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

This article focuses on developing a novel decision-making framework based on spherical linear Diophantine fuzzy sets (SLDFSs) to address complex multi-criteria group decision-making (MCGDM) problems. It introduces new distance and similarity metrics for SLDFSs, proving their mathematical properties and demonstrating their superiority over existing fuzzy set approaches. The study adapts the Vlse Kriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method to the SLDFS framework, creating the SLDF-VIKOR approach, which is applied to an electric vehicle selection problem considering multiple conflicting criteria. Additionally, the proposed similarity metric is utilized in clustering analysis for educational curriculum evaluation, with sensitivity analyses confirming the method’s stability. The research highlights the advantages of SLDFSs in handling uncertainty and human judgment flexibility, while noting limitations such as the need for decision-makers to understand SLDFNs and the lack of standardized evaluation benchmarks for fuzzy clustering.