Intuitionistic fuzzy group algebra
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Date
2025
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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.