Intuitionistic fuzzy group algebra

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.