Siting MSW landfills via the integration of DEMATEL-ANP and clustering algorithm in a fuzzy logic environment (Case Study: Lanzhou, China)


 The siting of Municipal Solid Waste (MSW) landfills is a complex decision based process that involves multiple hydrogeological, morphological, environmental, climatic, and socio-economic criteria. In a fuzzy logic environment, DEMATEL and ANP methods were employed to comprehensively consider uncertainty, fuzziness of data and the subjective scoring and stability of results to enhance the spatial decision-making process. Primarily, 21 criteria were identified in five groups through the Delphi method at 30m resolution, criteria weights were determined via the integration of DEMATEL and ANP, and seven sets of membership functions were simulated to obtain the best fuzzy logic environment. Combining GIS spatial analysis and the three clustering algorithms (DBSCAN, HDBSCAN, and OPTICS), candidate sites that satisfied the landfill conditions were identified, and the spatial distribution characteristics and reachability 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 paper focuses on a flexible and novel framework for the selection of MSW landfill sites for Lanzhou, which is a semi-arid valley basin city in China. In contrast to common techniques, this model not only made the best recommendation scientifically and efficiently but could also provide accurate assessment data for decision makers in landfill construction and high-quality urban development.

Hydrogeological aspects should be considered to avoid potential groundwater 251 contamination in semi-arid valley basins caused by the leakage of landfill leachate, while 252 ensuring the safety of construction and operation (Karakus et al., 2020). Morphological 253 aspects were taken into account to reduce construction costs and increase stability during 254 construction (Bahrani et al., 2016). Environmental aspects were taken into consideration to 255 minimize the impacts on neighboring residents, and land/water resources (Ozkan et al., 2019). 256 Climatic issues were reviewed to reduce potential threats and damage to the surrounding 257 environment posed by various pollutants released from the landfill through leachate or waste 258 gas (Lima et al., 2018). Socio-economic impacts were considered to prevent the landfill from 259 adversely affecting surrounding ecological reserves and regional economic development 260 (Asefi et al., 2020a). Further detailed information on the criteria selection is contained in 261 Table B.1 in Appendix B. The interval from 0 to 1 was adopted for normalization, where the 262 larger the value, the better the suitability (Fig. 2). distance from faults, (e) distance from earthquake points, (f) elevation, (g) slope, (h) soil type, (i) NDVI, 267 (g) landform type, (k) distance from surface water, (l) distance from roads, (m) land use type, (n) distance 268 from settlements, (o) precipitation, (p) temperature, (q) ecosystem service value, (r) population density, (s) 269 GDP, (t) distance from airports, (u) distance from protected areas.  According to the expert opinion obtained by Delphi method, a numerical scale of 0-4 is 287 adopted to indicate the degree of direct influence between criteria. Where, "no influence" is 288 0, "low influence" is 1, "medium influence" is 2, "high influence" is 3, and "very high 289 influence" is 4. A pairwise comparison judgment matrix is constructed respectively. Experts To unify the numerical scale into a comparable range, Eqs. 2, 3 are employed to obtain 296 the normalized direct relation matrix, whose value is between 0 and 1.  The comprehensive influence matrix represents the superposition of direct and indirect 301 influences between criteria. B T (criterion) (Eq. 5) and C T (sub-criterion) (Eq. 6) are  transpose. The weighted super matrix is limit until it converges to calculate the final weight 336 vector (Eq. 14).

M(R+C), N(R-C) and weights for criterion and sub-criterion. 341
Criterion The mapping and analysis of criteria attributes based on fuzzy logic, S-shape, Triangular 343 shape, and Gamma shape are commonly employed fuzzy membership functions to determine 344 fuzzy information in fuzzy logic ( S-shape S-shape   The input parameters are the neighborhood radius (ε) and the minimum number of 377 entities (MinPts). The data set is divide into core, boundary and noise points. A random point 378 is selected from the data set as the seed for traversal. When the density of any two points is 379 reachable or direct, it is classified into the same cluster, and the number of entities in the same 380 cluster must be greater than MinPts; when it is less, they are classified as noise points (Gui 381 et al., 2020). The input parameters were ε, MinPts, and sensitivity. The value of clustering sensitivity 394 is 0-100. The higher the sensitivity, the smaller the clustering interval is. And introduced the 395 "accessible distance" (Breunig et al., 2000).

396
(16) 397 Where, P, Q are the two core points, the core distance of P, and the Euclidean distance 398 between P and Q. i to criterion j. 403 Step 2 Normalize the decision matrix based on the maximum and minimum method (Eq. Step 3 Weight normalized decision matrix (Eq. 18), w is the weight of criterion j.

407
Step 4 Calculate the relative importance of alternatives by utilizing weighted sum model Step Step 1 Construct a decision matrix ] where ij x is the response of alternative item 416 i to criterion j.

417
Step 2  Step 4 Calculate the relative importance of alternatives by utilizing the ratio of the Step 5 Calculate the scores of each alternative according to Eq. 23, and arrange them in Step 1 Construct a decision matrix ] where ij x is the response of alternative item 430 i to criterion j.

431
Step 2 Normalize the decision matrix based on the summation method (Eq. 24), where Step 3 Weight normalized decision matrix (Eq. 25), w is the weight of criterion j. Step 5 Calculate the scores of each alternative according to Eq. 27, and arrange them in 440 descending order. The higher the score, the higher the priority. Step 1 Construct a decision matrix ] where ij x is the response of alternative item 444 i to criterion j. 445 Step 2 Normalize the decision matrix based on the minimum-maximum method (Eq. for negative criteria (28) 449 Step 3 Weight normalized decision matrix (Eq. 29), w is the weight of criterion j.
Step 4 Calculate the relative importance of alternatives by utilizing the distance index Step 5 Calculate the scores of each alternative according to Eq. 31, and arrange them in

544
The 11 candidate sites identified by cluster analysis were satisfactory from the 545 perspective of hydrogeological, morphological, environmental, climatic, and socio-economic 546 factors, as they were all based on criteria analysis. However, to ensure that the candidate sites 547 conformed to the CNS and the urban planning measures of the study area, it was necessary 548 to evaluate them relatively. We conducted field visits and selected four methods: WASPAS, 549 MOORA, COPRAS, and TOPSIS to determine the final ranking of the candidate sites by 550 according to expert opinions and regional characteristics. As can be seen from Table 3  conducted a field investigation to avoid the "NIMBY effect". In doing so, the 11 selected 573 candidate sites would not affect the health of the population, rivers, protected areas, etc., 574 which will enhance the acceptance of the government and be of benefit to society for at least 575 ten years. For this study, we initially established a standard evaluation system of semi-arid   The total influence matrix of the criteria (T C ). 617 C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 11 C 12 C 13 C 14 C 15 C 16 C 17 C 18 C 19 C 20 C 21