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Issue:Intuitionistic fuzzy sets and some of their so-called extensions

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Title of paper: Intuitionistic fuzzy sets and some of their so-called extensions
Author(s):
Krassimir Atanassov     0000-0001-5625-071X
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia–1113, Bulgaria
krat@bas.bg , k.t.atanassov@gmail.com
Peter Vassilev     0000-0002-7361-9272
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia–1113, Bulgaria
peter.vassilev@gmail.com
Vassia Atanassova     0000-0002-3626-9461
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia–1113, Bulgaria
vassia.atanassova@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3, pages 372–385
DOI: https://doi.org/10.7546/nifs.2025.31.3.372-385
Download:  PDF (563  Kb, File info)
Abstract: In the present paper we investigate the relationship between intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and some proposed extensions of fuzzy sets, intuitionistic fuzzy sets, and sets that have similar structure. In many cases we establish that the proposed concepts claiming to be extensions of the intuitionistic fuzzy sets are either incorrect in their definitions or offer nothing new compared to the already existing notions. Finally, we formulate four requirements that must be observed so that a new concept claiming to extend an existing one can be considered legitimate and viable, expanding the boundaries of the existing mathematical theory in a meaningful way.
Keywords: Fuzzy sets, Intutionistic fuzzy sets, Extensions.
AMS Classification: 03E72.
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