Development of AHP-Based Divergence Distance Measure between $\mathit{p},\mathit{q},\mathit{r}$–Spherical Fuzzy Sets with Applications in Multi-Criteria Decision Making

This study introduces a novel distance measure (DM) for $(p,q,r)-$spherical fuzzy sets ( $(p,q,r)-$SFSs) to improve decision-making in complex and uncertain environments. Many existing distance measures either fail to satisfy essential axiomatic properties or produce unintuitive outcomes. To address these limitations, we propose a new three-dimensional divergence-based DM that ensures mathematical consistency, enhances the discrimination of information, and adheres to the axiomatic framework of distance theory. Building on this foundation, we construct a multi-criteria decision-making (MCDM) model that utilizes the proposed DM to evaluate and rank alternatives effectively. The applicability and robustness of the model are validated through a practical case study, demonstrating that it leads to more rational, consistent, and reliable decision outcomes compared to existing approaches.