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