The economy-society-environment system is a composite system which is composed of economic subsystem, social subsystem and environmental subsystem. On the basis of previous research results (Li et al., 2015; Peng et al., 2017; He et al., 2019; Li et al., 2019), index system of the coordinated development of economy-society-environment system for industrial transfer area was built according to the principles of systematization, scientificity and feasibility and the development characteristics of Wanjiang urban belts (Table 1).

The index system of the coordinated development of economy-society-environment system consisted of three layers: target, criteria and index, including economic, society, environment etc. 3 targets, 9 criteria and 21 indicators.

This research would study the impact of different factors on the coordinated development of economy-society-environment system both from the overall level of the Wanjiang urban belt and from the 9 individual cities under the jurisdiction of Wanjiang urban belt. Hence, 10 samples’ coordinated development level of economy-society-environment system need to be evaluated, which included the overall of Wanjiang urban belt and 9 cities under its jurisdiction, like Hefei, Wuhu, Ma’anshan, Anqing, Chuzhou, Chizhou, Tongling, Xuancheng and Lu’an (since the data of Jin’an District and Shucheng County in Lu’an can not be obtain, so using the data of Lu’an instead). The period of this research is 2011-2018. The data of this research comes from Anhui Statistical Yearbook (2012-2019) and Anhui Environmental Quality Report (2011-2018) and 2018 Statistics Bulletin of the National Economic and Social Development of Hefei, Chuzhou, Lu’an, Ma’anshan, Wuhu, Xuancheng, Tongling, Chizhou, Anqing. As the latest Anhui Statistical Yearbook only updated the data of the industrial wastewater production, industrial waste gas production and industrial solid waste production to 2017, the data of these three indicators for 2018 were replaced by the data in

Note 1: urban registered unemployment rate = number of urban registered unemployed people/(number of urban employees + number of urban registered unemployed people) × 100%; Note 2: per capita disposable personal income = per capita disposable income of urban residents × proportion of urban population + per capita disposable income of rural residents × proportion of rural population. Note 3: surface water quality means the proportion of water quality monitoring spot which were III water quality standard and above. Note 4: air quality index = annual mean concentration of PM₁₀/70 + annual mean concentration of SO₂/60 + annual mean concentration of NO₂/40, where 70, 60 and 40 are respectively the annual mean concentration limits of PM₁₀, SO₂ and NO₂ in Chinese Ambient Air Quality Standard (GB 3095-2012) Class II.

2017. According to the index system in Table 1, ten 21 × 8 evaluation matrices were built through collecting and sorting the data. Here, x i j k stands for the original data value of index i in region k in year j.

The concept and model of capacity coupling in physics are used to calculate the coordinated development degree of economy-society-environment system. According to (Jiang et al., 2017), D j k was used to evaluate the coordinated development degree of economy-society-environment system in region k in year j, which is defined as:

where is the coupling degree of economy-society-environment system, and is the complex development index of economy-society-environment system, they were defined as:

where, , both were undetermined coefficients, whose value represent the importance of economic subsystem, social subsystem and environmental subsystem respectively. Considering that the development of economic subsystem, social subsystem and environmental subsystems are equally important, so.

, , respectively represent economic subsystem development index, economic subsystem development index and economic subsystem development index in region k in year j, which were defined as:

where is the standardized value of, λ i k is the weight of index i in region k. In order to make U e c o n , j k , U s o c , j k and U e n v , j k comparability between different regions, two conditions need to be met: 1) standardization process of x i j k in different region were referred to the same background value; 2) the values of λ i k in different region were same.

Therefore, let the maximum value and minimum value of each index from 10 sample including 80 original values as the background value, and the standardization formula is:

x ′ i j k = { ( x i j k − x i min ) / ( x i max − x i min )   positive index ( x i max − x i j k ) / ( x i max − x i min ) negative index (5)

The weights of each index ( λ i k ) were computed by using entropy method to reduce the subjectivity during the evaluating process. Referencing (Tian & Tu, 2017), let X i j k = x ′ i j k + 1 . The calculation process of entropy method is as follows:

Calculate the normalization matrix

P i j k = X i j k / ∑ j = 1 8 ∑ k =1 10 X i j k (6)

Calculate the entropy of each index

e i = − 1 / ln ( 80 ) × ∑ j = 1 8 ∑ k = 1 10 P i j k (7)

Calculate the weight of each index

λ i k = λ i = ( 1 − e i ) / ∑ i = m n ( 1 − e i ) (8)

when i = 1 , ⋯ , 7 , then m = 1 , n = 7 ; when i = 8 , ⋯ , 14 , then m = 8 , n = 14 ; when i = 15 , ⋯ , 21 , then m = 15 , n = 21 , and ∑ i = 1 7 λ i k = ∑ i = 8 14 λ i k = ∑ i = 15 21 λ i k = 1 . The result of the weights value of each index were in Table 1.

The basic idea of grey incidence analysis is to use the degree of similarity of the geometric curves of available data sequences to determine whether or not their connection are close. The closer the curve is, the closer the incidence between the sequences, and vice versa. The calculation steps are as follows (Liu et al., 2010):

1) Determine the system’s behavioral sequence. It includes the sequence system’s behavioral characteristic: X 0 = ( x 0 ( 1 ) , x 0 ( 2 ) , ⋯ , x 0 ( n ) ) and the relevant factor sequence: X i = ( x i ( 1 ) , x i ( 2 ) , ⋯ , x i ( n ) ) .

2) Nondimensionalize the system’s behavioral sequence. Take the averaging operator as example, the average image of X 0 and X i were:

x ′ 0 ( k ) = x 0 ( k ) X ¯ 0 , X ¯ 0 = 1 n ∑ k = 1 n x 0 ( k ) , k = 1 , 2 , ⋯ , n (9)

x ′ i ( k ) = x i ( k ) X ¯ i , X ¯ i = 1 n ∑ k = 1 n x i ( k ) , k = 1 , 2 , ⋯ , n (10)

3) Calculate the degree of grey incidence.

γ ( x 0 ( k ) , x i ( k ) ) = min i min k | x ′ 0 ( k ) − x ′ i ( k ) | + ξ max i max k | x ′ 0 ( k ) − x ′ i ( k ) | | x ′ 0 ( k ) − x ′ i ( k ) | + ξ max i max k | x ′ 0 ( k ) − x ′ i ( k ) | (11)

γ ( X 0 , X i ) = 1 n ∑ k = 1 n γ ( x 0 ( k ) , x i ( k ) ) (12)

where γ ( X 0 , X i ) is a degree of grey incidence between X 0 and X i , ξ is known as the distinguishing coefficient.

4) Compare the degree of grey incidence. If γ ( X 0 , X i ) > γ ( X 0 , X j ) , it represents that the degree of X i affects X 0 is greater than the degree of X j affects X 0 , and be written as X i ≻ X j . Among them, “ ≻ ” is a special symbol in grey incidence mode.

Since this paper need to analyze the driving factors of the coordinated development of economy-society-environment system in 10 regions, including Wanjiang, Hefei, Chuzhou, Lu’an, Ma’anshan, Wuhu, Xuancheng, Tongling, Chizhou and Anqing, different types of grey incidence analysis models were built according to different relevant factor sequences (Table 2).

Using coupling and coordinated development model, it calculated ten samples’

economic subsystem development index, economic subsystem development index, environmental subsystem development index and the coordinated development degree of economy-society-environment system respectively, their averages and average annual growth rate were also be calculated (Table 3).

From 2011 to 2018, the development index of each subsystem in the overall level of Wanjiang urban belt showed an increasing trend, ranking by size as follows: environmental subsystem (0.6534) > economic subsystem (0.4796) > social subsystem (0.4013), by the average annual growth rate as: social subsystem (9.94%) > economic subsystem (6.70%) > environmental subsystem (1.50%). As time goes by, development index of social subsystem were closing the development index of economic subsystem, but their development index also has a gap with the development index of environmental subsystem.

From 2011 to 2018, the coordinated development degree of economic-social-environment system in the overall level of Wanjiang urban belt increased from 0.6359 to 0.7795 with an average annual growth rate of 2.94%, showing an increasing trend. The coordinated development level in the overall level of Wanjiang urban belt is at the primary level in 2011-2014 is, and reached to the intermediate level in 2015-2018. For the 9 individual cities under the jurisdiction of Wanjiang urban belt, their coordinated development degree of economic-social-environmental system also showed an increasing trend, and their average annual growth rate between 0.59% and 3.82%.

Using the grey incidence analysis method, it calculated the degree of grey incidence between the development index of economic subsystem and the coordinated development degree of economic-social-environment system, the development index of social subsystem and the coordinated development degree of economic-social-environment system, the development index of environmental subsystem and the coordinated development degree of economic-social-environment system, and recorded their order number according the numerical calculation respectively (Table 4 and Table 5).

From the overall level of Wanjiang urban belt, the impact of the development of environmental system on the coordinated development is the largest, the second largest is the development of economic system, and the impact of the development of environmental system on the coordinated development is the smallest.

From the 9 individual cities under the jurisdiction of Wanjiang urban belt, the degree of influence of the development of each subsystem on the coordinated development of Hefei, Chuzhou, Lu’an, Chizhou, Anqing are both ranked: environmental subsystem ≻ economic subsystem ≻ social subsystem; Xuancheng’s is ranked: environmental subsystem ≻ economic subsystem = social subsystem; Wuhu’s is ranked: economic subsystem = environmental subsystem ≻ social subsystem; Ma’anshan’s and Tongling’s are both ranked: social subsystem = economic subsystem ≻ environmental subsystem.

According to the Model 1 and Model 2 in Table 2, the degree of grey incidence between economic factors (criteria layer and index layer) and the coordinated development degree of economic-social-environment system were calculated, and their order number were recorded according the numerical calculation respectively (Table 5 and Table 6).

According to the Model 3 and Model 4 in Table 2, the degree of grey incidence between social factors (criteria layer and index layer) and the coordinated development degree of economic-social-environment system were calculated, and their order number were recorded according the numerical calculation respectively (Table 7 and Table 8).

According to the Model 5 and Model 6 in Table 2, the degree of grey incidence between environmental factors (criteria layer and index layer) and the coordinated development degree of economic-social-environment system were calculated, and their order number were recorded according the numerical calculation respectively (Table 9 and Table 10).