TY  - EJOU
AU  - Liu, Zhe 
AU  - Zhu, Sijia 
AU  - Huang, Yulong 
AU  - Senapati, Tapan 
AU  - Li, Xiangyu 
AU  - Mbasso, Wulfran Fendzi 
AU  - Dhumras, Himanshu 
AU  - Hosseinzadeh, Mehdi 

TI  - A Unified Parametric Divergence Operator for Fermatean Fuzzy Environment and Its Applications in Machine Learning and Intelligent Decision-Making
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2025
VL  - 145
IS  - 2
SN  - 1526-1506

AB  - 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 χ<sup>2</sup>-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.
KW  - Fermatean fuzzy sets; divergence operator; pattern classification; hierarchical clustering; multiattribute decision-making

DO  - 10.32604/cmes.2025.072352