Effect Evaluation of Ecological Compensation for Strategic Mineral Resources Exploitation Based on VIKOR-AISM Model

Abstract

Energy security and ecological and environmental security are some of the most basic and important preconditions for national development, and ecological compensation is an important institutional guarantee for construction of China’s ecological civilization. The Chinese government has always made it clear that it will “step up efforts to protect the ecosystem” and establish market-based and diversified ecological compensation mechanisms. However, the existing system and mechanism design of ecological environment protection has been unable to meet the needs of economic and social development in the new era. On the basis of the psychological account theory and prospect theory, this paper constructed an evaluation system of strategic mineral resources exploitation and ecological environmental protection effects in Western China using the VIKOR-AISM model. In this paper, the VIKOR-AISM model comprehensively considers the maximization of group utility and minimization of individual regrets, and conducts a cluster analysis based on the compromise value Q and its inflection $k$. The comprehensive ranking changes of evaluation subjects under different decision preferences and hesitation interval measures were studied according to the antagonist hierarchy topology. The research results provide decision-making support for China to formulate ecological compensation policies in line with regional characteristics.

1. Introduction

The security of energy and the ecological environment is one of the most basic and important prerequisites for national survival and development. Due to the increasing intensity of resource exploitation and the related ecological environmental risks, the uncertainty facing national energy and environmental security also has been increasing [1,2]. With the rapid development of the social economy, the trend of economic globalization and diversification of human needs has further aggravated the challenges and governance complexity of energy environmental security [3].

In recent years, the international community has paid more attention to energy and ecological security [4,5,6]. In 2015, the United Nations General Assembly adopted the 2030 Agenda for Sustainable Development and made sustainable development an important development goal. In addition, China has also put forward the goal of “emission peak” by 2030 and “carbon neutrality” by 2060, which puts forward higher requirements for energy efficiency and low-carbon development in the future energy sector. However, according to the International Carbon Action Partnership, the energy sector is the main source of China’s carbon emissions, accounting for 78% of China’s total emissions [7], putting enormous pressure on China’s energy sector to reduce carbon emissions. At the same time, the Communist Party’s latest conference report states that “the concept of lucid waters and lush mountains are invaluable assets”, elevating ecological protection to a strategic level. Given the enormous pressure on the energy sector and the importance of ecological issues, the issue of ecological compensation in the energy sector under the Sustainable Development Goals (SDGs) has attracted increasing discussion and attention internationally [8,9].

However, at present, how to realize the coordination and sustainability of resource exploitation and environmental protection in the exploitation of strategic mineral resources is an issue which requires optimization of the system design [10]. Mineral resources are the bottleneck in economic and social development. The trend of tightening restrictions on mineral resources in China has not changed. Resource security is facing challenges such as weak resources [11], insufficient global market control [12], high dependence on foreign countries for some important domestic minerals [13], Sino–US trade frictions, ecological environment constraints. In addition, problems such as supply chain security and transportation security exposed in COVID-19 have made the situation of strategic mineral resources in China more severe. At present, there is a lack of innovation in the exploitation mechanism of strategic mineral resources [14], especially in the ecological compensation mechanism [15]. The existing ecological environmental protection system and mechanism design has been unable to adapt this situation. Therefore, it is urgent to conduct in-depth research on energy and environmental safety management system design and policy formulation, so as to provide scientific and technological support for the modernization of China’s energy and environmental safety governance system and governance capacity [16].

The western region of China is rich in resources and has outstanding advantages in mineral resources. An industry formed by the exploitation of mineral resources has gradually become an important pillar industry in the western region. At the same time, Western China is also an important ecological protection area, an important ecological barrier, and a national comprehensive ecological compensation pilot area. Therefore, the comprehensive evaluation of ecological compensation benefits of mineral resources strategic exploitation in 12 provinces and regions in Western China is helpful to improve the level of ecological protection and environmental restoration in the Western region. In this paper, a comprehensive evaluation model of ecological compensation mechanism for strategic mineral resources exploitation in Western China has been established by the VIKOR-AISM method, and the compromise value of the evaluation sample (i.e., compromise value) is based on the comprehensive consideration of maximized group utility and minimized individual critical value, and the inflexion and cluster of compromise value $Q$ is further analyzed.

According to national policy guidance and practical needs, it is necessary to deeply analyze and evaluate the ecological compensation mechanism for the exploitation of national strategic mineral resources, to optimize and improve the internal and external environment and system design for the exploitation of strategic mineral resources, resolve the conflicts between economic and social development and the environmental impact of the mining industry, and form a sustainable development pattern with positive interaction. This can ease the resource bottleneck constraints in China, ensure national security and the development of national high-tech industries, help people increase their income, and thus promote the harmonious development of the economy and society.

2. Theoretical Basis and Literature Review

The prospect theory suggests that under uncertain conditions, individuals will have different risk attitudes based on different psychological reference points [17,18,19]. While the mental accounting theory suggests that the mental account includes editing, classification, budget and evaluation of economic behavior [20,21]. Different decision-makers differ in their decision preferences due to their different mental accounts. The same problem may have different decision outcomes through different decision-makers. With the increasing complexity of decision-making problems and the fuzzy nature of people’s thinking, decision-makers may hesitate when facing multiple decision alternatives. The concept of the hesitation fuzzy set is proposed, to objectively reflect people’s hesitation in decision-making [22]. As a group decision, the comprehensive evaluation of ecological compensation for strategic mineral resource exploitation may be characterized by objectivity and fuzziness, with both certainty and uncertainty at the same time. Its unity of opposites is also the dilemma selection of decision preference, which can also be regarded as the interval of decision preference. The interval value can be regarded as a squeeze interval or as a rough set interval [23]. The decision-making dilemma zone can be expressed as the $k$ value section, which reflects the compromise degree of cooperative decision-making to the maximum value of group utility and the minimum individual regret critical value. Therefore, the comprehensive evaluation of ecological compensation for strategic mineral resource exploitation is applicable to the prospect theory and mental accounting theory.

The comprehensive evaluation of the ecological compensation mechanism for strategic mineral resources exploitation is a complex multi-attribute decision-making problem. In the 1990s, VIKOR (1998) [24] proposed an ideal solution-based compromise ranking method, which maximizes group utility and minimizes individual regret, to achieve the optimal ranking of limited decision-making alternatives. It is a multi-attribute decision-making method based on compromise optimization, that is, for the optimization decision problem of multi-objective multi-scheme; firstly, determine the positive and negative ideal scheme, then compare the evaluation value of alternative scheme, and select the best scheme according to the gap between alternative scheme and ideal scheme. Compared with other multi-attribute decision-making methods, this one has the advantages of maximizing group utility and minimizing individual regret. The best solution of each alternative plan is obtained, and then the advantages and disadvantages of the alternative plan are finally ranked. It can be seen that this method is easier to reach consensus and implement, so that the decision-making process is more scientific and reasonable. By improving the method, Opricovi and Tzeng (2004) [25] integrate the subjective preferences of decision-makers, reduce the contradictions among evaluation indicators, and make the decision-making results more reasonable [26]. According to the existing literature, Chinese scholars Chen Xiaohong et al. (2018) [27] proposed the definition of stochastic dominance considering the psychological behavior preferences of decision makers in the face of risk based on the four psychological behavior preferences expressed by decision-makers. Apart from that, they ranked the alternatives by the stochastic dominance under the association attribute of fuzzy measures and integral aggregation. Dong Wenxin et al. (2018) [28] proposed a multi-attribute decision-making model based on DEMATEL fuzzy-correlation analysis and VIKOR gray-correlation analysis in view of the shortcomings of traditional supply chain performance evaluation in index screening, weight determination and sample data information mining. Mi Wanjun et al. (2019) [29] studied the effect of VIKOR defuzzification with triangular fuzzy numbers on compromise solutions. Ju Pinghua et al. (2020) [30] proposed a VIKOR method based on regret theory, which adopted the decision mechanism coefficient measure to evaluate the index value and solved the point probability vector by constructing an optimization model to minimize the index value, so as to obtain the final scheme ranking result. Yu Qian et al. (2020) [31] proposed using the defined dilemma triangle fuzzy language set and extending the VIKOR method to its language environment to determine the scheme ranking. In summary, it can be seen that most of the improved VIKOR methods focus on the formula construction that maximizes the group utility and minimizes the individual regret critical value, and there are few literatures discussing the calculation interval of the compromise value and few intuitive visual displays of the evaluation effect through the ISM (interpretive structure modeling) model.

Therefore, it is feasible and necessary to establish a comprehensive evaluation index system of ecological compensation for strategic mineral resources exploitation in the Western region, to adopt an improved multi-attribute decision-making method VIKOR-AISM to evaluate the samples of 12 provinces and autonomous regions (including the ethnic minority autonomous regions) in Western China, to discuss the calculation interval of compromise value and provide an intuitive visualization of the evaluation effect with the application of AISM through strengthening the scientific quantitative calculation of specific index on the basis of existing literature.

3. Construction of the Joint Model of VIKOR-AISM

3.1. Ranking Based on Compromise Solutions

As a ranking method based on a compromise solution, VIKOR presents a fixed compromise value after the maximization of group utility and minimization of individual regret, respectively, and accordingly so as to obtain the sorted results under a compromise state. As shown in Figure 1:

Among them, $O$ is the original matrix, $N$ is the normalized matrix, and $S$ is a list of numerical values representing the maximum group utility of the evaluation object (sample, scheme) by grouping. $R$ is a column of values, its value represents the individual regret critical value of the evaluation object (sample, scheme). $S$ and $R$ are both negative indexes, that is, the smaller the value is, the better the maximum group utility and the individual regret critical value of the evaluation object are.

From the normalized matrix, the $S$ column and $R$ column are obtained by the following two general formulas:

$$S_i={\displaystyle \sum _{j=1}^m{\omega }_j\frac{F[d(f_j^{-},f_{ij}),d(f_j^{+},f_{ij})]}{d(f_j^{+},f_j^{-})}}$$

(1)

$$R_i=\underset{j}{\max }\left({\omega }_j\frac{\mathrm{F}\left[\mathrm{d}\left(f_j^{-},f_{ij}\right),\mathrm{d}\left(f_j^{+},f_{ij}\right)\right]}{\mathrm{d}\left(f_j^{+},f_j^{-}\right)}\right)$$

(2)

In the two general formulas, ${\omega }_j$ is the weights of each column, and $f_j^{+},f_j^{-}$ correspond to the positive ideal solution (positive ideal point) and the negative ideal solution (negative ideal point). The positive and negative ideal points are sets, and the values in the set correspond to the maximum and minimum values of each column in the normalized matrix. The positive ideal point is recorded as $Zon{e}^{+}$; The negative ideal point is written as $Zon{e}^{-}$.

$$Zon{e}^{+}=(z_1^{+},z_2^{+},z_3^{+},\cdots ,z_m^{+}),\mathrm{in}\mathrm{which}{z}_j^{+}=\max (n_{ij}),n_{ij}\in N,0\le i\le n$$

(3)

$$Zon{e}^{-}=(z_1^{-},z_2^{-},z_3^{-},\cdots ,z_m^{-}),\mathrm{in}\mathrm{which}{z}_j^{-}=\max (n_{ij}),n_{ij}\in N,0\le i\le n$$

(4)

The positive and negative ideal points can also be regarded as a matrix with a single row, which is expressed as:

$$Zon{e}^{+}={\left[z^{+}\right]}_{1\times \mathrm{m}}\hspace{1em}\hspace{1em}Zon{e}^{-}={\left[z^{-}\right]}_{1\times \mathrm{m}}$$

(5)

When the range method is adopted for normalization, the numerical value of all positive ideal solutions is 1; the numerical value of all negative ideal solutions is 0.

Compromise solution Q refers to a row of numerical values representing the compromise value obtained by $S$ and $R$ for the evaluation object (sample, solution). Q is a negative index, which means that the index is negatively correlated with the numerical value. Q is calculated according to the compromise solution formula shown below:

$$Q_i=(1-k)(\frac{S_i-Min(S_i)}{Max(S_i)-Min(S_i)})+k(\frac{R_i-Min(R_i)}{Max(R_i)-Min(R_i)})$$

(6)

3.2. The Drawing of Directed Graph of Topological Level Based on AISM

AISM is derived from Interpretative Structural Modeling Method (ISM) and Hasse Diagram Technique ($HDT$). The essence of the antagonist hierarchy topology is to draw two pairs of directed topologies, based on the $UP|DOWN$ oriented topology hierarchy, by introducing the opposite hierarchical extraction method in the classic hierarchical division operation of the ISM model. The process is shown below:

$$\begin{array}{l}O\underset{calculation}{\overset{Conversion}{\to }}D\stackrel{\begin{array}{ccc}Partial& order& rules\end{array}}{\to }A\stackrel{\begin{array}{ccc}Reachable& matrix& solution\end{array}}{\to }R\\ R\underset{\begin{array}{cc}or& cause\end{array}}{\overset{\begin{array}{ccc}Priority& rule& result\end{array}}{\to }}\{UP|DOWN\}\stackrel{\begin{array}{cc}Substitute& \begin{array}{cc}S& \mathrm{int}o\end{array}\end{array}}{\to }\mathrm{Antagonist}\mathrm{hierarchy}\mathrm{topology}\mathrm{graphs}\end{array}$$

(7)

In this process, $D$ refers to decision matrix, $A$ refers to relation matrix, $R$ refers to reachable matrix, and $S$ refers to general skeleton matrix (skeleton matrix or skeleton decomposition matrix). The whole process of decision appraisal is regarded as a process of constant matrix squeeze, in which the matrix corresponding to each node is regarded as a system. The steps of the entire decision appraisal are adopted to turn the process from a variable and topological system to a completely rigid one.

The decision matrix is expressed as $D={\left[d\right]}_{n\ast m}$, also known as decision appraisal matrix. In this matrix, n refers to row, representing the evaluation object, and m refers to column, representing the dimension (criteria, index and objective). The dimensions represented by m have strict comparability in terms of dominance relation.

A refers to the relation matrix in the form of the Boolean matrix, $A={\left[a\right]}_{n\ast n}$, in which n represents the evaluation object. The steps from decision appraisal matrix D to relation matrix A is obtained through partial order. For any two evaluation objects ($x$,$y$ in the decision matrix D, corresponding relations are as follows: the negative index includes $d_{(x,n1)}\ge d_{(y,n1)}$ and $d_{(x,n2)}\ge d_{(y,n2)}$, … and $d_{(x,nm)}\ge d_{(y,nm)}$. Meanwhile, positive indexes have all included $d_{(x,p1)}\ge d_{(y,p1)}$ and $d_{(x,p2)}\ge d_{(y,p2)}$, … and $d_{(x,pm)}\ge d_{(y,pm)}$. The partial order between x and y is expressed as $P{S}_{(x\to y)}$.

$P{S}_{(x\to y)}$ means that as essential factors, y is dominant, and x is subordinate.

Relation matrix A includes $A={(a)}_{n\ast n}$, which can also be expressed in either of the following two ways. In this matrix:

$$a_{xy}\{\begin{array}{l}1,\mathrm{when} P{S}_{\left(x\to y\right)}\\ 0, \mathrm{no}\mathrm{complete}\mathrm{dominance}\mathrm{and}\mathrm{inferiority}\mathrm{between}\mathrm{x}\mathrm{and}\mathrm{y};\mathrm{or}\mathrm{x}\mathrm{is}\mathrm{superior}\mathrm{to}\mathrm{y}\end{array}$$

(8)

Relation matrix is herein acknowledged as reachable matrix. For relation matrix A, it shall be firstly transformed into multiplicative matrix B.

$$B=A+I$$

(9)

In this formula, $B$ refers to multiplicative matrix, and $I$ refer to identity matrix. The identity matrix represents the Boolean matrix with 1 as its diagonal. Apply successive multiplication to $B$, and the process is shown below:

$$B^{K-1}\ne B^K=B^{K+1}=R$$

(10)

In this formula, $R$ is acknowledged as a reachable matrix. For the non-backtracking matrix, the relation matrix $A=R$ can be justified after being processed by partial order.

As for node contraction, it is a process that contracts the loop included in the reachable matrix to a node. The reachable matrix after node contraction is expressed as $R^{\prime }$, based on which the edge contraction operation shall be conducted. In essence, the edge contraction operation is mainly adopted to delete duplicate routes, as shown below:

$$S^{\prime }=R^{\prime }-{(R^{\prime }-I)}^2-I$$

(11)

$R^{\prime }$ after edge contraction is then acknowledged as $S^{\prime }$, namely, skeleton matrix. $S^{\prime }$ after the removal of the loop is expressed as S, referring to the general skeleton matrix.

As for the Boolean matrix, it includes reachable set R, antecedent set Q and collective set T, in which $T=R\cap Q$. Taking the relation matrix, A, as an example, its essential factor $e_i$:

The reachable set of $e_i$ is recorded as $R(e_i)$, that is, all elements whose corresponding row value is 1.

The antecedent set of $e_i$ is recorded as $Q(e_i)$, that is, all elements whose corresponding column value is 1.

The collective set of $e_i$ is recorded as $T(e_i)$, that is, $R(e_i)\cap Q(e_i)$.

The UP-type level graph represents a result-oriented level division with the extraction rule shown as $T(e_i)=R(e_i)$. For a non-backtracking directed graph (DAG), the matrix $S+I$ can apply to its operation, that is, fill all the main diagonals in the skeleton matrix with 1. As long as the reachable set turns out to be the same as the collective set, the relevant elements will be extracted. The elements extracted each time are placed above, and the subsequent extracted elements are placed accordingly from top to bottom.

The down-type level graph represents a cause-oriented level division with the extraction rule shown as $T(e_i)=Q(e_i)$. The elements extracted each time are placed below, and the subsequent extracted elements are placed accordingly from bottom to top.

$UP$ and $DOWN$ belong to a group of opposite (adversarial) methods in terms of the topological level graph drawing. The elements in the relationship matrix are the evaluation objects. The dominance and inferiority (quality and priority) between the evaluation objects are represented by directed line segments. The qualified evaluation object will be placed on the top in terms of its dominance, which is to say that the evaluation object on the top represents Pareto optimal. The worse the elements are, the lower they will be placed on the bottom, where the directed line segments are used to arrange the elements from the worst to the best.

VIKOR is a common method for multi-attribute decision-making of finite scheme 0. It seeks to obtain a reasonable and effective Pareto optimal solution to compromise solution with the shortest distance to the ideal solution by maximizing the group benefit and minimizing individual loss. The combination of VIKOR and AISM can not only enable a better interpretation of the behavior characteristics of supply chain decision-makers under uncertain conditions and different risk values, but also have an edge in terms of easy access to relevant compromise solutions. It is suitable for studying the comprehensive evaluation of ecological compensation for strategic mineral resources and intuitively displaying the comprehensive ranking results of ecological compensation in Western China.

4. Empirical Study

4.1. Selection of Empirical Object

To carry out the comprehensive evaluation of ecological compensation for strategic mineral resources exploitation, the selection of evaluation samples must be representative. The sample of the comprehensive evaluation in this paper was selected from 12 provinces and autonomous regions in Western China (including ethnic minority autonomous regions), and the ecological compensation for strategic mineral resources exploitation in these 12 provinces and autonomous regions as the sample for research, investigation, data collection and ranking. The 12 provinces and regions in Western China are selected as the evaluation objects in terms of the requirements of research and the reality of data acquisition. The main reason is that the Western region accounts for 70.6% of the total area of China. There are 44 ethnic minorities, accounting for 80% of the total ethnic minority population. It is the region with the most concentrated distribution of ethnic minorities in China. Most of the regions are underdeveloped and require further development. Western China is rich in natural resources. The potential total value of all minerals retained in reserves accounts for 66.1% of the total amount in China. The geological conditions enable an excellent environment for mineralization and there is huge potential for mineral exploitation and utilization. The Western region is an important distribution area of strategic emerging minerals, and its metallogenic types, tenors, reserves and exploitation maturity are among the top in China, and it is a cluster of national strategic mineral resources. As an important national ecological function reserve and ecological screen, some provinces in the Western region have taken the lead in carrying out pilots of comprehensive ecological compensation. These regions are generally categorized as having weak economic strength, fragile ecological functions and sensitive ecological environment in China. The comprehensive evaluation will help to elevate the level of ecological conservation and environment restoration in the Western region, establish and improve the national comprehensive ecological compensation mechanism with the characteristics and features of ecological compensation in the West. They are also important guides and demonstration areas for ecological compensation practice in minority areas in particular.

4.2. Construction of Evaluation Index System

4.2.1. Selection and Interpretation of Indexes

• Related Indexes of Economic Compensation

The economy is the foundation of all sustainable development, and economic benefits are the most direct benefits in the development of regional mineral resources exploitation. The current situation of mineral resources exploitation and utilization reflects the mineral industry base of the region and has an important impact on the development of the regional economy. In addition, economic compensation is an important part of the compensation of mineral resources exploitation. The economic compensation of mineral resources exploitation is manifested by local mining enterprises. After obtaining economic benefits, these enterprises will increase the demand for talents to seek their own development, recruit talents from society so as to increase the economic benefits of ordinary people. Thus, enterprises promote social development and participate in the process of ecological restoration, while creating a more favorable development environment for themselves, which in turn enhances the economic benefits of enterprises, forming a virtuous cycle of corporation development and social development. Therefore, indexes in economic compensation should include the current situation of regional mineral resources exploitation and utilization, the economic benefits of regional mining enterprises and other aspects [32]. Specifically, referring to previous studies, this paper selects the number of mining enterprises, annual production volume [32,33], total mining output value of non-oil/gas resources [34,35], and comprehensive utilization output value as the descriptive indexes of the current situation of regional mineral resources exploitation and utilization [34,35], and the number of employees [34], sales revenue of mineral products [33], and total profits [34] as the proxy indexes of economic benefits of mining enterprises.

2.

Related Indexes of Environmental Compensation

Ecological treatment is an important part of mineral resources exploitation that cannot be ignored and is directly related to the well-being of the people. Mineral resources exploitation mainly involves three stages: ore selection, mining and smelting, each of which will have different degrees of impact on the land, vegetation and surrounding environment of the mine. Mining enterprises should not only strengthen the ecological restoration of the mining environment by paying relevant taxes and fees, preparing environmental restoration and land reclamation plans, but also install additional infrastructure to strengthen the treatment of pollutants such as “three wastes”, waste gas, waste water and waste residue. Therefore, the indexes of mine, land, forest and environmental treatment should be included in the indexes of environmental compensation. Specifically, with reference to previous studies, eight indexes are selected in this paper: the area of damaged land newly occupied by mining [36,37], the number of mines restored [38], the area of restoration and treatment [36,37], the funds invested in mine environmental treatment this year [39], the area of new soil erosion treatment [40], the area of afforestation [41], the amount of completed forestry investment [42], and the amount of investment in environmental infrastructure investment [43].

3.

Related Indexes of Social Compensation

The social compensation indexes can reflect the social responsibility performed by the compensation subject in the process of developing strategic mineral resources, which involves several aspects such as driving the development of other local industries, encouraging mining enterprises to employ local workers, improving infrastructure construction, and promoting local social security, etc. The better the social compensation effect, the greater the social benefits brought by ecological compensation for mineral resources exploitation. Therefore, in this paper, seven indexes are selected to measure the impact of strategic mineral resources exploitation on local social security: the number of employed people [44], unemployment rate [45], number of health institutions [46], number of beds in medical institutions [47], number of basic pension insurance participants (Statistical Yearbook), number of unemployment insurance participants (Statistical Yearbook), and number of basic medical insurance participants (Statistical Yearbook).

4.

Related Indexes of Cultural Compensation

Minority culture is an integral part of the excellent Chinese traditional culture. Respecting and protecting the culture of ethnic minorities is conducive to enhancing the cohesion and vitality of the Chinese nation. Therefore, it is of great importance to pay attention to and protect the culture of ethnic minorities when developing strategic mineral resources in minority areas. In the process of resource exploitation, it is necessary to adhere to the principle of giving equal importance to ethnic culture and resource exploitation and pay attention to the interactive relationship between ethnic culture protection and economic development, so as to promote the sustainable exploitation of resource exploitation and ethnic culture. In this paper, the number of performances by art performance groups [48], the number of museums [36], the number of secondary and higher education institutions [49], and the number of students enrolled in secondary and higher education schools are selected as indexes to measure the degree of protection to ethnic minority cultures [49]. The indicators selected for this paper are shown in

Table 1. Comprehensive evaluation index system of ecological compensation for strategic mineral resources development.

Level Index	Second Level Index	Units	Index Attribute
Economic Compensation Dimension	Total industrial output (A1)	10 thousand RMB	+
	Number of mining enterprises (A2)	PC	−
	The number of employees (A3)	person	−
	Annual mine output (A4)	10 thousand tons	+
	Output value of comprehensive utilization (A5)	10 thousand RMB	+
	Sales of mineral products (A6)	10 thousand RMB	+
	Total profit (A7)	10 thousand RMB	+
Environmental Compensation Dimension	Mining exploitation new occupation of damaged land area this year (B1)	Hectare	−
	Number of mines restored and treated this year (B2)	PC	+
	Area restored and treated this year (B3)	Hectare	+
	Mine environmental management funds investment this year (B4)	10 thousand RMB	+
	New soil erosion control area this year (B5)	Hectare	+
	Afforestation are (B6)	Hectare	+
	Forestry investment completion amount (B7)	10 thousand RMB	+
	Environmental infrastructure investment amount (B8)	10 thousand RMB	+
Social Compensation Dimension	Employment is divided into private sector and self-employment by industrialization (C1)	Ten thousand persons	+
	Unemployment rate (C2)	Percentage	+
	Health agency (C3)	PC	+
	Number of beds in medical institutions (C4)	PC	+
	Primary endowment insurance (C5)	Ten thousand persons	+
	Unemployment insurance (C6)	Ten thousand persons	+
	Basic health insurance (C7)	Ten thousand persons	+
Cultural Compensation Dimension	Art performance groups performance (D1)	Times	+
	Museums (D2)	PC	+
	Number of secondary and higher education institutions (D3)	PC	+
	Number of students in secondary and higher schools (D4)	Person	+

.

4.2.2. Data Source and Pre-Processing

Through authoritative data from relevant statistical yearbooks of National Ministries and Commissions and authoritative published monographs and research reports in the industry field, the data studied in this paper mainly come from the following: the China Statistical Yearbook, the China Energy Statistical Yearbook, the China Environmental Statistical Yearbook, the China Land and Resources Statistical Yearbook, the China Social Statistical Yearbook, the China Mineral and Geological Journal and the National Mineral Resources Plan (2016–2020). In the case that some data are not counted in the minority autonomous regions, or some index data are missing in other provinces and regions, the interpolation refers to an approximate calculation method that approximately calculates unknown points from given points, that is, constructing a polynomial function so that it passes through all known points, and then using the obtained function to predict the location points. The missing data were supplemented by a reasonable fitting using the interpolation method, and all index data from 1998 to 2017 were calculated. An averaging method was used to meet the needs of the comprehensive evaluation in the later paper.

Firstly, the raw data of the comprehensive evaluation of ecological compensation effectiveness of strategic mineral resources exploitation were standardized and achieved dimensionless by using cosine similarity, thus the new matrix was obtained by normalization, as shown in Appendix A 

Table A1. The normalized matrix T.

M12*26.	A1	−2	−A3	A4	A5	A6	A7	−B1	B2	B3	B4	B5	B6
Yunnan	0.34	0	0.209	0.57	0.249	0.304	0.181	0.739	0.814	0.196	0.406	0.512	0.693
Inner Mongolia	1	0.37	0.381	1	1	1	1	0.108	1	1	1	0.874	1
Sichuan	0.258	0.022	0	0.774	0.322	0.242	0.125	0.87	0.335	0.624	0.233	0.471	0.55
Ningxia	0.092	0.924	0.888	0.113	0.028	0.085	0.078	0.907	0.112	0.185	0.242	0.087	0.103
Guangxi	0.096	0.395	0.713	0.36	0.081	0.078	0.068	0.831	0.23	0.104	0.117	0.126	0.181
Xinjiang	0.273	0.481	0.666	0.364	0.099	0.279	0.283	0.802	0.837	0.16	0.155	0.161	0.352
Gansu	0.17	0.539	0.62	0.26	0.059	0.179	0.107	0.751	0.888	0.223	0.167	0.437	0.346
Tibet	0	1	1	0	0	0	0	1	0	0	0	0.019	0
Guizhou	0.342	0.187	0.434	0.44	0.67	0.392	0.343	0.902	0.421	0.001	0.444	0.252	0.391
Chongqing	0.114	0.529	0.566	0.344	0.135	0.107	0.021	0.913	0.124	0.029	0.068	0.154	0.259
Shaanxi	0.686	0.404	0.398	0.635	0.026	0.694	1	0.793	0.574	0.342	0.221	1	0.529
Qinghai	0.138	0.839	0.901	0.113	0.161	0.122	0.136	0	0.071	0.16	0.12	0	0.094
M12*26	B7	B8	C1	C2	C3	C4	C5	C6	C7	D1	D2	D3	D4
Yunnan	0.125	0.258	0.555	0.814	0.278	0.492	0.302	0.467	0.429	0.575	0.496	0.665	0.413
Inner Mongolia	0.203	1	0.377	0.77	0.249	0.285	0.339	0.454	0.337	0.518	0.375	0.467	0.266
Sichuan	0.698	0.637	1	1	1	1	1	1	1	1	0.915	1	1
Ningxia	0.009	0.081	0.058	0.902	0	0.048	0.068	0.084	0.111	0.122	0.046	0.049	0.053
Guangxi	1	0.438	0.511	0.402	0.39	0.437	0.308	0.412	0.4	0.24	0.461	0.608	0.509
Xinjiang	0.194	0.654	0.325	0.289	0.198	0.332	0.49	0.657	0.514	0.65	0.615	0.416	0.322
Gansu	0.124	0.265	0.272	0	0.319	0.267	0.237	0.382	0.28	0.38	0.738	0.569	0.326
Tibet	0	0	0	0.473	0.016	0	0	0	0	0	0	0	0
Guizhou	0.069	0.167	0.288	0.626	0.295	0.344	0.209	0.302	0.214	0.383	0.293	0.356	0.3
Chongqing	0.074	0.45	0.585	0.645	0.197	0.328	0.423	0.557	0.676	0.867	0.288	0.408	0.397
Shaanxi	0.129	0.56	0.484	0.506	0.422	0.456	0.428	0.621	0.393	0.54	1	0.66	0.598
Qinghai	0.018	0.017	0.052	0.466	0.019	0.046	0.073	0.09	0.061	0.121	0.12	0.141	0.055

.

We calculated the weights of each indicator and obtained the result of ranking the index weights. The main purpose of ranking the index weights was to avoid the huge calculation quantity of the 26! permutation combinations. After the most representative maximum and minimum values are accumulated, the relationship matrix A is obtained to sort the dominance and inferiority of the samples. Since weights are calculated in various ways, weights determined by different methods may lead to uncertainty in the allocation of weights, and ultimately make the evaluation results different. In order to reduce subjectivity, this paper adopts the entropy weight method to find weights according to the VIKOR maximization of group benefits $S_i$ and minimization of individual regrets of objections $R_i$

$$S_i={\displaystyle {\sum }_{j=1}^m{\omega }_j\left(\frac{Zon{e}_j^{+}-n_{ij}}{Zon{e}_j^{+}-Zon{e}_j^{-}}\right)}\hspace{1em}{R}_i=\underset{j=1}{\max }\left({\omega }_j\left(\frac{Zon{e}_j^{+}-n_{ij}}{Zon{e}_j^{+}-Zon{e}_j^{-}}\right)\right)$$

(12)

where ${\omega }_j$ represents the weight, and $Zon{e}^{+}$ and $Zon{e}^{-}$ represent the positive and negative extremum points, respectively. Therefore, the weight results are calculated according to the above formula, the plus or minus ideal points, weights, and weights ranking are listed in

Table 2. Plus, or minus ideal points, weights, and weights ranking.

$M_{4\ast 26}$	A1	−2	−A3	A4	A5	A6	A7	−B1	B2	B3	B4	B5	B6
Zone+	1	1	1	1	1	1	1	1	1	1	1	1	1
Zone−	0	0	0	0	0	0	0	0	0	0	0	0	0
EWM Weights	0.0434	0.0298	0.0186	0.0287	0.0698	0.0458	0.0676	0.0167	0.0377	0.06	0.0427	0.0482	0.032
Weights Ranking	8	19	24	20	2	6	3	25	11	4	9	5	17
$M_{4\ast 26}$	B7	B8	C1	C2	C3	C4	C5	C6	C7	D1	D2	D3	D4
Zone+	1	1	1	1	1	1	1	1	1	1	1	1	1
Zone−	0	0	0	0	0	0	0	0	0	0	0	0	0
EWM Weights	0.0781	0.0381	0.0328	0.0164	0.0448	0.0344	0.0341	0.0279	0.0318	0.0277	0.0323	0.027	0.0338
Weights Ranking	1	10	15	26	7	12	13	21	18	22	16	23	14

.

4.2.3. Solution Results and Ranking of $S$ and $R$

According to the results above, the two columns of matrix ($S,R$) are substituted to obtain the weight values and so on, and the corresponding values of the sample are obtained, as shown in

Table 3. Values of $S_i$, $R_i$ and the sorted table.

M12*2	Expectation Value ${\mathit{S}}_{\mathit{i}}$	Ranking of Expected Value ${\mathit{S}}_{\mathit{i}}$	$\mathbf{Re}\text{-}\mathbf{Gretfulvalue}{\mathit{R}}_{\mathit{i}}$	Ranking of Re-Gretfulvalue ${\mathit{R}}_{\mathit{i}}$
Yunnan	0.6218	4	0.0684	6
Inner Mongolia	0.3278	1	0.0623	2
Sichuan	0.3905	2	0.0592	1
Ningxia	0.8518	10	0.0775	11
Guangxi	0.6612	6	0.0642	4
Xinjiang	0.6456	5	0.063	3
Gansu	0.6995	8	0.0685	7
Tibet	0.9257	12	0.0781	12
Guizhou	0.6783	7	0.0727	9
Chongqing	0.7218	9	0.0724	8
Shaanxi	0.4821	3	0.0681	5
Qinghai	0.8696	11	0.0767	10

and Figure 2.

According to the above formula, the general skeleton matrix construction is shown in

Table 4. General skeleton matrix.

	${\mathit{M}}_{12\ast 12}$	Yunnan	Inner Mongolia	Sichuan	Ningxia	Guangxi	Xinjiang	Gansu	Tibet	Guizhou	Chongqing	Shaanxi	Qinghai
$R=$	Yunnan						1
	Inner Mongolia
	Sichuan
	Ningxia										1
	Guangxi						1
	Xinjiang											1
	Gansu	1				1
	Tibet				1								1
	Guizhou							1
	Chongqing									1
	Shaanxi		1	1
	Qinghai										1

.

4.2.4. Inflection Point and Cluster Analysis

In the process of evaluation, the compromise value $Q_i$ that maximizes the utility of the group and minimizes the regret of the individual is sorted by the compromise value $Q$ in the intercept method. By analyzing the inflection point value $k$, the matrix $Q{k}_{matrix}$ is listed, and the ranking matrix with the smallest value of each column according to the rule negative direction indicator is listed according to this rule, as shown in

Table 5. Matrix sorted based on compromise value $Q$.

	${\mathit{M}}_{12\ast 10}$	k = 0	k = 0.122	k = 0.137	k = 0.227	k = 0.39	k = 0.429	k = 0.506	k = 0.594	k = 0.785	k = 1
$Q_{rank}=$	Yunnan	4	4	5	5	6	6	6	6	6	6
	Inner Mongolia	1	1	1	1	1	2	2	2	2	2
	Sichuan	2	2	2	2	1	1	1	1	1	1
	Ningxia	10	10	10	10	10	10	11	11	11	11
	Guangxi	6	6	6	5	5	5	5	4	4	4
	Xinjiang	5	4	4	4	4	4	3	3	3	3
	Gansu	8	8	7	7	7	7	7	7	7	7
	Tibet	12	12	12	12	12	12	12	12	12	12
	Guizhou	7	7	7	8	8	8	8	8	8	9
	Chongqing	9	9	9	9	9	9	9	9	8	8
	Shaanxi	3	3	3	3	3	3	3	4	5	5
	Qinghai	11	11	11	11	11	10	10	10	10	10

:

It can be seen that each column corresponding to the inflection point has two features with the same order, and the clustered columns do not have two features of the same order. The $Q$ is clustered together by two inflection point values in any proximity, which is $[0,0.122)(0.122,0.137)\dots \dots (0.594,0.785)(0.785,1]$ for a total of nine clusters, where the compromise value ranking results of the samples in the cluster are consistent, and the ranking of the clustering area is a straight-chained type, so it belongs to a completely rigid system.

According to the result of the compromise value calculated by the $k$ value, the hierarchical topology diagram of each column is made separately, and the sample ranking obtained from the different inflection points can be seen from the comparison of the hierarchical topology diagram of the following figure. As can be seen from the directed topology hierarchy diagram, the results of the $UP$ type and $DOWN$ type directed topology hierarchy diagrams of the sample ranking results are consistent and are presented as straight-chained types. There is a definite comparison relationship between any two evaluation samples. Therefore, it can be seen from the above definition.

The topological hierarchy diagrams obtained by $S$, $R$, $Q$ are all straight-chained, and $S$, $R$, and $Q$ all have only one column, so they are all completely rigid systems. The decision-making mechanism coefficient $k$ is actually a compromise on the maximum value of the benefit of the majority group and the minimum of personal regret. Therefore, the change in the value of $k$ provides the decision subject with the flexibility to make decisions using subjective preferences. Combined with $k$ sensitivity analysis, a cross-inflection point-polyline distribution is plotted as shown in Appendix A,

Table A2. Sensitivity-Clustering feature analysis.

Clustering Characteristics-Corresponding Value K Section	Q Value Ranking
0 < $k$ < 0.12192	Inner Mongolia > Sichuan > Shaanxi > Yunnan > Xinjiang > Guangxi > Guizhou > Gansu > Chongqing > Ningxia > Qinghai > Tibet
0.1219 < $k$ < 0.13705	Inner Mongolia > Sichuan > Shaanxi > Xinjiang > Yunnan > Guangxi > Guizhou > Gansu > Chongqing > Ningxia > Qinghai > Tibet
0.1371 < $k$ < 0.22701	Inner Mongolia > Sichuan > Shaanxi > Xinjiang > Yunnan > Guangxi > Gansu > Guizhou > Chongqing > Ningxia > Qinghai > Tibet
0.227 < $k$ < 0.39003	Inner Mongolia > Sichuan > Shaanxi > Xinjiang > Guangxi > Yunnan > Gansu > Guizhou > Chongqing > Ningxia > Qinghai > Tibet
0.39 < $k$ < 0.4294	Sichuan > Inner Mongolia > Shaanxi > Xinjiang > Guangxi > Yunnan > Gansu > Guizhou > Chongqing > Ningxia > Qinghai > Tibet
0.4294 < $k$ < 0.50602	Sichuan > Inner Mongolia > Shaanxi > Xinjiang > Guangxi > Yunnan > Gansu > Guizhou > Chongqing > Qinghai > Ningxia > Tibet
0.506 < $k$ < 0.59384	Sichuan > Inner Mongolia > Xinjiang > Shaanxi > Guangxi > Yunnan > Gansu > Guizhou > Chongqing > Qinghai > Ningxia > Tibet
0.5938 < $k$ < 0.78458	Sichuan > Inner Mongolia > Xinjiang > Guangxi > Shaanxi > Yunnan > Gansu > Guizhou > Chongqing > Qinghai > Ningxia > Tibet
0.7846 < $k$ < 1	Sichuan > Inner Mongolia > Xinjiang > Guangxi > Shaanxi > Yunnan > Gansu > Chongqing > Guizhou > Qinghai > Ningxia > Tibet

.

$UP$ and $DOWN$ belong to a group of opposite(adversarial) methods in terms of the topological level graph drawing. The elements in the relationship matrix are the evaluation objects. The dominance and inferiority (quality and priority) between the evaluation objects are represented by directed line segments. The qualified evaluation object will be placed on the top in terms of its dominance, which is to say that the evaluation object on the top represents the Pareto optimum. The extraction analysis is shown in

Table 6. $UP$ and $DOWN$ Extraction Results.

Level	Result Priority-UP Type	Effect Priority-DOWN Type
Level 0	Inner Mongolia, Sichuan	Inner Mongolia, Sichuan
Level 1	Xinjiang, Shaanxi	Xinjiang, Shaanxi
Level 2	Yunnan, Guangxi	Yunnan, Guangxi
Level 3	Gansu, Guizhou	Gansu
Level 4	Chongqing	Guizhou, Chongqing
Level 5	Ningxia, Qinghai	Ningxia, Qinghai
Level 6	Tibet	Tibet

below.

A series of cause to effect hierarchical graphs are drawn for a set of adversarial hierarchical graphs $\left\{UP/DOWN\right\}$, with $UP$-type daisy chains being result-first directed graph of topological level and $DOWN$-type daisy chains being cause-first directed graph of topological level, as shown in Figure 3.

5. Discussion

Through the comparison of individual index data of all samples, Inner Mongolia has the best values in the economic compensation dimension $\left\{A1,A4,A5,A6,A7\right\}$ and ecological compensation dimension $\left\{B2,B3,B4,B6,B8\right\}$. Sichuan has the best values in the social compensation dimension $\left\{C1,C2,C3,C4,C5,C6,C7\right\}$ and the cultural compensation dimension $\left\{D1,D3,D4\right\}$ [50]. According to the analysis results, it can be seen that the economic benefits brought by the exploitation of strategic mineral resources in Inner Mongolia are far ahead, which is due to its outstanding resource advantages, especially in the development and utilization of rare earth and coal, and it has made great contributions to the local economic development and financial revenue. In addition, while developing resources, Inner Mongolia optimized the pattern of strategic mineral resources development and protection, strengthened the protection and rational utilization of mineral resources, and implemented a series of effective ecological environmental protection measures, which has made outstanding contributions to consolidating the security of the important ecological barrier in Northern China, and effectively achieved the goal of benefiting people through resource development. Based on the characteristics of the development of strategic mineral resources in Sichuan, the strategic mineral resources in the western Sichuan region are rich, and it is the raw material supply area of the country’s important cutting-edge technology products [51]. However, the industrial chain in this area is relatively short, and the problem of insufficient deep processing leads to low added value of products and insignificant economic benefits. But as an important birthplace of the Yangtze River Basin, it has outstanding social benefits. In addition, Sichuan is a concentrated area of ethnic minorities, and it has invested a lot of financial and material resources in cultural protection, such as the construction of ethnic culture, the protection and inheritance of folk culture, and the promotion of education and personnel training, which is highly consistent with the actual situation.

Under the ranking of zone interception method $Q$, Shaanxi, Xinjiang, Guangxi, Yunnan, Gansu, Guizhou and Chongqing are in the second to eighth ranking, respectively. The Shaanxi advantage evaluation index is mainly reflected in $\left\{A7,B5,D2\right\}$. Shaanxi Province, as an important energy and chemical base and an important coal production base in China, has brought considerable resource benefits through the development of strategic mineral resources. However, Shaanxi’s natural conditions are relatively harsh, so it is necessary to increase investment in soil and water control. Through soil and water conservation and environmental restoration, remarkable results have been achieved. In the process of resource exploitation and industrial development, cultural protection has always been placed in the most important position, and the cultural compensation effect is far ahead in the Western region. For Xinjiang, the performance of various evaluation indicators in Xinjiang is relatively balanced. As an important province with large energy and resources, it enjoys the dividend of relevant policies in ethnic autonomous areas, and has many beneficial practices and measures in maintaining border ecological security and optimizing mineral resource development. Guangxi ranks the best in forestry investment indicators, which shows that Guangxi pays attention to protecting forest green space in the process of mining development. However, the economic benefits of resource development in Guangxi are not reflected enough. Due to the large number of employees in the mining industry and the insufficient investment in mineral resources development technology, the labor-intensive effect is becoming increasingly obvious. Yunnan, as a national kingdom of non-ferrous metals and a major province of phosphating industry, has the characteristics of good mining conditions, small impact on the environment and high utilization efficiency of a single mine in terms of the number of mining enterprises. For Gansu Province, the unemployment rate is very prominent among all the evaluation indicators, which shows that in the process of mineral resources development and utilization, Gansu’s contribution to social compensation is still insufficient, and no obvious results have been achieved in employment. Among all the evaluation indicators in Guizhou, the restoration and harnessing area ranks second from the bottom, from which it can be inferred that in the process of mineral resources development in Guizhou, the forest plants are seriously damaged and the utilization efficiency of land resources is not high, so it is necessary to increase investment in ecological and environmental protection. Chongqing ranks second from the bottom in terms of total profit of mineral resources and investment in mine environmental treatment. It can be inferred that the development and utilization structure of mineral resources in Chongqing is not reasonable enough, the mine environment governance is insufficient, and the capital investment is insufficient, so the ecological environment problem is very prominent [52].

Ningxia and Qinghai ranked ninth. From the evaluation indicators, it was found that Qinghai ranked the bottom in the governance area of soil erosion index, while Ningxia ranked the bottom in health institutions, which indicates that Qinghai needs to strengthen water and soil control in the process of the exploitation and utilization of strategic mineral resources to prevent wind erosion desertification, desertification and salinization caused by exploitation from getting worse. In the field of mineral resources development, Ningxia’s resource development structure is unreasonable, and the supporting conditions such as health care are insufficient, which shows that the development efficiency is still insufficient. Therefore, it is necessary to strengthen the contribution of resource development to social compensation, enhance the function of medical and health services, and realize the two-way improvement of resource development and social benefits. As an important strategic resource reserve base in China, Tibet has a fragile ecosystem, which is characterized by its sensitivity to environmental impact, small and scattered mining enterprises, insufficient technology for mineral resources development, and almost all evaluation indicators at the bottom. Therefore, Tibet needs to maintain the important national ecological protection area, limit the exploitation of mineral resources, effectively improve the efficiency of the exploitation of existing resources, and realize the comprehensive and coordinated development of ecological environment protection and economy, society and culture [53].

Through the above analysis, we can draw the following conclusions: the development of strategic mineral resources in the Western region has its own characteristics, and its development effect and impact on ecology, environment, economy and society are different, and there are also significant differences in policies, measures and effects of ecological compensation. Therefore, it is necessary to find out the advantages and disadvantages of each province in the relevant evaluation indicators through evaluation and analysis. The next step will be more targeted, to improve the ability to promote the coordinated development of resources exploitation and environment, economy and society [54].

6. Conclusions

In this paper, a comprehensive evaluation model of ecological compensation mechanism for strategic mineral resources exploitation in Western China was established by the VIKOR-AISM method, and the compromise value of evaluation sample (i.e., compromise value) was based on the comprehensive consideration of maximized group utility and minimized individual critical value, and the inflexion and cluster of compromise value $Q$ was further analyzed.

The study found that, as a group decision, the decision of comprehensive evaluation of the ecological compensation mechanism for strategic mineral resources exploitation may have both objectiveness and corresponding fuzziness with both certain and uncertain parts. The process of unity of opposites of these parts is also the process of dilemma selection of decision preference, and it can also be regarded as the interval features of decision-making preference. The interval value can be regarded as a squeeze interval or a rough set interval. The dilemma zone of decision can be expressed by $k$ zone field, which actually reflects the degree of compromise of collaborative decision between the maximum benefit of the majority and the minimum individual regret critical value. When comprehensively evaluating the ecological compensation mechanism for strategic mineral resources exploitation, based on the mental accounting and prospect theory, the decision preference and dilemma zone of decision-makers are taken into account, which will help to make a more objective judgment on the comprehensive evaluation of the compensation mechanism. Through empirical analysis in this paper, it is proved again that the VIKOR-AISM model has the characteristics of clear structure, simple calculation, intuitive conclusion and easy understanding, which can be widely used in similar ecological compensation comprehensive evaluation and corresponding policy formulation.