Open Access

ARTICLE

Development of AHP-Based Divergence Distance Measure between –Spherical Fuzzy Sets with Applications in Multi-Criteria Decision Making

Shah Zeb Khan¹, Muhammad Rahim², Adel M. Widyan^3,*, A. Almutairi³, Njood Shaher Ethaar Almutire³, Hamiden Abd El-Wahed Khalifa³

1 Department of Mathematics and Statistics, University of Swat, Swat, 19120, Pakistan
2 Deparament of Mathematics, Hazara University, Mansehra, 21300, Pakistan
3 Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

* Corresponding Author: Adel M. Widyan. Email:

(This article belongs to the Special Issue: Algorithms, Models, and Applications of Fuzzy Optimization and Decision Making)

Computer Modeling in Engineering & Sciences 2025, 143(2), 2185-2211. https://doi.org/10.32604/cmes.2025.063929

Received 29 January 2025; Accepted 23 April 2025; Issue published 30 May 2025

Abstract

This study introduces a novel distance measure (DM) for spherical fuzzy sets (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.

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Keywords

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