Study on Economic-Ecological Resilience Measurement and Improvement Strategy of Yunnan Ethnic Regions

Data standardization

The original indicators have different effects on ecological resilience, it is necessary to standardize the data before assigning weights to the selected index. In this paper, the vector gauge method ( Tong, 2013) is adopted to deal with the indexes with different properties. The formula is as follows:

$$X_{ij}^{*}=\frac{X_{ij}}{\sqrt{\underset{i=1}{\overset{n}{\sum }}\left(x_{ij}^2\right)}}\left(1\right)$$

$X^{*}$ is the normalized index value; $X$ is the original value.

Determine the index weight

This paper uses the entropy method to determine the weights of the selected indicators, the specific calculation steps are as follows:

• Determine the information entropy increase

Calculate the proportion $P_{ij}$of the index value of the i-th year under the j-th indicator, and the formula is as follows:

$$P_{ij}=\frac{X_{ij}^{\mathrm{*}}}{\underset{i=\mathrm{1}}{\overset{n}{\sum }}{X}_{ij}^{\mathrm{*}}}\mathrm{}\left(\mathrm{2}\right)$$

According to the definition of entropy, the information entropy value e of the j-th index is calculated by formula (3)

$$e_j=-k\underset{i=\mathrm{1}}{\overset{n}{\sum }}{P}_{ij}\ln p_{ij}\left(\mathrm{3}\right)$$

• (2) Determine the information utility value, the formula is

$$d_j=\mathrm{1}-e_j\mathrm{}\left(\mathrm{4}\right)$$

• (3) Determine the index weight:

$$a_j=\frac{d_j}{\underset{j=\mathrm{1}}{\overset{m}{\sum }}{d}_j}\mathrm{}\left(\mathrm{5}\right)$$

Economic and ecological resilience value

The economic resilience f(x) and ecological resilience g(y) were calculated by formulas (6) and (7) respectively.

$$f\left(x\right)=\underset{j=\mathrm{1}}{\overset{m}{\sum }}{a}_j{x}_j^{\mathrm{*}}\mathrm{}\left(\mathrm{6}\right)$$

$$g\left(y\right)=\underset{j=\mathrm{1}}{\overset{m}{\sum }}{b}_j{y}_j^{\mathrm{*}}\mathrm{}\left(\mathrm{7}\right)$$

Among them, the number of indicators is $j\left(=\mathrm{1,2},\dots ,m\right);X^{*},Y^{*}$ are the standard values of economic and ecological resilience after standardization has remained; $a_j$ means the weight of indicators of economic resilience, and $\sum a_j=1;$ $b_j$ represents the weight of indicators of ecological resilience, and $\sum b_j=1$.

Analyse the coordination relationship

• Calculate the degree of development

Using the degree of development (T) to measure the level of economic and ecological resilience. Its calculation formula is as follows:

$$T=\alpha f\left(x\right)+\beta g\left(y\right)\left(\mathrm{8}\right)$$

$\alpha ,\beta$ is the undetermined coefficient and $\alpha +\beta =1$. This paper considers that economic resilience is as important as ecological resilience, so $\alpha =\beta =0.5$.

• (2) Calculate the coupling coordination degree

The term of “coupling coordination” reflects the interaction of two or more systems under their own and external influences. The economy and ecology of the region are interdependent. Therefore, the coupling coordination model can be used to analyse the coordination relationship between economic and ecological resilience. Its calculation formula is as follows:

$$C={\left\{\begin{array}{c}\frac{f\left(x\right)*g\left(y\right)}{{\left[\frac{f\left(x\right)+g\left(y\right)}{2}\right]}^2}\end{array}\right\}}^{\theta }\left(9\right)$$

$\theta$ is the adjustment factor, usually $2\le \theta \le 5$, this paper takes $\theta =2$; $C$ is the coupling value for them, the range: $C\in \left[\mathrm{0,1}\right]$ , the larger $C$, the closer to 1 is, the more coordinated the two are; otherwise, the worse.

• (3) Calculate the degree of coordinated development

Coordinated development degree (D) is a comprehensive evaluation index that measures the degree of coordinated development of economic resilience and ecological resilience and its development degree. Its calculation formula is as follows:

$$D=\sqrt{C*T}\left(10\right)$$

The value of D ranges from 0 to 1, and the larger the D value, the closer to 1, indicating that the coordinated development of them is better; otherwise, the worse.