*2.2. Research Methods*

The entropy method is suitable for determining the weight of each index in the multiindex comprehensive evaluation. Because it calculates the weight based on the information entropy, the result is more objective [26–28]. The TOPSIS method (the distance method between superior and inferior solutions) is suitable for decision analysis for multiple targets [29]. Firstly, standardize the data to obtain a normalized vector *rlz*, and establish a normalized decision matrix R. The calculation formula is:

$$r\_{lz} = \frac{\mathbf{x}\_{lz} - \mathbf{x}\_{\min}}{\mathbf{x}\_{\max} - \mathbf{x}\_{\min}} \tag{1}$$

In the formula: *xlz* is the actual value of the *z* index of project area *l*; *xmax* and *xmin* are the maximum and minimum value of the single index, respectively, where *l* = 1, 2, ··· , *m*, *z* = 1, 2, ··· , *n*.

Then, use the entropy method to calculate the index weight, and its calculation formula is:

$$E\_z = -k \sum\_{l=1}^{m} f\_{lz} \ln f\_{lz} \tag{2}$$

$$w\_z = \frac{1 - N\_z}{n - \sum\_{z=1}^{n} N\_z} \tag{3}$$

In the formula: *Ez* represents the entropy value of the *z* index, and *wz* represents the entropy weight coefficient of the *z* index; information entropy *k* = <sup>1</sup> ln *<sup>m</sup>* ; the characteristic proportion of the index *flz* = *rlz* ∑*<sup>m</sup> <sup>i</sup>*=<sup>1</sup> *rlz* , assuming that when *flz* <sup>=</sup> 0, *flz* ln *flz* <sup>=</sup> 0.

On the basis of the normalized decision matrix, the entropy weight coefficient was added to establish a weighted normalized decision matrix. The calculation formula is:

$$w\_{lz} = w\_z \cdot r\_{lz} \tag{4}$$

Determining the positive ideal solution *V*<sup>+</sup> and the negative ideal solution *V*<sup>−</sup> according to *vlz*, and calculating the distance *<sup>D</sup>*<sup>+</sup> *<sup>l</sup>* from the evaluation vector to the positive ideal solution *V*<sup>+</sup> and *D*<sup>−</sup> *<sup>l</sup>* from the evaluation vector to the negative ideal solution *V*−, the calculation formula is as follows:

$$V^{+} = \{ \max v\_{lz} \mid z = 1, 2, \dots, n \} = \{ v\_1^{+}, \ v\_2^{+}, \dots, v\_n^{+} \} \tag{5}$$

$$V^- = \{ \min v\_{lz} \mid z = 1, 2, \dots, n \} = \{ v\_1^-, \ v\_2^-, \ \dots \ v\_n^- \} \tag{6}$$

$$D\_l^+ = \sqrt{\sum\_{z=1}^n \left(v\_{lz} - v\_z^+\right)^2} (l = 1, 2, \cdots, m) \tag{7}$$

$$D\_l^- = \sqrt{\sum\_{z=1}^n \left(v\_{lz} - v\_z^-\right)^2} (l = 1, 2, \dots, m) \tag{8}$$

Finally, the closeness was calculated, and the formula is as follows:

$$\mathcal{C}\_{l} = \frac{D\_{l}^{-}}{D\_{l}^{+} + D\_{l}^{-}} ; (l = 1, 2, \cdots, m) \tag{9}$$

In the formula: 0 - *Cl* - 1, the smaller the closeness *Cl*, the lower the degree; the greater the closeness *Cl*, the higher the degree.
