*4.3. Entropy Method Weights*

The entropy approach is a goal-undertaking method, and the weights determined with this method are more accurate than those obtained with the subjective challenge method. Entropy is a measure of the disorder of a system, and by measuring the degree of disorder in the variables, the weights of indicator variables can be obtained by comparing the amount of information possessed by the variables. However, the method is prone to imbalanced weights due to the large dispersion of a certain indicator.

In the entropy weight approach, the entropy weight of the index is first calculated by applying the record's entropy after standardizing the authentic data. The rank of item *X*, when the index is positive, is standardized with the following system.

$$\mathcal{Y}\_{ij} = \frac{X\_{ij} - X\_{i\_{\text{min}}}}{X\_{i\_{\text{max}}} - X\_{i\_{\text{min}}}} \tag{11}$$

When the indicator is negative, its normalization treatment formula is:

$$Y\_{ij} = \frac{X\_{i\_{\max}} - X\_{ij}}{X\_{i\_{\max}} - X\_{i\_{\min}}} \tag{12}$$

where *Ximax* and *Ximin* are the maximum and minimum values of the indices, respectively; *Yij* is the normalized result setting of the first impact factor affecting prevention and control. For a certain impact factor *j*, its information entropy calculation formula *E<sup>j</sup>* is:

$$E\_{\bar{j}} = -\frac{1}{\ln m} \sum\_{i=1}^{m} P\_{\bar{i}\bar{j}} \ln P\_{\bar{i}\bar{j}} \tag{13}$$

$$P\_{ij} = \frac{\mathbf{Y}\_{ij}}{\sum\_{i=1}^{m} \mathbf{Y}\_{ij}} \tag{14}$$

where *Pij* is the proportion of the standardized value and *Yij* is the total standardized value. If the information entropy *E<sup>j</sup>* of the factor influencing prevention and control is smaller, the degree of variability in the factor is smaller, the sample data are more orderly, the differentiation ability of the evaluation object is larger, and the information utility value provided by the factor is larger. The stronger the influence on border prevention and control, the higher the weight; conversely, the larger the information entropy *E*, the larger the degree of variability is for the influence factor, and the information utility value provided by the factor and the weight is smaller.

According to the calculated information entropy of each factor, *E*1, *E*2,· · · ,*E<sup>k</sup>* , the weight formula *W<sup>j</sup>* for each factor can be calculated as follows:

$$\mathcal{W}\_{\dot{\jmath}} = \frac{1 - E\_{\dot{\jmath}}}{k - \sum\_{j=1}^{k} E\_{\dot{\jmath}}} \tag{15}$$

Based on Equations (11)–(15), we calculated the weights of each index (Tables 12 and 13).

**Table 12.** Weight results of each criterion layer based on entropy method.



