@article{Khan2025, 
author = {Shah Zeb Khan and Muhammad Rahim and Adel M. Widyan and A. Almutairi and Njood Shaher Ethaar Almutire and Hamiden Abd El-Wahed Khalifa},
title = {Development of AHP-Based Divergence Distance Measure between  p,q,r–Spherical Fuzzy Sets with Applications in Multi-Criteria Decision Making},
year = {2025},
journal = {Computer Modeling in Engineering & Sciences},
volume = {143},
number = {2},
pages = {2185-2211},
keywords = {p, q, r-spherical fuzzy sets, divergence, distance measures, AHP, decision making},
url = {https://www.sciopen.com/article/10.32604/cmes.2025.063929},
doi = {10.32604/cmes.2025.063929},
abstract = {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.}
}