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ARTICLE

A Unified Parametric Divergence Operator for Fermatean Fuzzy Environment and Its Applications in Machine Learning and Intelligent Decision-Making

Zhe Liu^1,2,3,*, Sijia Zhu⁴, Yulong Huang^1,*, Tapan Senapati^5,6,7, Xiangyu Li⁸, Wulfran Fendzi Mbasso⁹, Himanshu Dhumras¹⁰, Mehdi Hosseinzadeh^11,12,*

1 College of Mathematics and Computer, Xinyu University, Xinyu, 338004, China
2 School of Computer Sciences, Universiti Sains Malaysia, Penang, 11800, Malaysia
3 Jadara Research Center, Jadara University, Irbid, 21110, Jordan
4 Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA
5 School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
6 Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, 602105, India
7 Centre for Research Impact & Outcome, Chitkara University Institute of Engineering and Technology, Chitkara University, Rajpura, 140401, India
8 Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
9 Technology and Applied Sciences Laboratory, U.I.T. of Douala, University of Douala, Douala, P.O. Box 8689, Cameroon
10 Department of Applied Sciences, Advanced Centre of Research and Innovation, Chandigarh Engineering College, Chandigarh Group of Colleges, Jhanjeri, Mohali, 140307, India
11 School of Engineering & Technology, Duy Tan University, Da Nang, 550000, Vietnam
12 Department of AI, School of Computer Science and Engineering, Galgotias University, Greater Noida, 203201, India

* Corresponding Authors: Zhe Liu. Email: ; Yulong Huang. Email: ; Mehdi Hosseinzadeh. Email:

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

Computer Modeling in Engineering & Sciences 2025, 145(2), 2157-2188. https://doi.org/10.32604/cmes.2025.072352

Received 25 August 2025; Accepted 10 October 2025; Issue published 26 November 2025

Abstract

Uncertainty and ambiguity are pervasive in real-world intelligent systems, necessitating advanced mathematical frameworks for effective modeling and analysis. Fermatean fuzzy sets (FFSs), as a recent extension of classical fuzzy theory, provide enhanced flexibility for representing complex uncertainty. In this paper, we propose a unified parametric divergence operator for FFSs, which comprehensively captures the interplay among membership, non-membership, and hesitation degrees. The proposed operator is rigorously analyzed with respect to key mathematical properties, including non-negativity, non-degeneracy, and symmetry. Notably, several well-known divergence operators, such as Jensen-Shannon divergence, Hellinger distance, and χ²-divergence, are shown to be special cases within our unified framework. Extensive experiments on pattern classification, hierarchical clustering, and multiattribute decision-making tasks demonstrate the competitive performance and stability of the proposed operator. These results confirm both the theoretical significance and practical value of our method for advanced fuzzy information processing in machine learning and intelligent decision-making.

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Keywords

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