Intuitionistic Fuzzy Hom-Subgroups

This study introduces and investigates intuitionistic fuzzy Hom-subgroups, extending the concept of fuzzy Hom-subgroups in the context of Hom-group theory. This approach integrates Atanassov’s intuitionistic fuzzy sets with Hom-group structures, allowing each element to be represented through both membership and non-membership degrees, thus offering a richer description of uncertainty. Fundamental properties and characterizations are established using level subsets, and the behavior of these subgroups under Hom-group homomorphisms is investigated. Several illustrative examples, including constructions on the real-line Hom-group, are provided to demonstrate the developed concepts. The proposed framework extends existing results on fuzzy Hom-groups and illustrates the developed algebraic concepts within the intuitionistic fuzzy setting.