**2017**} \\ \cline{2-3}  & **Variance Inflation Factor** & **Tolerance** \\ \cline{2-3}  & **VIF** & **TOL** \\ \hline PRE & 8.097 & 0.123 \\ TEMP & 9.411 & 0.106 \\ NPP & 5.758 & 0.174 \\ NDVI & 5.922 & 0.169 \\ DEM & 2.975 & 0.336 \\ LUCC & 4.095 & 0.244 \\ POP & 1.349 & 0.741 \\ PET & 2.634 & 0.380 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Index collinearity diagnosis results.  
\[e_{j}=-k\sum\limits_{i=1}^{n}w_{ij}\ln w_{ij},\ k=(\ln n)^{-1} \tag{4}\]  
\[f_{j}=1-e_{j} \tag{5}\]  
\[w_{j}=\frac{f_{j}}{\sum\
olimits_{j=1}^{m}f_{j}} \tag{6}\]  
where, \(w_{ij}\) is the corresponding weight of the \(i\)th indicator of the \(j\)th city; \(e_{j}\) is the entropy value of the \(j\)th indicator; \(f_{j}\) is the redundancy factor of the \(j\)th indicator; \(w_{j}\) is the weight corresponding to the \(j\)th indicator; In this paper, \(i\) and \(j\) are 369 and 8, respectively.