AHP-EWM Based Model Selection System for Subsidence Area Research

Abstract

Coal mining can create a variety of environmental, ecological, and land-use problems. Subsidence areas resulting from coal mining are a common and particularly difficult problem to manage. Despite much discussion in the academic literature as well as among local and international stakeholders, there is neither a uniform standard nor a universally accepted approach for selecting an appropriate governance model for a subsidence area. In particular, the lack of quantitative evaluation methods and excessive subjectivity represent key obstacles to the effective selection of governance models for subsidence areas. This paper proposes a selection framework for a coal mining subsidence governance model that integrates the analytic hierarchy process (AHP) and entropy weight method (EWM). The model comprehensively considers the settlement characteristics of the subsidence area, its geographic location, the water index, as well as the vegetation index. These variables are used as indicators to develop an evaluation framework upon which different subsidence zones can be quantitatively analyzed. The selection framework is demonstrated using examples from three subsidence areas in the Huainan and Huaibei mining areas in China, for which relevant data were collected and processed with the help of field surveys, remote sensing images, and subsidence prediction software. Applying the novel selection framework, the most suitable governance model for each subsidence area was obtained and determined to be consistent with the recommendations of an academic panel composed of multiple experts. The novel selection framework has high efficacy and potential to overcome the problem of subjectivity in the selection of governance models for coal mining subsidence areas. It is also envisaged that future incorporation of the selection framework into a user-friendly software package will significantly improve the efficiency with which suitable governance models for coal mining subsidence areas are selected.

1. Introduction

Coal, one of the largest sources of fossil fuel globally, makes tremendous contributions to economic and social growth but also causes a range of ecological and environmental problems [1,2,3]. In China, one of the world’s leading coal producers, approximately 96% of total coal production is realized through underground mining. This process has resulted in the creation of colossal goafs and surface subsidence over the years [4,5,6,7]. Importantly, the subsidence from large-scale coal mining has also led to variety of problems, such as the fragmentation and increased exposure of land areas, the destruction of vegetation and farmland, damages caused to roads, bridges, and other infrastructure, as well as interference with agricultural activities in the vicinity [8,9].

There has been much research aimed at reconciling the conflicting goals of coal mining with the protection of arable land. Several studies have investigated the mechanisms by which coal mining damages arable land and impacts food production, while others have explored countermeasures to protect arable land from such impacts [10,11]. In the 1980s, the China Institute of Coal Science pioneered research on land reclamation technology in coal mining subsidence areas, and established a suite of essential approaches and technical methods for land reclamation and utilization in such areas [12,13,14]. Since 2000, land governance and utilization in subsidence areas has been increasingly geared towards the restoration of ecosystems. With the advancement of social development, more diverse approaches to land governance and utilization in coal mining subsidence areas have also emerged [15]. For instance, following the model by which reclaimed land is repurposed for agricultural use, land in mining areas has been repurposed for urban construction and ecological restoration [16,17,18,19,20,21,22,23,24].

Although many different governance models for coal mining subsidence areas have been proposed, few have managed to successfully alleviate the impacts of coal mining subsidence in practice. Moreover, any governance model must ultimately take into account a variety of factors, such as the specific type of mining associated with the subsidence area, its geographical location, stability, size, and depth, as well as the presence of water bodies and other features of the surrounding ecological environment [25,26,27,28]. Indeed, it is the sheer diversity of factors to account for that makes the selection of a suitable governance model for subsidence areas a daunting task. Simple, qualitative approaches to selecting governance models risk being too subjective. Hence, there is an urgent need for a more objective and quantitative framework for selecting appropriate governance models for subsidence areas [29,30,31,32,33].

In this study, we develop a data-driven quantitative selection framework for governance models of subsidence areas. Specifically, we build a model that integrates the AHP with the EWM, and which includes the NDWI (Normalized Difference Water Index), two subsidence prediction parameters (maximum sinking depth, maximum subsidence area), the FVC (Fractional Vegetation Cover) and other environmental indicators to construct an evaluation system for governance models for three different types of subsidence areas. The main highlights of this paper are as follows.

First, a quantitative framework for the selection of governance models for coal mining subsidence areas is constructed. The framework provides a useful reference for carrying out the modification of subsidence areas and the selection of ecological governance schemes, especially when many different types of indicators are potentially available.

Second, an evaluation method based on the integration of AHP and EWM is proposed. By allowing for different expert opinions to be quantified into a common evaluation model, this method addresses the problem of subjectivity when selecting a suitable governance model for a subsidence area.

Third, in the construction of the model, the maximum subsidence depth and maximum subsidence area are predicted using the subsidence prediction method. This ensures that the process of selecting a governance model for a subsidence area will not only consider the existing conditions, but also take into account future trends in subsidence within the area.

2. Materials and Methods

2.1. Materials

2.1.1. Study Area

The Huainan and Huaibei mining area is situated within a nationally significant region for grain and oil production, and supports a high population density. When subsidence occurs because of coal mining, the groundwater level in the area often rises above the surface elevation, causing an extensive area of high-yielding and high-quality arable land to become waterlogged all year round (or seasonally). This can cause a significant reduction in yield and even result in the permanent loss of arable land [34,35,36]. Subsidence from coal mining in Huainan and Huaibei has resulted in huge losses to the local agricultural economy [37] and exacerbated social problems. Similar problems arising from the environmental and economic impacts of subsidence have also emerged with the more recent albeit rapid expansion of coal mining in the Guoyang Mining District (a branch of the Huainan and Huaibei Mining area). There is hence an urgent need for more wholistic and effective governance of subsidence in the Guoyang Mining District. To this end, our study focuses on three key coal mining subsidence areas located within the Guoyang Mining District.

The Guoyang Mining District is situated in the southwest of the Huabei coalfield, in the territory of Bozhou City’s Guoyang County. It is bordered by the Linhuan Mining District in the east and Henan Province in the northwest. The Guoyang Mining District spans approximately 60 km from north to south and 80 km from east to west, encompassing a total area of approximately 4800 square kilometers. All exploration areas within the district are within 10 km from the Suixi–Guoyang railroad, which passes through the district’s southeast. A network of roads leading directly to each mine within the district makes transportation relatively convenient. At present, the district contains three active mines: the Guobei coal mine, the Yuandian Erjing coal mine, and the Xinhu coal mine (Figure 1).

The Guobei Coal Mine is situated in the western region of Huabei Plain and is administratively a subordinate to Guoyang County, Bozhou City, Anhui Province. Its center lies 4 km south from the city of Guoyang County. At present, the empty and waterlogged areas of Guobei Coal Mine are mainly distributed in Area 81 and Area 82 which have both been mined for a long time. The locations, sizes, and volume of water accumulated in these two areas are well documented. Within each area, mineable material is distributed relatively evenly; although the material varies in thickness, the mine has a simple structure, and almost the entire area is mineable, making it a stable source of coal.

Yuandian Erjing Coal Mine is situated at the intersection of Suixi County and Guoyang County, Anhui Province, in the region of Gaochangyingzi and Xulou. Its center is approximately 55 km east of Suzhou City and 52 km northeast of Huaibei City. At present, the mine contains four closed and active mining areas, of which Area 81 and Area 82 have been shut down, while Area 83 remains in operation. In the three active mining areas, collapse pits constitute an area of 6.63 km² while waterlogged areas comprise an area of 1.46 km². While Area 82 has stabilized, Areas 81 and 83 still contain sinking ground, and therefore continue to contribute to the collapse pit.

Xinhu Coal Mine is located in the territory of Guoyang County, Anhui Province, approximately 14 km away from the city center. The mine was commissioned in May 2021, and is being mined in seven seams, namely Area 3, Area 53, Area 6, Area 7, Area 81, Area 82 and Area 11. Among these, the main coal seams are in Area 3, Area 81 and Area 82, of which the latter two are the most stable. As mining operations only began recently in the Xinhu Coal Mine, with the current mining face being the 818 working face of Area 81, obvious areas of collapse have yet to appear.

2.1.2. Data Sources

We obtained remotely sensed multispectral images of the study areas that were captured at a spatial resolution of 10 m by Sentinel 2 on 10 November 2021 and which had been subjected to radiometric and geometric corrections. Each image contained thirteen spectral bands, among which the blue (B2), green (B3), red (B4) and near-infrared (B8) bands had a spatial resolution of 10 m. We combined the B4 and B8 bands and the B3 and B8 bands to extract values of the Fractional Vegetation Cover (FVC) and the Normalized Difference Water Index (NDWI) of the study areas, respectively.

We have collected data on the working faces in Guoyang Mining District for many years for the purposes of estimating subsidence parameters.

Table 1. Information on the working faces of the Guoyang mine.

Study Area	Working Face Time Span	Number of Working Surfaces
Guobei Coal Mine, Area 81	23 February 2008–31 May 2019	8
Guobei Coal Mine, Area 82	26 July 2010–6 February 2022	7
Yuandian Erjing Coal Mine, Areas 81 and Area 82	11 January 2011–19 October 2022	15
Yuandian Erjing Coal Mine, Area 83	11 March 2015–20 February 2022	6
Xinhu Coal Mine, Area 818	18 May 2021–6 February 2022	1

summarizes the details of the working faces within each mining region. A range of deformation parameters, including the maximum sinking depth and maximum sinking area, can be estimated for a given working face based on parameters such as the strike azimuth (degree), the mining thickness (mm), the coal seam inclination (degree) and the sinking coefficient (Table 1).

2.1.3. Subsidence Area Governance Model

The most significant detriment to coal mines is the impact of mining on the ground surface and the movement of rock following extraction. The extent of environmental damage resulting from mining is typically shaped by the existing geological conditions, the type of land surface, the ecological environment and other factors. As coal mining activities persist, patterns of land use, geomorphic features of the surrounding landscape, as well as roads, water systems and above-ground structures within the vicinity can be heavily affected. These environmental impacts of subsidence from coal mining have become an urgent problem that needs to be addressed by the coal industry. Accordingly, a variety of models for the governance of subsidence areas have been proposed by researchers. These are outlined below.

(1)

Agricultural construction model

The agricultural construction model is a governance model that emphasizes planting and farming. This model generally does not include any demands for extensive infrastructure for transport, water bodies and sinking. It also places low requirements on vegetation, and is therefore applicable to subsidence areas. Nonetheless, the potential economic benefits that can be generated by this model are low. The model can further be subdivided into specific programs, such as agricultural cultivation, aquaculture, base pond governance and eco-agricultural integrated farming. Agricultural cultivation refers to the restoration of arable capacity by digging deeper or shallower, land leveling, providing sound supporting facilities, and improving soil fertility. On the other hand, aquaculture refers to the development of poultry farming, the planting of orchards and the processing of agricultural by-products. Base pond governance involves obtaining a given proportion of the dry land and water surface by digging deep and matting shallow, and managing these areas according to ecological principles. Lastly, eco-agricultural integrated farming involves the farming of fish and shrimp in deep water areas, aquatic products and the building of breeding facilities for livestock. By digging deep and matting shallow, land leveling, transforming dry fields into paddy fields, planting crops, planting forest belts, developing the fruit industry, and improving facilities for conserving water, a diverse land-use pattern is created, thus allowing for joint development of farming and planting.

(2)

Ecological function area construction model

The Ecological Functional Area Construction Model is a governance model that combines the ecological system to bring out its full ecological value. This model is particularly applicable to large subsidence areas, and has stringent requirements for ecological indicators as well as the ecological and economic values that it can generate. This model also places higher demands on vegetation; specifically, it requires medium to high levels of vegetation to be present in the landscape. The model can be further subdivided into three programs: an Ecological Economic Forest model, an Ecological Wetland Wastewater Treatment System model, and a Plain Reservoir Construction model. Through land leveling or the deposition of gangue, fly ash, and other materials, subsidence areas can be developed into ecologically and economically valuable forests, and thereby serve to enhance the wider ecological environment. These forests can also contribute to water conservation and slope protection, act as “carbon sinks” and increase landscape diversity. At the same time, areas of deep subsidence can be designated for the construction of an ecological wetland that serves as a natural treatment system for sewage produced in the mine. Moreover, taking advantage of subsidence from coal mining, depressions from natural lakes and other favorable environmental conditions, plain reservoirs can be built to control stagnation and floods.

(3)

Ecological landscape construction model

The ecological landscape construction model is a governance model which seeks to restore and optimize the environment by allowing the ecosystem to recover its ecological functions naturally. The model has similar requirements as the ecological functional area construction model, but emphasizes ecologically sound environmental governance to improve the ecological environment with the ultimate aim of enhancing ecological value. It can be further broken down into three specific programs. The ecological gardening model focuses on engineering and biological measures, such as the planting of ornamental plants in the watershed, the establishment of forest belts on leveled land, and the provision of recreational and leisure facilities. The leisure and tourism agriculture model seeks to transform subsidence areas from coal mining into multi-functional leisure centers that will maximize the capacity of the area for ecological conservation, leisure, and tourism. The wetland park model seeks to maintain the characteristics and basic ecosystem functions of urban wetlands while also improving the urban ecological environment, beautifying the cityscape, and providing opportunities for scientific research, science education, and recreation.

(4)

Park construction model

The park construction model is a governance model that focuses on construction to maximize the economic value of the area. This model is well suited for a large area with a shallow depth and stable sedimentation. It has stringent requirements for geographic location and low requirements for ecological factors such as vegetation. The model is usually applied to the central part of a town, the suburbs, as well as other areas that have developed transportation. The model’s requirements for construction tend to be heavily centered on the economic value that can be generated. This model can be further subdivided into several specific programs, such as the eco-industrial park model and construction model of livable area. Under this model, in areas with stable subsidence, site leveling is carried out, infrastructure for roads, water, electricity, communication and other functions is constructed, industrial parks are built, and industrial projects are developed. In areas of unstable subsidence, the development of industries is achieved via backfilling of the subsidence area, the construction of easily-demolished and easily-built houses from light steel boards, and the development of suitable projects. The construction model of livable area coordinates the arrangement of coal gangue piling and sink area governance. It uses coal gangue generated at low heat as a filler for sink areas. This creates land for coal mine infrastructure and the construction of new villages that can be used for relocation purposes in mining areas.

2.2. Methods

When selecting a governance model for a subsidence area, one needs to consider the geographical location, NDWI, vegetation coverage, maximum subsidence depth, subsidence area and a range of other variables. This diversity of variables makes it challenging to achieve an objective evaluation during the selection process. The MCDM (Multi-Criteria Decision Making) model has been widely discussed and applied as a potential solution to this problem. As a representative of a class of models, the MCDM model provides a theoretical basis upon which individuals can make scientific decisions. The results of decisions produced by specific applications of the MCDM can vary across different application fields and application scenarios, and it remains unclear which method performs best overall. The Ordinal Priority Approach is based on operations research and is solved through correlation operations and transformations of mathematical nonlinear programming. Its main feature is to obtain the preference weight and individual weight of both sides by OPA method, which makes the solution of bilateral matching model more rigorous and scientific. It is more suitable to be used in the process of mutual evaluation between project bid section and subcontractor. Given that the AHP method is the most common application of the MCDM model—it has been successfully applied across a variety of fields such as agricultural planning [1,38], ecological assessment [2,3,39,40] and many others—the method also allows for consistency testing in the judgment space, which checks and reduces the inconsistency of opinions or judgments. This approach focuses on prioritizing selection criteria and separating the more important criteria from the less important ones. However, AHP also has some shortcomings that cannot be ignored. For example, AHP can only choose the best among the given strategies, but cannot offer new strategies. In addition, the index system used in the AHP method needs the support of the expert system. If the index given is not reasonable, the result will be inaccurate. It can be seen that the experience of experts has a significant impact on the applicability of results. Some experts have conducted a systematic analysis of the applicability of AHP, pointing out that the method of AHP is not suitable for complex scenarios and is effective in addressing. In addition, they believe that AHP method of addressing scenarios cannot be applied to most real-world problems in industry, commerce, construction, transportation, location, manufacturing, etc., where there is no room for personal judgements [41]. Our work is not a complex scenario. On the one hand, we introduce AHP to offer a quantitative framework for selecting governance models; on the other hand, it is to overcome the subjectivity in selecting governance models. The AHP method needs to provide consistency comparison after multi-level comparison, otherwise it loses its selection function. In addition, AHP method inevitably has some systematic errors. To solve this problem, this study selects several existing classic governance models for the study area. The governance model of the study area is the best choice among several classical governance models. Furthermore, to combine subjective and objective decision-making approaches, we use the AHP-EWM method to evaluate the suitability of a governance model for a subsidence area. This method addresses the issue of subjective error in the AHP method while simultaneously reducing the objective bias from EWM. In addition, based on AHP-EWM method, the consistency test based on results is carried out to seek more accurate and scientific results.

Specifically, our method was executed according to the following steps. First, the Water Body Index (NDWI) and the Vegetation Cover Index (FVC) were extracted from the Sentinel 2 remotely sensed images of Guoyang Mining District on November 10, 2021 and used to characterize the distribution of water bodies and the ecological status of the subsidence area, respectively. Second, based on a site survey and measurements obtained in field, the geographical location and traffic situation within the subsidence area as well as the straight-line distance from the nearest town were used to produce the geographical location index of the subsidence area. Third, a subsidence area projection model based on the Probabilistic Integral Method was used to extract two deformation values for the subsidence area, namely the maximum sinking depth and sinking area. These were predicted using long-term data on various parameters of the mining working face (e.g., the alignment direction angle, sinking coefficient, coal seam mining thickness) in the subsidence area. Fourth, the geographic location, NDWI, FVC, maximum subsidence depth, and maximum subsidence area were used as evaluation indicators in an AHP-EWM-based selection framework for identifying a suitable governance model for the subsidence area. Finally, the results of the AHP-EWM model were tested for consistency with those of an AHP evaluation model to verify their accuracy, and different subsidence area types are correlated with existing governance models and governance methods based on the model (Figure 2).

2.2.1. Determination of Evaluation Indicators

The process of determining the appropriate indicators for an evaluation can be tedious, as this often entails analyzing a range of criteria and synthesizing the results of multiple previous studies. To achieve a rapid evaluation of the overall ecological benefit, the selection of evaluation indicators should abide by four key principles, as follows.

① The practicality principle. The indicators should be straightforward and easy to obtain; for instance, they should be easily measured using instruments or manually.

② The principle of focus. The indicators should have a sizable impact on the overall assessment of ecological benefits and avoid putting the cart before the horse.

③ The principle of comprehensiveness. The selection of indicators should be comprehensive and organized, and they should also be representative of the full range of indicators in the governance model.

④ The principle of homogeneity. The average value of each indicator should be used instead of the instantaneous value.

Based on the above principles, as well as previously proposed governance standards for subsidence areas [42,43], and considering the principle of maximizing economic benefits, we selected five indicators for our evaluations and analyses: the geographic location of the subsidence area, the NDWI, the FVC, the maximum subsidence depth, and the maximum sinking area.

(1)

Geographic location

The geographic location of a subsidence area is determined through field surveys, and the distance of the area from the nearest county or city is used as a criterion for classification. In our study, this index includes three categories: 0–5 km, which corresponds to a well-traveled area; 5–15 km, which corresponds to a generally traveled area; and 15 km and beyond, which corresponds to an inaccessible area. Different governance models can be applied to accommodate different degrees of traffic development; for instance, parks can be constructed in locations close to urban areas with developed traffic.

The geographic location of a subsidence area significantly influences the governance model that can be applied. For example, a subsidence area designated as a park should not be situated in a remote location. Although the geographic location of an area can be measured via a variety of indicators—such as transportation, the level of economic prosperity, and the proximity to major cities—the distance of a subsidence area from the city center is a particularly important consideration in the selection of a suitable governance model. Therefore, we used this distance to quantify the geographical advantages and disadvantages of a given subsidence area.

(2)

NDWI

The Normalized Water Body Index reflects whether a given area contains water bodies. It is calculated based on the normalized ratio index of green and near infrared bands in a remotely sensed image. The NDWI is extremely useful for governance models with high demands for water bodies, such as reservoirs and wetland parks. The NDWI is calculated as follows:

$$\mathrm{NDWI}=\left[\mathrm{float}\left(\mathrm{b}3\right)-\mathrm{float}\left(\mathrm{b}8\right)\right]/\left(\mathrm{b}3+\mathrm{b}8\right).$$

(1)

b3: Green band;

b8: Near-infrared band.

(3)

FVC

The FVC refers to the amount of the vertical projection area that is occupied by vegetation (which includes leaves, stems and branches) on the ground, relative to the total area of the surveyed region. Vegetation cover can be used as a measure of the ecological environment of a given area. It provides a reference value for governance models with high ecological environment requirements, such as the ecological landscape construction model, which sets stringent criteria for ecological environment indicators.

The Normalized Difference Vegetation Index (NDVI), which is comprised of the Standard Deviation Difference Vegetation Index, is closely associated with plant transpiration, the interception of sunlight, photosynthesis, and the net primary productivity of the ground surface. The NDVI relates to vegetation cover and responds to a range of factors influencing the properties of the plant canopy, such as the conditions of the soil, ground moisture, snow, leaf litter, and leaf roughness.

Calculation of$\mathrm{NDVI}$:

$$\mathrm{NDVI}=\left(\mathrm{b}8-\mathrm{b}4\right)/\left(\mathrm{b}8+\mathrm{b}4\right).$$

(2)

b8: Near-infrared band;

b4: Infrared band.

Calculation of$\mathrm{FVC}$:

$$\mathrm{FVC}={\left[\left(\mathrm{NDVI}-\mathrm{NDVIs}\right)/\left(\mathrm{NDVIv}-\mathrm{NDVIS}\right)\right]}^2.$$

(3)

$\mathrm{NDVIs}=0.05$,$\mathrm{NDVIv}=0.7$;

$$\mathrm{FVC}={\left[\left(\mathrm{b}1-0.05\right)/\left(0.7-0.05\right)\right]}^2.$$

(4)

$\mathrm{FVC}$ is divided into five levels, and the higher the value, the higher the vegetation cover.

Level 1: 0–0.1;

Level 2: 0.1–0.3;

Level 3: 0.3–0.5;

Level 4: 0.5–0.7;

Level 5: 0.7–1.

(4)

Prediction of maximum subsidence depth

The maximum subsidence depth reflects the varying depths in a given subsidence area and provides a reference value for governance models that require an extensive depth; for instance, reservoirs and construction require deep subsidence areas. Nonetheless, models that require a shallow depth are also taken into account. The maximum subsidence depth of a subsidence area is obtained using the probability integral subsidence estimation method, which considers the movement of mine rock to be a random phenomenon that complies with statistical laws. This is also known as the random medium theory method. More precisely, the subsidence area estimation uses past data on parameters of the working face (walking direction angle, sinking coefficient, coal seam mining thickness, etc.) to attain the deformation parameters of the subsidence area, such as the maximum sinking depth.

Maximum subsidence depth:

$${\mathrm{W}}_{\mathrm{cm}} = \mathrm{mq}\cos \mathsf{\alpha }.$$

(5)

${\mathrm{W}}_{\mathrm{cm}}$—maximum surface subsidence value under full mining conditions;

m—thickness of the mined coal seam;

q—surface subsidence coefficient;

$\mathsf{\alpha }$—coal seam inclination.

(5)

Projection of the maximum subsidence area

The maximum subsidence area reflects variation in the area affected by subsidence within the study area. The construction of ecological gardens and wetland parks requires larger subsidence areas, while the agricultural construction model requires a smaller subsidence area. The maximum subsidence area can likewise be estimated by the subsidence estimation method, and is usually defined as an area of subsidence greater than 10 mm. This is because a contour of 10 mm of subsidence delineates the boundary of a subsidence area, and the presence of 10 mm of subsidence at a cross-section indicates that an area is a subsidence area. The maximum subsidence area is calculated using Formula (6).

$$\mathrm{A}=\frac{1}{2}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{i}}^{10}{\mathrm{y}}_{\mathrm{i}+1}^{10}-{\mathrm{x}}_{\mathrm{i}+1}^{10}{\mathrm{y}}_{\mathrm{i}}^{10}.$$

(6)

In the equation, A is the area of the subsidence area, (${\mathrm{x}}_{\mathrm{i}}^{10}$,${\mathrm{y}}_{\mathrm{i}}^{10}$) is the coordinate of the point of the cross section at 10 mm sinking of the subsidence area.

2.2.2. Calculation of Weights

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Calculation of AHP-based subjective weights

Analytic Hierarchy Process (AHP) is a systematic and hierarchical approach that combines qualitative and quantitative analysis [44,45]. The AHP breaks down a complex problem into several distinct hierarchical structures. It expresses and processes individual subjective judgments in quantitative terms, and determines the importance of factors relative to decision-making through a two-by-two comparison method to obtain a judgment matrix. By then obtaining the subjective weights of the indicator layers based on this matrix, the AHP effectively achieves the fusion of qualitative and quantitative analysis. Nevertheless, when the AHP is used to determine target and criterion layers through human subjectivity, it is subjective and may result in biased outcomes. Steps in the AHP are as follows.

① Establishing the evaluation matrix

Based on the selection of evaluation indicators, a three-layer progressive hierarchy model of the AHP method is established. This model includes the governance model of the study area as the target layer (A), the geographic location of the subsidence area, NDWI, FVC, maximum subsidence depth, and maximum subsidence area as the indicator layer (B), and the existing governance model as the bottom layer (C). These layers do not intersect with each other, as can be seen in the following

Table 2. Indicator system of the AHP-based subsidence area governance model.

Target Layer (A)	Indicator Layer (B)	Bottom (C)
Study of regional subsidence area governance model (A)	Geographic location of subsidence area (B1)	Existing subsidence area governance model (C)
	NDWI (B2)
	FVC (B3)
	Maximum sinkage depth (B4)
	Maximum subsidence area (B5)

.

② Constructing the judgment matrix

After a recursive hierarchy is established, it is necessary to obtain the aij value of a judgment by comparing the relative importance of factors in pairs. To do this, one must make a two-by-two comparison of the importance of each element of the same level in the indicator layer (C) based on a criterion in the previous level, and thus construct a judgment matrix with this judgment value. The values of the elements of the judgment matrix reflect the perception of the relative importance of each factor, and generally, the values 1, 3, 5, 7, and 9 are used to indicate that one factor is equally important, slightly important, obviously important, strongly important, and extremely important relative to another factor, respectively. Meanwhile, the values 2, 4, 6, and 8 indicate the intermediate values of 1 and 3, 3 and 5, 5 and 7, and 7 and 9, respectively. Judgments are then compared according to the above hierarchical relationships as can be seen in the following

Table 3. Judgment matrix scales and their interpretation.

Scale	Interpretation
1	Indicates that two elements are of equal importance when compared with each other
3	Indicates that when two elements are compared, the former is slightly more important than the latter
5	Indicates that when two elements are compared, the former is significantly more important than the latter
7	Indicates that when two elements are compared, the former is strongly more important than the latter
9	Indicates that when two elements are compared, the former is extremely more important than the latter
2, 4, 6, 8	Denotes the middle value of the above adjacent judgments
Countdown	If the ratio of the importance of element i to j is aij, then the ratio of the importance of element j to element i is aji = 1/aij

.

③ First, each column element of the judgment matrix is normalized, and the general terms of its elements are

$${\mathrm{P}}_{\mathrm{ij}}^{\prime }=\frac{{\mathrm{P}}_{\mathrm{ij}}}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{ij}}}.$$

(7)

P_ij: a_ij;

P’_ij: the value of a_ij normalized.

④ After each column is normalized, the rows of the normalized judgment matrix are summed to obtain the normalized mean value${\mathrm{W}}_{\mathrm{i}}$, that is, the subjective weights of the indicator layer.

$${\mathrm{W}}_{\mathrm{i}}=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{ij}}^{\prime }}{\mathrm{n}}.$$

(8)

W_i: the normalized mean value.

(2)

Calculation of objective weights based on EWM

The Entropy Weight Method (EWM), an objective assignment method, obtains weights with higher accuracy than subjective assignment methods. In the EWM, the weight of an indicator variable can be obtained by comparing the amount of information held by that variable [46]. Entropy is a measure of the degree of disorder in a system. Based on this concept of information entropy, the EWM obtains the amount of information possessed by each factor and decides the weight of the index according to the amount and quality of information captured by the factor. The EWM has played key roles in ecological risk evaluations and pipeline risk evaluations [47,48]. Nonetheless, it is prone to imbalanced weights when an indicator displays excessive dispersion. The specific steps of the EWM are as follows.

The score which indicates the importance of an indicator for a governance model is usually divided into three major levels: a score of 1–3 is considered important, a score of 4–6 is regarded as more significant, and a score of 7–10 is deemed very critical.

① De-quantization and standardization of the data

$${\mathrm{Y}}_{\mathrm{ij}}=\frac{{\mathrm{X}}_{\mathrm{ij}}-{\mathrm{X}}_{\mathrm{imin}}}{{\mathrm{X}}_{\mathrm{imax}}-{\mathrm{X}}_{\mathrm{imin}}},$$

(9)

where

${\mathrm{X}}_{\mathrm{ij}}$ is the value of different governance models j under the ith indicator;

${\mathrm{Y}}_{\mathrm{ij}}$ is the normalized value.

② Normalization of the indicators:

$${\mathrm{Q}}_{\mathrm{ij}}=\frac{{\mathrm{Y}}_{\mathrm{ij}}}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Y}}_{\mathrm{ij}}}.$$

(10)

Q_ij—normalization of the indicators (I = 1, 2, n, j = 1, 2, m).

③ Determination of the information entropy of each indicator Ej:

$${\mathrm{E}}_{\mathrm{j}}=-{\left[\ln \left(\mathrm{n}\right)\right]}^{-1}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Q}}_{\mathrm{ij}}{\mathrm{lnQ}}_{\mathrm{ij}}.$$

(11)

E_j—information entropy.

④ Determination of the weight of each indicator W by information entropy E jj:

$${\mathrm{W}}_{\mathrm{j}}=\frac{1-{\mathrm{E}}_{\mathrm{j}}}{\mathrm{k}-{{\displaystyle \sum }}^{}{\mathrm{E}}_{\mathrm{j}}}.$$

(12)

k is the number of indicators, and k = 5 in this paper.

2.2.3. Determination of the Governance Model

To identify a suitable governance model, it is crucial to conduct a thorough scoring of the baseline correlations under distinct evaluation indicators. This will facilitate the identification of a governance model that is best suited to the study area and provide a strong theoretical foundation upon which the final decision may rest.

(1)

Determination of AHP-EWM-based integrated weights

This method has potential to effectively address the problem of unbalanced weights caused by the excessive dispersion of an indicator in the EWM [49]. Furthermore, it addresses the problem of subjective bias in the hierarchical analysis method that arises due to the subjective determination of the target and criterion layers. Consequently, the method’s process of weight assignment is truly objective and conforms to the regularity of common sense judgment [50]. The method therefore effectively bridges the gap between subjectivity and objectivity, and renders the evaluation results more reliable, logical and reasonable.

Weights can be unbalanced when values of an indicator are excessively dispersed. The expression for the combination weight Wij is provided as

$${\mathrm{W}}_{\mathrm{ij}}={\mathrm{aW}}_{\mathrm{i}}+{\mathrm{bW}}_{\mathrm{j}.}$$

(13)

In the formula, $\mathrm{a}$ and $\mathrm{b}$ are the assigned values of subjective weights and objective weights, respectively, which satisfy $\mathrm{a}+\mathrm{b}=1$. The distance function of the subjective weight and objective weight $\mathrm{D}\left({\mathrm{W}}_{\mathrm{i}},{\mathrm{W}}_{\mathrm{j}}\right)$ is also introduced and expressed as

$$\mathrm{D}\left({\mathrm{W}}_{\mathrm{i}},{\mathrm{W}}_{\mathrm{j}}\right)={\left[\frac{1}{2}{{\displaystyle \sum }}_{\mathrm{m}=1}^{\mathrm{n}}{\left({\mathrm{W}}_{\mathrm{im}}-{\mathrm{W}}_{\mathrm{jm}}\right)}^2\right]}^{\frac{1}{2}}.$$

(14)

The above equation guarantees that the discrepancy between the subjective and objective weights of the mth indicator is minimized by evaluating the distance between the subjective weights and the objective weights and the degree of difference between them; this is subject to the following conditions being met:

$$\mathrm{D}\left({\mathrm{W}}_{\mathrm{i}},{\mathrm{W}}_{\mathrm{j}}\right)={\left(\mathrm{a}-\mathrm{b}\right)}^2.$$

(15)

By virtue of this prerequisite, the system of joint cubic equations can be solved, and the assigned value can be substituted into the subjective and objective weights to acquire the combined weights of each indicator based on hierarchical analysis and the EWM.

(2)

Determination of the governance model

The composite scores are calculated using the composite weights obtained from the AHP-EWM.

$${\mathrm{Z}}_{\mathrm{ij}}={{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{W}}_{\mathrm{ij}}\times {\mathrm{X}}_{\mathrm{ij}}.$$

(16)

The most suitable governance model for the study area is identified as the one with the highest composite score.

2.2.4. Result Verification

The evaluation model delineates the relevance and significance of factors in the overall evaluation criteria. Based on the evaluation index system, the governance model for the subsidence area is established using the AHP hierarchical analysis process, with the reliability of the results being verified for consistency.

(1)

Hierarchical single ranking and consistency test

The sum-product method is used to deduce the proportional weights of the elements being compared based on a single criterion, i.e., hierarchical single ranking. The maximum characteristic root λmax of each matrix and its corresponding eigenvector are computed by means of the arithmetic mean method, and the consistency test is performed with CR = CI/RI as shown below.

① $\mathrm{A}\mathsf{\omega }=\mathsf{\lambda }\mathsf{\omega }$ is used to determine λmax, the maximum eigenvector.

$${\mathsf{\lambda }}_{\max }=\frac{{\left(\mathrm{A}\mathsf{\omega }\right)}_{\mathrm{i}}}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{n}\mathsf{\omega }}_{\mathrm{i}}},$$

(17)

where $\mathsf{\omega }$ is the subjective weight in Equation (8) ${\mathrm{W}}_{\mathrm{i}}$.

② The consistency of the matrix is tested.

$$\mathrm{CI}=\frac{{\mathsf{\lambda }}_{\max }-\mathrm{n}}{\mathrm{n}-1}.$$

(18)

③ The corresponding average random consistency index RI is determined from

Table 4. RI correction table.

Number of steps	1	2	3	4	5	6	7	8	9
RI	0	0	0.58	0.89	1.12	1.24	1.32	1.41	1.45

.

④ The stochastic consistency index CR is calculated.

$$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}.$$

(19)

In the formula above, CI (Consistency Index) and n (matrix order) are present, and RI (Average Random Consistency Index) is also taken into account. As the dimension, n, of the judgement matrix increases, the consistency of the judgement decreases. Accordingly, the requirements for the consistency of the high-dimensional judgement matrix should be relaxed and the correction value method should be introduced. Generally, the lower the CR (Consistency Ratio), the better the consistency of the judgement matrix, and the W value can then be used as the B-layer factor judgement weight index (

Table 5. B-tier factor judgment matrix.

A	B1	B2	B3	B4	B5
B1	1	a12	a13	a14	a15
B2	a21	1	a23	a24	a25
B3	a31	a32	1	a34	a35
B4	a41	a42	a43	1	a45
B5	a51	a52	a53	a54	1

). It is usually accepted that when CR < 0.1, the judgement matrix passes the consistency test; otherwise, it should be adjusted accordingly.

(2)

Hierarchical total ranking and consistency test

The process of calculating the weights of relative importance of all factors at each level for the highest level (total target) is known as “hierarchical total ranking”. This process is carried out in a sequential manner, beginning from the highest level (Level A) and ending at the lowest level (Level C). The total ranking of each indicator at Level B for the total target A is a1, a2, … ai. The hierarchical single ranking of the four models at Level C for the various indicators at the upper level B is b1, b2, … bi. The hierarchical total ranking at Level C is the weight of the ith factor at Level C for the weight of the total objective A.

The consistency test of hierarchical total ranking entails calculating the consistency index of the hierarchical single ranking of C1 and C2…Ci in layer C to indicators B1 and B2…Bj in layer B above; this is denoted by CIk (k, I = 1, 2…m). Additionally, the random consistency index is denoted by RIi. Subsequently, the consistency ratio of hierarchical total ranking is calculated as follows:

$$\mathrm{CR}=\frac{{\mathrm{a}}_1{\mathrm{CI}}_1+{\mathrm{a}}_2{\mathrm{CI}}_2++{\mathrm{a}}_{\mathrm{m}}{\mathrm{CI}}_{\mathrm{m}}}{{\mathrm{a}}_1{\mathrm{RI}}_1+{\mathrm{a}}_2{\mathrm{RI}}_2++{\mathrm{a}}_{\mathrm{m}}{\mathrm{RI}}_{\mathrm{m}}}.$$

(20)

When the Consistency Ratio (CR) is less than 0.1, the hierarchical total ranking is considered to have passed the Consistency Test, and therefore displays satisfactory consistency. Otherwise, it is necessary to adjust the values of the elements of those judgment matrices that have higher Consistency Ratios. At this point, the final decision is made based on the lowest level of the hierarchical total ranking.

3. Results and Discussion

3.1. Extraction of Subsidence Indicators, Water Body Indicators and Ecological Indicators in Subsidence Area

(1) Figure 3 depicts (a) the distribution of vegetation cover (including the location of the subsidence area) and (b) the distribution of water bodies in the Guobei coal mine over a 21-year period. The subsidence area in the mine generally corresponds to the region with minimal vegetation cover and an extensive distribution of water bodies. From Figure 3, it is evident that the maximum subsidence depth of the working face in Area 81 is 1796 mm, and that the sinkage area encompasses 3.05 km². Likewise, the maximum sinkage of the working face in Area 82 is 1425 mm, and its sinkage area encompasses 2.30 km². It is thus apparent that Area 82 is a coal mining subsidence area with low vegetation cover, but abundant water bodies.

(2) Figure 4 illustrates (a) the distribution of vegetation cover (including the location of the subsidence area) and (b) the distribution of water bodies in the Yuandian Erjing coal mine over a 21-year period. The subsidence area in this mine is located in an area with abundant vegetation cover and an extensive distribution of water bodies. The maximum sinking depth across Areas 81 and 82 is 4088 mm, and the corresponding sinking area encompasses 3.95 km². In comparison, the maximum sinking depth in Area 83 is 3878 mm, with a sinking area that encompasses 1.56 km².

(3) Figure 5 illustrates (a) the distribution of vegetation cover (including the location of the subsidence area) and (b) the distribution of water bodies in the Xinhu coal mine over a 21-year period. The subsidence zone comprises an area with extensive vegetation cover, and from which water bodies generally appear to be absent. The maximum sinkage depth of working face 818 is 883 mm, and the sinkage area encompasses 1.87 km² (Figure 5).

3.2. Calculation of Weights

3.2.1. AHP-Based Determination of Subjective Weights

To conduct a subjective assessment, a two-by-two comparison of the reciprocal significance of two factors is used to generate the judgment matrix. Next, the subjective weights of each indicator layer to the target layer are acquired based on the matrix.

Indicators are collected for Guobei coal mine Area 81, Guobei coal mine Area 82, Yuandian Erjing coal mine Area 81, Area 82 and Area 83, and Xinhu coal mine Area 81.

Table 6. Summary of comparative importance among indicators.

Indicators	Guobei Coal Mine Area 81					Guobei Coal Mine Area 82					Yuandian Erjing Coal Mine Areas 81, 82, and 83					Xinhu Coal Mine Area 81
	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5
B1	1	4	6	5	4	1	6	7	4	4	1	1/5	1/3	1/5	1/4	1	4	4	1	3
B2	1/4	1	4	3	1	1/6	1	1	1/4	1/4	5	1	4	1	3	1/4	1	1	1/4	1/3
B3	1/6	1/4	1	1/3	1/4	1/7	1/3	1	1/5	1/5	3	1/4	1	1/4	1/3	1/4	1	1	1/4	1/3
B4	1/5	1/3	3	1	1/3	1/4	4	5	1	1	5	1	4	1	3	1	4	4	1	3
B5	1/4	4	4	3	1	1/4	4	5	1	1	4	1/3	3	1/3	1	1/3	3	3	1/3	1

presents a comparison of the importance between two indicators that takes into account the four major study areas, followed by the normalization of each column element and the subjective weight of the indicator layer. The formulas are shown in (7) and (8), and the results are shown in Figure 6 below.

3.2.2. Determination of Objective Weights Based on the EWM

The four major governance models are scored by indexing based on each study area (

Table 7. List of model index scores.

Governance Model and Indicators	Guobei Coal Mine Area 81					Guobei Coal Mine Area 82					Yuandian Erjing Coal Mine Areas 81, 82, and 83					Xinhu Coal Mine Area 81
	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5
Agricultural construction model	3	1	2	2	3	3	2	2	3	3	3	3	3	2	3	6	5	5	5	5
Eco-Functional Zone Construction model	4	3	3	4	5	5	3	2	3	5	3	6	4	5	6	5	4	5	4	4
Ecological landscape construction model	7	5	3	4	7	5	3	2	4	5	3	3	4	3	4	5	4	4	4	4
Park construction model	6	1	4	2	5	7	3	2	5	5	2	1	3	2	4	3	5	4	5	4

).

3.3. Determination of the Governance Model

3.3.1. Determination of AHP-EWM-Based Integrated Weights

After the subjective weight (Figure 6)and objective weight (Figure 7)are obtained by the analytic hierarchy process and entropy weight method, the comprehensive weight of the governance pattern index of the subsidence area is obtained by using the linear grouping method. That is, the subjective weight Wi obtained by AHP method and the objective weight Wj obtained by entropy weight method are synthesized by linear grouping method to obtain the comprehensive weight Wij. The combined weight Wij is then determined, and combined with a + b = 1 in Formulas (13), (14) and (15); the simultaneous equations can be used to obtain the distribution values of a and b (

Table 8. AHP-EWM weight assignments.

Study Area	$\mathit{a}$	$\mathit{b}$
Guobei Coal Mine Area 81	0.79	0.21
Guobei Coal Mine Area 82	0.78	0.22
Yuandian Erjing Coal Mine Areas 81, 82, and 83	0.735	0.265
Xinhu Coal Mine Area 81	0.73	0.27

).

Substituting the assigned value into the subjective and objective weights, we obtain the combined weight of each indicator based on hierarchical analysis and the EWM (Figure 8).

3.3.2. Determination of the Governance Model

The composite scores are calculated using the composite weights obtained by the AHP-EWM method using Equation (16) and the results are shown in

Table 9. List of comprehensive scores for different subsidence area governance models.

Governance Model	Guobei Coal Mine Area 81	Guobei Coal Mine Area 82	Yuandian Erjing Coal Mine Area 81, 82, and 83	Xinhu Coal Mine Area 81
Agricultural construction model	2.39	2.78	2.66	5.27
Eco-Functional Zone Construction model	3.89	4.15	5.18	4.37
Ecological landscape construction model	5.76	4.27	3.30	4.27
Park construction model	4.15	5.43	2.18	4.13

below.

By analyzing the scores of the respective governance models for the different subsidence areas (Table 9) based on the AHP-EWM scoring system, it can be concluded that the higher the score of a given model, the better it is suited to the corresponding subsidence area. Therefore, by combining the comprehensive scores of the governance models for different subsidence areas with information on the existing conditions of the subsidence areas, the final governance model for the subsidence area can be obtained. These results are presented in

Table 10. Governance models selected for different subsidence areas.

Subsidence Area	Selected Governance Model
Guobei Coal Mine Area 81	Ecological landscape construction model (wetland park construction model)
Guobei Coal Mine Area 82	Park construction model (eco-industrial park construction model)
Yuandian Erjing Coal Mine Area 81, 82, and 83	Ecological function zone construction model (plain reservoir construction model)
Xinhu Coal Mine Area 81	Agricultural construction model (agricultural plantation construction model)

below.

3.4. Discussion

After the best governance model for the Guoyang mine area was identified based on the AHP-EWM-based selection framework, we tested the results for consistency with those from an AHP evaluation system in order to verify their reliability. By combining the existing governance models, the appropriate governance models were chosen for Areas 81 and 82 of the Guobei Coal Mine, Areas 81, 82 and of the Yuandian Erjing Coal Mine, and Area 81 of the Xinhu Coal Mine. To ensure the validity of the results, the AHP evaluation system was used to validate the selection of governance models for the above study areas; the CR value of the final results was then employed to determine the accuracy of the results.

3.4.1. Hierarchical Single Ranking and Consistency Test

Taking into account the diverse governance models selected for the subsidence area of the Guoyang Mine, we evaluated the score of each indicator and determined their rankings in the corresponding hierarchy list for the Guoyang Mine accordingly. These calculations were based on the procedure of the consistency test (

Table 11. Relative importance of different indicators for subsidence areas.

Subsidence Area Indicators	B1				B2				B3				B4				B5
	Wetland Park	Industrial Park	Plain Reservoir	Agricultural Cultivation	Wetland Park	Industrial Park	Plain Reservoir	Agricultural Cultivation	Wetland Park	Industrial Park	Plain Reservoir	Agricultural Cultivation	Wetland Park	Industrial Park	Plain Reservoir	Agricultural Cultivation	Wetland Park	Industrial Park	Plain Reservoir	Agricultural Cultivation
B1	1	1	1	1	4	6	1/5	4	6	7	1/3	4	5	4	1/5	1	4	4	1/4	3
B2	1/4	1/6	5	1/4	1	1	1	1	4	1	4	1	3	1/4	1	1/4	1	1/4	3	1/3
B3	1/6	1/7	3	1/4	1/4	1/3	1/4	1	1	1	1	1	1/3	1/5	1/4	1/4	1/4	1/5	1/3	1/3
B4	1/5	1/4	5	1	1/3	4	1	4	3	5	4	4	1	1	1	1	1/3	1	3	3
B5	1/4	1/4	4	1/3	1	4	1/3	3	4	5	3	3	3	1	1/3	1/3	1	1	1	1

).

The calculation of the random consistency index CR was carried out using Equations (7), (8) and (17)–(19). The results are presented in

Table 12. List of single-order consistency tests for different subsidence area governance models.

Governance Model	λmax	CI	CR
Wetland Park Construction model	5.24	0.059	0.0529
Eco-industrial park construction model	5.36	0.091	0.081
Plain reservoir construction model	5.205	0.051	0.0458
Agricultural planting construction model	5.102	0.025	0.0223

below.

In the table, CI stands for the Consistency Index, and CR stands for the Random Consistency Index. In general, a smaller value of CR indicates that the judgment matrix has a higher level of consistency. It is usually accepted that the judgment matrix satisfies the consistency test when CR is less than 0.1; otherwise, it should be appropriately adjusted. Given that CR values for the four governance models fall below 0.1, we can conclude that the judgment matrix has fulfilled the consistency test; this also indicates that the hierarchical single ranking has passed the consistency test.

3.4.2. Hierarchical Total Ranking and Consistency Test

The next step is to assess the consistency of the model’s comprehensive hierarchical ranking. The consistency ratio of the hierarchical total ranking Formula (20) indicates that there is a need to calculate the CI value and RI value determined by the C layer of four subsidence area governance modes for each index B layer of subsidence area; to begin with, each governance model should be evaluated based on the five indicator values for the subsidence area. The results are presented in

Table 13. Comparison of the importance of subsidence area indicators.

Governance Model and Indicators	Guobei Coal Mine Area 81					Guobei Coal Mine Area 82					Yuandian Erjing Coal Mine Area 81, 82, and 83					Xinhu Coal Mine Area 81
	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5	B1	B2	B3	B4	B5
Agricultural construction model	1	1	1	1	3	3	4	1/5	1	1/4	1	4	1/6	3	1/6	1/5	4	1	1	1/4
Eco-Functional Zone Construction model	1/3	1/4	5	1	5	1	1	1	1	1	1/3	1	1/3	3	1/4	1/5	1	5	1	1
Ecological landscape construction model	1	1/4	6	1/3	7	3	1	3	1/3	4	1	1	1	1	1	1/4	1	6	1/3	4
Park construction model	4	1/4	1	1	5	5	1	1/5	1	1	4	1	1/6	3	1/4	1	1	1	1	1

below.

The above is based on the five indicators of the subsidence area of the governance model of the evaluation of the score. The next step is to carry out the B level of the indicators of the single ranking consistency index CI calculation. Based on Formulas (17) and (18), the values can be obtained.

The CI values of the four governance models in layer C with respect to each indicator in layer B are shown in

Table 14. List of Consistency Indicators (CI) for Indicator Sheet Ranking.

Indicators	λmax	CI
Location	4.09	0.031
NDWI	4	0
FVC	4.117	0.039
Sinking depth	4	0
Sinking area	4.13	0.0439

above. Table 4 also reveals that the RI value is 0.89. Consequently, Formula (20) for the consistency test of the hierarchical total ranking can be applied. This produces the consistency values of the hierarchical total rankings of different governance models in the Guoyang mine area (

Table 15. Results of consistency test for different subsidence area governance models.

Subsidence Area	Hierarchical Single Ranking CR Value	Hierarchical Total Ranking CR Value
Guobei Coal Mine Area 81	0.0529	0.026
Guobei Coal Mine Area 82	0.081	0.024
Yuandian Erjing Coal Mine Area 81, 82, and 83	0.0458	0.022
Xinhu Coal Mine Area 81	0.0223	0.021

).

The governance models selected for different subsidence areas all pass the consistency test; the CR values of both the hierarchical single ranking and the hierarchical total ranking fall below 0.1. This indicates that both rankings achieve satisfactory consistency. Hence, the final decision can be made according to the total ranking of the lowermost level. The governance model for the Guoyang mine is selected because it meets the existing local conditions and is supported by sufficient data.

4. Conclusions

To identify a suitable governance model for a coal mining subsidence area, one must carefully consider the physical characteristics of the area in question. To enhance the objectivity with which weights were determined in the AHP model, we incorporated the EWM for weight determination, and used the probability integral method and remote sensing index method to extract the parameters needed for the model. With data from three distinct coal mining subsidence areas in Guoyang, we constructed an AHP-EWM-based evaluation model for the selection of an appropriate governance model for coal mining subsidence areas. Our model includes informative and quantitative indicators such as the geographic location, the NDWI, the FVC, the maximum subsidence depth, and the maximum subsidence area. The results suggest that a wetland park model, an industrial park model, and a plain reservoir and agricultural planting model are the most suitable governance models for subsidence areas in the Guobei coal mine, Yuandian Erjing coal mine and Xinhu coal mine, respectively. In comparison with traditional approaches to selecting governance models for subsidence areas, the AHP-EWM-based evaluation displays advantages in terms of the reliability and accuracy of the results, as well as the efficiency with which they are obtained. By integrating theory and methods from a range of disciplines including biology, ecology, economics and environmental science, as well as specific techniques for managing subsidence areas such as dredging, deep excavation, and filling, subsidence areas can be better managed to strike a balance between the objectives of coal mining and ecological protection, as well as between industrial and agricultural production. Such approaches should help to mitigate the destructive impacts of mining activities on society, the economy and the environment.

Our study encountered several limitations. First, our study was region-specific, and as such did not examine the full range of indicators that are relevant to governance models for subsidence areas. In addition, while there exist several gray models and multi-objective decision models that are conceptually similar to the AHP-EWM-based model we propose, it remains difficult to ascertain which model ultimately performs best in the absence of direct comparisons.