Year: 2025
Type: article
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.
Author: Poonam Kumar Sharma
Language: English
Topic: Fuzzy and Soft Set Theory
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W4416825763
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