A Generalized Exponential Entropy Measure for Intuitionistic Fuzzy Sets and Its Application in Decision Making
Keywords:
Intuitionistic fuzzy sets, Exponential entropy, Uncertainty quantification, Information measure, Multi-criteria decision-making (MCDM), Parametric entropy, Decision-support systemsAbstract
Uncertainty quantification remains a foundation in fuzzy logic and decision sciences, where entropy functions serve as vital tools for measuring imprecision and hesitation. This paper introduces a parametrically extended exponential entropy measure for intuitionistic fuzzy sets (IFSs), integrating Hooda’s exponential entropy framework with the non-additive Sharma–Taneja model. The proposed measure incorporates two tunable parameters, α and β, which jointly control the sensitivity to information granularity and the degree of non-additivity, providing, enhanced flexibility in modeling complex uncertainty patterns. A rigorous theoretical analysis demonstrates that the proposed measure satisfies all fundamental axioms of intuitionistic fuzzy information measures. The formulation is further supported by a generating-function representation, linking entropy to derivative-based power sums and facilitating analytical tractability. Limiting cases show that the measure generalizes classical entropy models, including Shannon, De Luca–Termini, and Hooda’s exponential entropy. A numerical example illustrates the practical applicability of the measure in multi-criteria decision-making (MCDM), where entropy-based weighting effectively identifies informative criteria under intuitionistic fuzzy environments. Overall, the proposed measure provides a unified, flexible, and computationally efficient framework for quantifying intuitionistic fuzzy uncertainty, with potential applications in decision-support systems, pattern recognition, and complex information processing.
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