Application of a nonlinear TOPSIS algorithm to human settlement suitability evaluation in central Xi'an, Northwest China.

Traditional methods for evaluating human settlement suitability often fail to effectively characterize the nonlinear influence of indicator values on overall suitability, such as diminishing marginal effects or counterproductive outcomes from excessive input. To overcome those shortages, we proposed a Nonlinear Technique for Order Preference by Similarity to Ideal Solution (nonlinear-TOPSIS) to achieve a refined quantitative evaluation of human settlement suitability, with the central urban area of Xi'an as the study area. We constructed an evaluation framework based on urban block units as the fundamental analysis granularity, and developed an indicator system from four dimensions: natural environment, economic prosperity, living convenience, and building morphology. Based on the distributional characteristics of each indicator, we introduced nonlinear fitting methods, including power-law functions, Gaussian functions, Beta functions, and Gaussian mixture models, to characterize their nonlinear impacts and marginal effects, and then established an improved TOPSIS model based on nonlinear function to identify ideal and negative ideal solutions. Meanwhile, we compared multiple subjective and objective weighting methods to provide a more rational weight assignment for the evaluation algorithm. The results showed that the human settlement suitability index values within the research area approximated a normal distribution and exhibited a mixed spatial pattern at the parcel level. High-suitability areas covered 167.82 km²(accounting for 17.5% of the total area), mainly distributed in Beilin District, Xincheng District, and parts of Yanta District. These areas were generally characterized by moderate greening rates, appropriate building density, and well-developed living facilities. Low-suitability areas were concentrated in old urban neighborhoods and underdeveloped zones, exhibiting spatial imba-lances in greening rates, building density, and infrastructure. The spatial lag model and spatial error model further validated the applicability and robustness of the proposed evaluation method. The nonlinear-TOPSIS algorithm proposed here would enrich the theoretical framework of human settlement suitability assessment, expand the methodological approach of spatial decision support, and provide theoretical basis and methodological support for urban spatial optimization and refined governance.