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 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:
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.
b8: Near-infrared band;
b4: Infrared band.
,
;
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:
—maximum surface subsidence value under full mining conditions;
m—thickness of the mined coal seam;
q—surface subsidence coefficient;
—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).
In the equation, A is the area of the subsidence area, (,) is the coordinate of the point of the cross section at 10 mm sinking of the subsidence area.
2.2.2. Calculation of Weights
- (1)
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.
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.
③ First, each column element of the judgment matrix is normalized, and the general terms of its elements are
Pij: aij;
P’ij: the value of aij normalized.
④ After each column is normalized, the rows of the normalized judgment matrix are summed to obtain the normalized mean value
, that is, the subjective weights of the indicator layer.
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
where
is the value of different governance models j under the ith indicator;
is the normalized value.
② Normalization of the indicators:
Qij—normalization of the indicators (I = 1, 2, n, j = 1, 2, m).
③ Determination of the information entropy of each indicator Ej:
Ej—information entropy.
④ Determination of the weight of each indicator W by information entropy E jj:
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
In the formula,
and
are the assigned values of subjective weights and objective weights, respectively, which satisfy
. The distance function of the subjective weight and objective weight
is also introduced and expressed as
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:
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.
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
is used to determine λmax, the maximum eigenvector.
where
is the subjective weight in Equation (8)
.
② The consistency of the matrix is tested.
③ The corresponding average random consistency index RI is determined from
Table 4.
④ The stochastic consistency index CR is calculated.
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). 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:
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.