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Issue:New implication deviation and entropy measures in intuitionistic fuzzy sets

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Title of paper: New implication deviation and entropy measures in intuitionistic fuzzy sets
Author(s):
Ria Rejal Sharma     0009-0008-4032-4014
Department of Mathematics, Gauhati University, Guwahati-781014, Assam, India
sharmariarejal@gmail.com
Santanu Acharjee     0000-0003-4932-3305
Department of Mathematics, Gauhati University, Guwahati-781014, Assam, India
sacharjee326@gmail.com
Mihir Kumar Chakraborty     0009-0003-7669-3720
Department of Mathematics, University of Calcutta, Kolkata-780073, West Bengal, India
mihirc4@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2, pages 105–132
DOI: https://doi.org/10.7546/nifs.2026.32.2.105-132
Download:  PDF (319  Kb, File info)
Abstract: This paper presents two new concepts within the framework of intuitionistic fuzzy set (IFS). An implication deviation is introduced, formulated using the implication operator together with a universal quantifier in the framework of intuitionistic fuzzy set. In addition to being a crucial analytical tool, this measure emphasizes its theoretical significance in the study of intuitionistic fuzzy sets by making it easier to define basic notions like inclusion and similarity. In addition, the paper introduces two new entropy measures, referred to as the α-intuitionistic fuzzy entropy and the β-intuitionistic fuzzy entropy, to quantify uncertainty of intuitionistic fuzzy sets. The α-intuitionistic fuzzy entropy evaluates uncertainty in terms of the deviation from the extreme situations of complete inclusion and complete exclusion. In contrast, the β-intuitionistic fuzzy entropy reflects maximum uncertainty when degrees of membership and non-membership are balanced or when the degree of hesitancy is maximal, while minimum entropy corresponds to the case, when complete inclusion or exclusion is there. Both entropy measures are constructed using the Hamming distance to ensure a consistent and intuitive representation of uncertainty.
Keywords: Intuitionistic fuzzy set, Implication deviation, Entropy.
AMS Classification: 03B52, 03B50, 94D05.
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