A Novel Spherical Distance Measure for SF-TOPSIS: A Generalized MCDM Framework via Application to Municipal Solid Waste Landfill Site Selection

Municipal solid waste (MSW) landfill site selection is a complex multi-criteria decision-making (MCDM) problem involving uncertainty and conflicting criteria. Although spherical fuzzy extensions of the Technique for Order Preference by Similarity to Ideal Solution (SF-TOPSIS) are widely used, existing studies rely on conventional distance measures that do not fully capture the geometric structure of spherical fuzzy sets. To address this limitation, this study proposes an enhanced SF-TOPSIS framework incorporating a novel spherical distance measure to improve consistency, discrimination capability, and structural compatibility. The framework integrates Spherical Fuzzy Weighted Arithmetic Mean (SWAM) and Spherical Fuzzy Weighted Geometric Mean (SWGM) operators and evaluates robustness using Spearman rank correlation. Additionally, a coefficient of variation (CV)-based analysis is conducted to examine the dispersion of closeness coefficients. The applicability of the approach is demonstrated through a landfill site selection case; however, the main contribution lies in a generalized distance-based formulation applicable to various MCDM problems. Results show that the proposed distance improves agreement between aggregation operators, increasing correlation values from 0.905 to 0.976, while producing a more stable distribution of closeness coefficients. Overall, the study advances spherical fuzzy MCDM by introducing a geometrically consistent distance formulation.