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Issue:Intuitionistic fuzzy group algebra

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Title of paper: Intuitionistic fuzzy group algebra
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 31 (2025), Number 4, pages 465–478
DOI: https://doi.org/10.7546/nifs.2025.31.4.465-478
Download:  PDF (225  Kb, File info)
Abstract: This paper introduces the concept of an intuitionistic fuzzy group algebra associated with a finite group G and an intuitionistic fuzzy group A on G. We establish its structural properties, showing that it simultaneously behaves as an intuitionistic fuzzy algebra and an intuitionistic fuzzy G-module. Extending author's earlier results on the semi-simplicity of intuitionistic fuzzy G-modules, we explore links to complete reducibility and injectivity. Further, we study intersections, (α,β)-cuts, and homomorphic images of such algebras, and define intuitionistic fuzzy group algebra homomorphisms. Finally, we prove that the class of all intuitionistic fuzzy group algebras forms a category.
Keywords: Intuitionistic fuzzy G-module, Intuitionistic fuzzy group, Intuitionistic fuzzy group algebra, Intuitionistic fuzzy group algebra homomorphism, Category.
AMS Classification: 03F55, 16D10, 16D90, 16W22, 22D20.
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