Coupling Fuzzy Multi-Criteria Decision-Making and Clustering Algorithm for MSW Landfill Site Selection (Case Study: Lanzhou, China)

The siting of Municipal Solid Waste (MSW) landfills is a complex decision process. Existing siting methods utilize expert scores to determine criteria weights, however, they ignore the uncertainty of data and criterion weights and the efficacy of results. In this study, a coupled fuzzy Multi-Criteria Decision-Making (MCDM) approach was employed to site landfills in Lanzhou, a semi-arid valley basin city in China, to enhance the spatial decision-making process. Primarily, 21 criteria were identified in five groups through the Delphi method at 30 m resolution, then criteria weights were obtained by DEMATEL and ANP, and the optimal fuzzy membership function was determined for each evaluation criterion. Combined with GIS spatial analysis and the clustering algorithm, candidate sites that satisfied the landfill conditions were identified, and the spatial distribution characteristics were analyzed. These sites were subsequently ranked utilizing the MOORA, WASPAS, COPRAS, and TOPSIS methods to verify the reliability of the results by conducting sensitivity analysis. This study is different from the previous research that applied the MCDM approach in that fuzzy MCDM for weighting criteria is more reliable compared to the other common methods.


Introduction
Rapid urbanization and population growth have posed serious challenges to the sustainable development of cities, which have also led to environmental pollution and a dramatic increase in the generation of waste [1]. Over the last decade, global Municipal Solid Waste (MSW) generation has increased from 0.68 billion tons per year (0.64 kg of MSW per person per day) to 1.3 billion tons per year (1.2 kg per person per day), which is likely to reach 2.2 billion tons per year by 2025 [2]. MSW is a critical issue with the potential to have severe negative impacts on the environment and public health [3]. Therefore, the disposal of immense volumes of MSW has become a matter of great concern for urban planners and environmental managers on a global scale [4].
Although China has experimented with waste classification and harmless treatment policies in Shanghai and other developed cities since 2018, landfill remains the most essential and efficacious means for disposing of most MSW for the majority of economically underdeveloped areas [5]. It was revealed that improper landfills can have long-lasting damaging impacts and cause potential harm to the surrounding ambient soil, groundwater, and atmosphere [6]. Thus, the selection of suitable sites for landfills is considered a complex and urgent task in Municipal Solid Waste Management (MSWM) [7].
Numerous Multi-Criteria Decision-Making (MCDM) methods have been developed to support decision-making in MSWM, including AHP [2,8], Analytic Network Process [9], Fuzzy logic [10], Ordered Weighted Average (OWA) [11], Weighted Linear Combina- As of July 2020, the city has jurisdiction over five districts and three counties, with an approximate area of 1.31 × 10 4 km 2 and a population of over 4.13 × 10 6 people. According to statistics from the Gansu Environmental Statistics Bulletin (GESB, 2009), 7.30 × 10 5 tons of domestic waste are generated annually in the four suburban districts of Lanzhou city, with 3.30 × 10 5 tons (45.7%) from Chengguan, 1.26 × 10 5 tons (17.3%) from Qilihe, 1.43 × 10 5 tons (19.6%) from Xigu, and 1.27 × 10 5 tons (17.4%) from Anning, as a rate of 5% to 8% per year. The output of domestic waste is 3000 tons in the urban area every day; however, only 2100 tons can be effectively disposed of, with a disposal rate of 70% (http://sthj.gansu.gov.cn/, accessed on 20 December 2019). The remaining waste is spread across the surrounding areas of the city, which seriously restricts the development of Lanzhou. Figure 2 illustrates the framework proposed in this study. As of July 2020, the city has jurisdiction over five districts and three counties, with an approximate area of 1.31 × 10 4 km 2 and a population of over 4.13 × 10 6 people. According to statistics from the Gansu Environmental Statistics Bulletin (GESB, 2009), 7.30 × 10 5 tons of domestic waste are generated annually in the four suburban districts of Lanzhou city, with 3.30 × 10 5 tons (45.7%) from Chengguan, 1.26 × 10 5 tons (17.3%) from Qilihe, 1.43 × 10 5 tons (19.6%) from Xigu, and 1.27 × 10 5 tons (17.4%) from Anning, as a rate of 5% to 8% per year. The output of domestic waste is 3000 tons in the urban area every day; however, only 2100 tons can be effectively disposed of, with a disposal rate of 70% (http://sthj.gansu.gov.cn/, accessed on 20 December 2019). The remaining waste is spread across the surrounding areas of the city, which seriously restricts the development of Lanzhou. Figure 2 illustrates the framework proposed in this study.

Data Sources
The data used in this study are mainly divided into vector data (point, polygon, polygon) and raster data, which are large in quantity and time-consuming in preprocessing. Vector data focused on recording the properties of criterion, while raster data focused on representing the spatial distribution of the criterion. According to the data sources, the data were obtained from open-source geographic information-sharing platforms, online websites, and government agencies. The open-source geographic information sharing platform included the Resource and Environmental Science and Data Center, Chinese Academy of Sciences and National Catalogue Service for Geographic Information.
Online websites included the official of MODIS, USGS Earth Explorer, and Gaode Maps. Government agencies included the Gansu Water Resources Department, Gansu Bureau of Geology and Mineral Hydrogeology Engineering Geological Exploration Institute, Gansu Earthquake Agency, and Portal website of Gansu Forestry and Grass Bureau. All of the criterion data sets used in this study, as well as their formats and sources, are described in Table A1

Data Sources
The data used in this study are mainly divided into vector data (point, polygon, polygon) and raster data, which are large in quantity and time-consuming in preprocessing. Vector data focused on recording the properties of criterion, while raster data focused on representing the spatial distribution of the criterion. According to the data sources, the data were obtained from open-source geographic information-sharing platforms, online websites, and government agencies. The open-source geographic information sharing platform included the Resource and Environmental Science and Data Center, Chinese Academy of Sciences and National Catalogue Service for Geographic Information.
Online websites included the official of MODIS, USGS Earth Explorer, and Gaode

Identification of Evaluation Criteria
The CNS has set strict standards for the evaluation criteria of landfill site selection and construction. The specific CNS for reference include: Delphi is an improved expert scoring method, which utilizes the questionnaire to continuously iterate four times anonymously to investigate the scientific evaluation of multi-domain experts on decision-making problems [40]. The expert group consists of 30 MSW experts, including academic researchers and professors in waste, environmental, municipal management, land-use planning, and geology, with an average of 12 years of practical or teaching experience in waste management. Combined with the CNS and Delphi method, 21 sub-criteria (C1, C2, C3, ..., C21) were identified and were categorized into five dimensions (B1, B2, B3, B4, and B5).
Furthermore, hydrogeological aspects were also considered to avoid potential groundwater contamination in semi-arid valley basins caused by the leakage of landfill leachate, while ensuring the safety of construction and operation [41]. Morphological aspects were taken into account to reduce construction costs and increase stability during construction [10]. Environmental aspects were taken into consideration to minimize the impacts on neighboring residents, and land/water resources [42]. Climatic issues were reviewed to reduce potential threats and damage to the surrounding environment posed by various pollutants released from the landfill through leachate or waste gas [43]. Socioeconomic impacts were considered to prevent the landfill from adversely affecting surrounding ecological reserves and regional economic development [8]. Further detailed information on the criteria selection is contained in Table A2 in Appendix B. The interval from 0 to 1 was adopted for normalization, where the larger the value, the better the suitability (Figure 3).

Fuzzy DEMATEL-ANP
This study aimed to integrate the DEMATEL-ANP method to establish a network structure to clarify the interdependent relationship between criteria and determine their relative weights. DEMATEL has the following advantages: (1) Distinguishing the attributes of criteria (positive and negative). (2) The prominence of the criteria can be determined. (3) The relationship between criteria can be quantified (direct and indirect influences). (4) A large number of samples are not required [44]. ANP was introduced to modify the AHP process, which finds the best possible solution for complex decision-making issues in the model of an ordered network structure [45]. Considering the mechanisms of dependency and feedback between the criteria makes the decision-making model closer to the actual situation. To reduce the uncertainty of data and expert ratings, ANP can utilize the causal relationship determined by DEMATEL to calculate weights [46].

Construction of Direct Influence Matrix
According to the expert opinion obtained by the Delphi method, a numerical scale of 0-4 is adopted to indicate the degree of direct influence between criteria. Where "no influence" is 0, "low influence" is 1, "medium influence" is 2, "high influence" is 3, and "very high influence" is 4. A pairwise comparison judgment matrix is constructed, respectively. Experts (E = 1, 2 · · · , E) judged the criteria in order to derive a square matrixis A E expressed in Equation (1). Subsequently, Equation (1) indicates the average direct impact matrix, according to the equation, calculating the average value of the numerical scale for each matrix.   groundwater quality, (c) groundwater richness, (d) distance from faults, (e) distance from earthquake points, (f) elevation, (g) slope, (h) soil type, (i) NDVI, (g) landform type, (k) distance from surface water, (l) distance from roads, (m) land use type, (n) distance from settlements, (o) precipitation, (p) temperature, (q) ecosystem service value, (r) population density, (s) GDP, (t) distance from airports, (u) distance from protected areas.

Construction of Direct Influence Matrix
According to the expert opinion obtained by the Delphi method, a numerical scale of 0-4 is adopted to indicate the degree of direct influence between criteria. Where "no influence" is 0, "low influence" is 1, "medium influence" is 2, "high influence" is 3, and "very high influence" is 4. A pairwise comparison judgment matrix is constructed, respectively. Experts 1,2, ⋯ , judged the criteria in order to derive a square matrix is expressed in Equation (1). Subsequently, Equation (1) indicates the average direct impact matrix, according to the equation, calculating the average value of the numerical scale for each matrix.

Normalization Directly Influences the Matrix
To unify the numerical scale into a comparable range, Equations (2) and (3) are employed to obtain the normalized direct relation matrix, whose value is between 0 and 1.

Normalization Directly Influences the Matrix
To unify the numerical scale into a comparable range, Equations (2) and (3) are employed to obtain the normalized direct relation matrix, whose value is between 0 and 1.

Deriving the Comprehensive Influence Matrix
The comprehensive influence matrix represents the superposition of direct and indirect influences between criteria. T B (criterion) (Equation (5)) and T C (sub-criterion) (Equation (6)) are calculated using Equation (4), where I is the identity matrix.

Computing and Being Influences of the Matrix
Based on the comprehensive influence matrix, the row vectors are summed to obtain the influence of the criterionon other criteria (influence). The column vectors are summed to obtain the influence of the other criteria on the criterion i (being influence). Further, the values of R B and C B denote the influence and being influence of the criteria, whereas the values of R C and C C denote the influence and being influence of the sub-criteria (Equations (7) and (8)).

Establishing the Network Structure
ANP establishes the network structure with assistance from the comprehensive influence matrix and constructs the super matrix to allocate the weight for the criteria. To distinguish the difference between the criteria, Equation (9) is employed to calculate the centrality M and causation N. The network structure is based on coordinate values (M,N) to express the interdependence and feedback influences between criteria, and its comprehensive threshold is set as the average value of the matrix and medium numerical scale.

Normalization of Comprehensive Influence Matrix
Based on the comprehensive influence matrix, the criterion normalized comprehensive iα ij m×m (Equations (10 and (11)) was calculated by the row vector of criterion divided by the sum of the row vector of its corresponding row. The sum of the numerical scales for each row vector is 1: ∑ m j=1 t B α ij = 1. Similarly, the normalized comprehensive influence matrix of the sub-criterion is obtained by the same method (Equation (12)).

Construct and Solve the Limit Super Matrix
The weighted super matrix W C (Equation (13)) is expressed by multiplying the normalized comprehensive influence matrix of the criterion of transpose and the sub-criterion of transpose. The weighted super matrix is limited until it converges to calculate the final weight vector (Equation (14)).

Fuzzy Logic
The mapping and analysis of criteria attribute based on fuzzy logic, trapezoidal, interval, S-shape, Triangular shape, and Gamma shape are commonly employed fuzzy membership functions to determine fuzzy information in fuzzy logic [47][48][49]. According to the existing research, we have determined the appropriate membership function for each criterion to improve the accuracy of the results and optimize the uncertainty of the evaluation criteria (Table 1) [50][51][52]. Table 1. M(R + C), N(R − C) and weights for criterion and sub-criterion.

Spatial Analysis
In this study, based on the unified projection coordinate system, all data are converted to raster format and resampled for 30 m. Modeling is carried out with the help of spatial analysis tools in ArcGIS software to obtain reasonable results of landfill site selection. Buffer zones are established for faults, earthquake points, surface water, settlements, roads, protected areas, and airports in accordance with the CNS for waste landfill sites, and the regional characteristics of the valley basins in the semi-arid area of Lanzhou. The weights and fuzzy layers calculated by DEMATEL-FANP are integrated, and the weighted overlay of layers and smooth the neighborhood are implemented to obtain the landfill site selection results.

Cluster Analysis
Compared with the K-Means method, the density-based clustering analysis does not require prior knowledge of the number of clusters to be formed, the shape of the clusters is not limited, and noise points can be identified.
I. Density-Based Spatial Clustering of Applications with Noise (DBSCAN) The input parameters are the neighborhood radius (ε) and the minimum number of entities (MinPts). The data set is divided into core, boundary, and noise points. A random point is selected from the data set as the seed for traversal. When the density of any two points is reachable or direct, it is classified into the same cluster. The number of entities in the same cluster must be greater than MinPts; when it is less, they are classified as noise points [53].
II. Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) The input parameter is MinPts, ε changes with the point density change, automatic clustering can be implemented without parameter adjustment. On the basis of DBSCAN and in combination with the hierarchical clustering algorithm, the concept of "Mutual Reachability Distance" was introduced [54].
where A, B are two core points; Core k (A) is the distance between A and the K-th adjacent point; Core k (B) is the distance between B and the K-th adjacent point; d(A, B) is the Euclidean distance between A and B. III. Ordering Points to Identify the Clustering Structure (OPTICS) The input parameters were ε, MinPts, and sensitivity. The value of clustering sensitivity is 0-100. The higher the sensitivity, the smaller the clustering interval is. And introduced the "accessible distance" [55].
where, P, Q are the two core points, the core distance of P, and the Euclidean distance between P and Q.

WASPAS (Weighted Aggregated Sum Product Assessment)
Step 1 Construct a decision matrix X = x ij , where x ij is the response of alternative item i to criterion j.
Step 2 Normalize the decision matrix based on the maximum and minimum method (Equation (17)) [56].
Step 3 Weight normalized decision matrix (Equation (18)), w is the weight of criterion j.
Step 4 Calculate the relative importance of alternatives by utilizing the weighted sum model (WSM) and weighted product model (WPM) [57], where n is the number of alternatives.
Step 5 Calculate the scores of each alternative according to Equation (19) and arrange them in descending order.
3.4.2. MOORA (Multi-Objective Optimization by Ratio Analysis) Step 1 Construct a decision matrix X = x ij , where x ij is the response of alternative item i to criterion j.
Step 2 Normalize the decision matrix based on the vector method (Equation (20)), where m is the number of alternatives.
Step 3 Weight normalized decision matrix (Equation (21)), w is the weight of criterion j.
Step 4 Calculate the relative importance of alternatives by utilizing the ratio of the system (Equation (22)) [58], where n is the number of criteria.
Step 5 Calculate the scores of each alternative according to Equation (23) and arrange them in descending order.

COPRAS (COmplex PRoportional ASsessment)
Step 1 Construct a decision matrix X = x ij , where x ij is the response of alternative item i to criterion j.
Step 2 Normalize the decision matrix based on the summation method (Equation (24)), where m is the number of alternatives.
Step 3 Weight normalized decision matrix (Equation (25)), w is the weight of criterion j.
Step 4 Calculate the relative importance of alternatives by utilizing the complex scale evaluation index (Equation (26)) [59], where n is the number of criteria. Step 5 Calculate the scores of each alternative according to Equation (27) and arrange them in descending order. The higher the score, the higher the priority.
3.4.4. TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) Step 1 Construct a decision matrix X = x ij , where x ij is the response of alternative item i to criterion j.
Step 2 Normalize the decision matrix based on the minimum-maximum method (Equation (28)), where m is the number of alternatives.
Step 3 Weight normalized decision matrix (Equation (29)), w is the weight of criterion j.
Step 4 Calculate the relative importance of alternatives by utilizing the distance index (Equation (30)) [60], where n is the number of criteria.
Step 5 Calculate the scores of each alternative according to Equation (31), and arrange them in descending order.

Determining the Weight
The comprehensive influence matrix of the criterion and sub-criterion (Tables A3  and A4 fin Appendix B) are derived by calculating the mean value of the direct and the normalized direct impact matrix. Ultimately, a statistical analysis was performed on the criteria (Table 2). It can be seen from the table that in the criteria, the environmental criterion shows the highest M value (2.5949) and the highest N value (0.7060). The climatic criterion M value (1.1510) is the lowest, and the hydrogeological criterion N value (−0.8155) is the lowest. In the sub-criteria, soil type, landform type, land use type, distance from settlements, population density, GDP, and distance from airports are the being affected criteria, while the others are affected criteria. The M value (6.5923) of distance from surface water was the highest, and the N value (0.6806) of groundwater quality was the highest. The M value (1.2955) of temperature was the lowest, and the N value (−0.9090) of NDVI was the lowest. Furthermore, the weight of temperature (0.0142) and precipitation (0.0214) was lowest, due to the dry climate, low annual precipitation, and lower leachate pollution generated by landfills in the semi-arid region of Northwest China, which is significantly different from that in humid regions. The weights of land use type (0.0531) and ecological service value (0.0641) were relatively high, which was due to the scarcity of land in river valleys and basins. In particular, urban expansion leads to the development and utilization of farmland, forestland, water, and other ecological land that is close to central urban areas. Lanzhou is one of the cities with the most serious geological disasters in China. It is located in the Qilian Mountain earthquake belt, where the abundance of historical landslides, debris flows, and earthquakes should not be underestimated. Considering the geological structure and development of the study area, the weights of faults and earthquake points are 0.0582 and 0.0398, respectively. Water areas, settlements, and protected areas are constraints that are strictly stipulated by the CNS; thus, the relative weight value is also high.

Fuzzy Membership Function Figure Formula
S-shape S-shape (increasing) by landfills in the semi-arid region of Northwest China, which is significantly different from that in humid regions. The weights of land use type (0.0531) and ecological service value (0.0641) were relatively high, which was due to the scarcity of land in river valleys and basins. In particular, urban expansion leads to the development and utilization of farmland, forestland, water, and other ecological land that is close to central urban areas. Lanzhou is one of the cities with the most serious geological disasters in China. It is located in the Qilian Mountain earthquake belt, where the abundance of historical landslides, debris flows, and earthquakes should not be underestimated. Considering the geological structure and development of the study area, the weights of faults and earthquake points are 0.0582 and 0.0398, respectively. Water areas, settlements, and protected areas are constraints that are strictly stipulated by the CNS; thus, the relative weight value is also high.

Fuzzy Membership Function Figure Formula
S-shape S-shape (increasing) by landfills in the semi-arid region of Northwest China, which is significantly different from that in humid regions. The weights of land use type (0.0531) and ecological service value (0.0641) were relatively high, which was due to the scarcity of land in river valleys and basins. In particular, urban expansion leads to the development and utilization of farmland, forestland, water, and other ecological land that is close to central urban areas. Lanzhou is one of the cities with the most serious geological disasters in China. It is located in the Qilian Mountain earthquake belt, where the abundance of historical landslides, debris flows, and earthquakes should not be underestimated. Considering the geological structure and development of the study area, the weights of faults and earthquake points are 0.0582 and 0.0398, respectively. Water areas, settlements, and protected areas are constraints that are strictly stipulated by the CNS; thus, the relative weight value is also high.

Fuzzy Membership Function Figure Formula
S-shape S-shape (increasing) by landfills in the semi-arid region of Northwest China, which is significantly different from that in humid regions. The weights of land use type (0.0531) and ecological service value (0.0641) were relatively high, which was due to the scarcity of land in river valleys and basins. In particular, urban expansion leads to the development and utilization of farmland, forestland, water, and other ecological land that is close to central urban areas. Lanzhou is one of the cities with the most serious geological disasters in China. It is located in the Qilian Mountain earthquake belt, where the abundance of historical landslides, debris flows, and earthquakes should not be underestimated. Considering the geological structure and development of the study area, the weights of faults and earthquake points are 0.0582 and 0.0398, respectively. Water areas, settlements, and protected areas are constraints that are strictly stipulated by the CNS; thus, the relative weight value is also high.

Fuzzy Membership Function Figure Formula
S-shape S-shape (increasing)

Identifying the Landfill Site
The suitability map is generated by overlaying the fuzzy normalized layer of all criteria and assigning weights for each criterion. Subsequently, the results are divided into five categories: "most suitable, more suitable, suitable, less suitable, and unsuitable". Its area and proportions were "6288 km 2 (0.48), 3275 km 2 (0.25), 2358 km 2 (0.18), 917 km 2 (0.07), and 262 km 2 (0.02)", respectively. Simultaneously, non-constructible areas are eliminated according to the CNS, including mainly rivers, protected areas, central urban areas, airports, and so on.
The "most suitable" category in the results was selected, and 140,103 data points were

Identifying the Landfill Site
The suitability map is generated by overlaying the fuzzy normalized layer of all criteria and assigning weights for each criterion. Subsequently, the results are divided into five categories: "most suitable, more suitable, suitable, less suitable, and unsuitable". Its area and proportions were "6288 km 2 (0.48), 3275 km 2 (0.25), 2358 km 2 (0.18), 917 km 2 (0.07), and 262 km 2 (0.02)", respectively. Simultaneously, non-constructible areas are eliminated according to the CNS, including mainly rivers, protected areas, central urban areas, airports, and so on.
The "most suitable" category in the results was selected, and 140,103 data points were

Identifying the Landfill Site
The suitability map is generated by overlaying the fuzzy normalized layer of all criteria and assigning weights for each criterion. Subsequently, the results are divided into five categories: "most suitable, more suitable, suitable, less suitable, and unsuitable". Its area and proportions were "6288 km 2 (0.48), 3275 km 2 (0.25), 2358 km 2 (0.18), 917 km 2 (0.07), and 262 km 2 (0.02)", respectively. Simultaneously, non-constructible areas are eliminated according to the CNS, including mainly rivers, protected areas, central urban areas, airports, and so on.
The "most suitable" category in the results was selected, and 140,103 data points were

Identifying the Landfill Site
The suitability map is generated by overlaying the fuzzy normalized layer of all criteria and assigning weights for each criterion. Subsequently, the results are divided into five categories: "most suitable, more suitable, suitable, less suitable, and unsuitable". Its area and proportions were "6288 km 2 (0.48), 3275 km 2 (0.25), 2358 km 2 (0.18), 917 km 2 (0.07), and 262 km 2 (0.02)", respectively. Simultaneously, non-constructible areas are eliminated according to the CNS, including mainly rivers, protected areas, central urban areas, airports, and so on.
The "most suitable" category in the results was selected, and 140,103 data points were extracted for density-based cluster analysis to intuitively display the spatial distribution characteristics of candidate sites (Figs. C.1 in Appendix C). The DBSCAN method has the fastest calculation speed, where following many experiments and comparisons, it selects the ε of 1600 m and the MinPts of 1000 for cluster analysis, and obtains 15 clusters, and 1 is the noise point. Overall, the U-3 candidate sites located~1700 m southeast of Liangjiawan in the Xigu District had the smallest density and area, and were closest to the Yellow River among all candidate sites; thus, they were classified as noise points. As a method to merge as many entities as possible, HDBSCAN is data-driven and can directly reflect the aggregation of the data itself. 1000 MinPts were taken to obtain 15 clusters, and 1 was the noise point. As can be seen from the results, a small part of the U-3 candidate sites located~1700 m southeast of Liangjiawan in the Xigu District were divided into noise points, while the rest were grouped together with S-11, and the value of probability 1 was the highest in the membership probability distribution presented. OPTICS overcomes the shortcoming that low-density clusters within a neighborhood radius contains high-density clusters. Meanwhile, it is not completely data-driven and has obvious advantages for the analysis of spatial distribution characteristics. The ε was set to 1600 m, MinPts to 1000, and cluster sensitivity to 10, after which a total of 13 classes of clusters were obtained, and the 1 was the noise point, including U-1, U-2, and U-3. Eleven candidate sites were identified by integrating the three clustering algorithms (Figure 4). It can be seen that the sites are primarily distributed across Yongdeng, Gaolan, and Yuzhong Counties, with a lower distribution in central urban areas and smaller areas. The major reasons are that counties contain more unused land, are close to central urban areas, and transportation is convenient. Conversely, in central urban areas, there are mass settlements, the land is limited, and water resources are scarce.  The daily MSW capacities of the candidate sites were calculated according to the "Construction Standard of MSW Landfill Disposal Engineering Project" ( Table 3, Table  A5 in Appendix D). There were four candidate landfills (S-3, S-5, S-7, and S-8) in Yongdeng, three candidate sites (S-1, S-2, and S-6) in Gaolan, and one candidate site (S-2) in Yuzhong, each of which could accommodate more than 1200 tons/day of MSW. One of The daily MSW capacities of the candidate sites were calculated according to the "Construction Standard of MSW Landfill Disposal Engineering Project" (Table 3, Table A5 in Appendix D). There were four candidate landfills (S-3, S-5, S-7, and S-8) in Yongdeng, three candidate sites (S-1, S-2, and S-6) in Gaolan, and one candidate site (S-2) in Yuzhong, each of which could accommodate more than 1200 tons/day of MSW. One of the most suitable candidate landfill sites in Honggu (S-9) had a capacity of 500 to 1200 tons/day of MSW. The candidate sites in Xigu and Anning were S-10 and S-11, both of which could accommodate 200 to 500 tons/day of MSW. Qilihe and Chengguan had no optimal sites.

Validation
The 11 candidate sites identified by cluster analysis were satisfactory from the perspective of hydrogeological, morphological, environmental, climatic, and socio-economic factors, as they were all based on criteria analysis. However, to ensure that the candidate sites conformed to the CNS and the urban planning measures of the study area, it was necessary to evaluate them relatively. We conducted field visits and selected four methods: WASPAS, MOORA, COPRAS, and TOPSIS to determine the final ranking of the candidate sites by according to expert opinions and regional characteristics. As can be seen from Table 4, the ranking results of WASPAS and COPRAS were the same, as were MOORA and TOPSIS, whereas the four methods were slightly different for S-5, S-7, S-8, and S-10. The correlation coefficient of WASPAS-COPRAS and MOORA-TOPSIS was 1, and for WASPAS-MOORA, WASPAS-TOPSIS, COPRAS-MOORA, and COPRAS-TOPSIS was 0.94. As such, it was confirmed that there was a high degree of consistency between the ranking results of the candidate sites, with S-1 being the most suitable. In this study, sensitivity analysis charts were established for 13 scenarios with different weights to reflect the influences of changes in criterion weights on the final results and ranking stability ( Figure A2 in Appendix E). Spearman's correlation coefficient was employed to analyze four ranking methods in the scenario simulation with different weights ( Table 5). As can be seen from the Figure, the ranking of scenarios 4, 6, and 7 changed among the four ranking methods, which was due to their low correlation coefficients between and the original weighting scenario 1. The ranking order of the other 10 scenarios remained unchanged, which indicated the stability of the site selection results and the reliability of the method. Furthermore, the criteria for ranking the first, second, and third sites were all decisive and evenly distributed. Their relative importance was balanced, although the scores of candidate sites varied under different scenarios. Omitting the third-ranking criterion 1 1 1 1

Discussion
By discussing the features of this study and those of the closely related research [21,25,28], the reliability of the MCDM model to find suitable landfills for each geographical area is verified. The case study of the current paper is related to a typical semi-arid valley basin city landfill site selection problem in which more than 21 criteria such as hydrogeological, morphological, environmental, climatic, and socioeconomic are considered. A novel integrative decision-making algorithm is proposed, the DEMATEL-ANP, GIS, and Density clustering, with the fuzzy environment. The candidate landfill sites for MSW were identified by recognizing these criteria and their internal relationships. Finally, a comprehensive analysis of optimal landfill sites is provided from the perspective of landfill capacity and visibility perspectives by site visiting and assessing the site's conditions. Eghtesadifard et al. (2020) [28] suggested the DEMATEL-ANP, GIS, and K-Means model to identify six candidate sites, however, their methodology is limited to a trigonometric fuzzy membership function. Different evaluation criteria are suitable for corresponding fuzzy membership functions to reflect its fuzzy logic relationship. Rahimi et al. (2020) [30] determined an optimal site by considering only ten site selection factors in northwest Iran. The influencing factors are not considered comprehensively. Moreover, in the most of previous studies, after selecting landfills by GIS software, the classification of candidate sites was made by K-means techniques, noise points cannot be identified, and the number of candidate sites needs to be set artificially, which greatly reduces the scientific of the results. Density-based clustering algorithm can overcome these shortcomings and can be applied to classify the candidate sites, which can be a new approach in waste management.

Conclusions
This study identified and assessed the most suitable landfill sites in Lanzhou and conducted a field investigation to avoid the "NIMBY effect". In doing so, the 11 selected candidate sites have a low effect on the health of the population, rivers, protected areas, etc., which will enhance the acceptance of the government. For this study, we initially established a standard evaluation system of semi-arid valley basin municipal waste landfill site selection. This was a coupled flexible and novel comprehensive framework for reducing the uncertainty of data and criterion weights and verifying the efficacy of criterion weights and results.
The fuzzy DEMATEL-ANP method proved to be more preferable to ANP as it could deal with all types of dependencies systematically. The simple ANP method directly constructed the network relations between the input criteria according to a scale of 1-9, which had the subjective disadvantage of AHP. Selecting different membership functions for evaluation criteria is helpful to express its fuzzy logic relationship. This integration framework allowed for complex issues to be explored and fed back to decision-makers.
The three density-based clustering algorithms were utilized to identify 11 candidate sites for landfills, analyze their spatial distribution characteristics, and calculate the relative MSW capacities according to the area. The high consistency of the four sorting methods of MOORA, WASPAS, COPRAS, and TOPSIS fulfilled a comprehensive ranking of candidate sites. According to the ranking results and the opinions of experts, the optimal candidates are S1 (103 • 58 40" E, 36 • 29 14" N) and S2 (104 • 27 50" E, 36 • 22 56" N), ranking 1 and 2, which are located in the east of Gaolan and the northeast of Yuzhong in Lanzhou. Sensitivity analysis enabled scenario simulation with different weights set by multiple criteria, which can effectively guide planners to consider the uncertainty of weights in the decision-making evaluation process to obtain more satisfactory solutions. The findings revealed that the highest weights were assigned to the environmental criterion (0.2398) and the distance from the surface water criterion (0.0758).
Although the coupled model proposed in this study achieved better results in the landfill site, there remain some deficiencies due to limitations in data collection and research methods. Firstly, since the ANP stems directly from the AHP, it also inherits theoretical weaknesses of the assumptions of the AHP, including rank reversal problem, priorities derivation method, and comparison scale. In this study, the Fuzzy membership function was employed to overcome the above problems, but it cannot be fundamentally solved. Secondly, the ANP method is still unable to avoid the subjective problem of expert scoring. Deep learning algorithms can utilize existing conforming landfills for supervised or unsupervised classification to eliminate uncertainties in site selection. Thirdly, due to the study area is located in the ecologically fragile semi-arid area, there are obvious differences in hydrology, temperature, and topography from humid areas. The evaluation criteria and approaches that adapt to the semi-arid area are mainly selected, especially the fuzzy membership function of each evaluation criterion. Therefore, the evaluation approach is suitable for MSW landfill site selection in a semi-arid area. It is necessary to adjust the influencing factors and fuzzy membership function when selecting landfill sites in humid areas. Ultimately, the classification of MSW is not complete, and industrial solid waste is still divided as MSW for landfill disposal, which has an impact on the site selection. The site selection of industrial solid waste landfill provides a new idea for MSW.      Appendix D Table A5. "Construction Standard of MSW Landfill Disposal Engineering Project". The landfill is divided into four levels according to the area of the landfill. The smaller the area, the higher the level, and the lower the amount of MSW to be disposed.