Spherical Linear Diophantine Fuzzy Similarity Metric and its Applications to VIKOR and Sensitivity-Cluster Analysis

With rising pollution, depleting fossil fuels, and the urgent need to combat climate change, switching to electric vehicles is no longer a choice but a necessity. Conducting constructive research is crucial for selecting the right electric vehicle to ensure a sustainable and energy-secure future. An effective decision-making process requires a method that evaluates multiple criteria to ensure the best choices. To support this goal, this study develops a decision model using the spherical linear Diophantine fuzzy (SLDF) method. SLDF sets enhance traditional fuzzy sets by incorporating three control parameters, which better capture human judgment and provide deciders with the flexibility to handle complex decision-making scenarios. Additionally, distance-similarity metrics serve as key information tools for ranking alternatives based on their closeness. So, this study presents a new distance-based similarity metric for spherical linear Diophantine fuzzy sets (SLDFSs) and thoroughly examining its attributes. To evaluate the effectiveness of the proposed metric, we perform a comparative analysis with existing methods in the literature. Furthermore, for the selection process, we adapt the Vlse Kriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method to the SLDF framework, leading to the innovative SLDF-VIKOR approach. Additionally, we apply the proposed similarity metric to clustering analysis, demonstrating its practical value in Multi-Criteria Group Decision Making (MCGDM). To double-check the veracity of SLDF-clustering methodology, we conduct sensitivity analysis in three special cases.