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Issue:Intuitionistic fuzzy group subalgebras

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Title of paper: Intuitionistic fuzzy group subalgebras
Author(s):
Poonam Kumar Sharma     0000-0001-5463-8665
Post-Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2, pages 89–104
DOI: https://doi.org/10.7546/nifs.2026.32.2.89-104
Download:  PDF (272  Kb, File info)
Abstract: This paper presents a systematic investigation of intuitionistic fuzzy algebraic structures associated with group algebras. We introduce the concept of an intuitionistic fuzzy group subalgebra (IFGSA) of an intuitionistic fuzzy group algebra (IFGA) constructed from the group algebra K[G], where G is a finite group and K is a field. Structural properties of IFGSAs are examined, with particular emphasis on their behavior under intuitionistic fuzzy group algebra homomorphisms (IFGA-homomorphisms). The image and inverse image of IFGSAs are studied, and it is proved that the intersection of an arbitrary family of IFGSAs is again an IFGSA. Furthermore, the notion of an intuitionistic fuzzy augmentation ideal (IFAI) in an IFGA is introduced and analyzed. It is shown that the intersection of an arbitrary family of IFAIs remains an IFAI. The image and inverse image of IFAIs under IFGA-homomorphisms are also investigated. Finally, isomorphism theorems for IFGAs are established, extending classical group algebra results to the intuitionistic fuzzy framework.
Keywords: Intuitionistic fuzzy algebra, Group algebra, Intuitionistic fuzzy group subalgebra, Intuitionistic fuzzy augmentation ideal, IFGA-homomorphism.
AMS Classification: 03F55, 16D10, 16W22, 22D22.
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