Hybrid T-spherical fuzzy decision analytics Methodology: Leveraging Lance Distance induction

T-Spherical Fuzzy (T-SF) set theory provides an advanced approach for modeling uncertain and imprecise information by incorporating degrees of positivity, impartiality, negativity, and refusal. The present research devises new T-SF Lance distances designed to accommodate biased data and quantify dissimilarities in complex decision scenarios. Integrated into the MEthod based on the Removal Effects of Criteria (MEREC) and the Multi-Attribute Ideal-Real Comparative Analysis (MAIRCA), the Lance distance supports the development of a hybrid T-SF MEREC-MAIRCA framework. The proposed methodology enhances objectivity in weight determination and consistency in evaluating alternative solutions under uncertainty. The T-SF MEREC component employs the Lance distance to construct a synthesized index that quantifies performance reductions, while the T-SF MAIRCA component integrates theoretical and actual appraisal outcomes, score functions, and Lance distance-based assessments to effectively prioritize alternatives. A case study on smart farming in Taoyuan City, Taiwan, illustrates the framework's practical value. Seven smart farm operation models were evaluated, with the rooftop urban agriculture model (s₃) identified as optimal, achieving the lowest adverse gap measure (Q₃= 0.4395). These findings validate the proposed framework's robustness and suitability for complex real-world decision problems, offering policymakers a reliable, data-driven tool for sustainable urban agriculture planning.