Intuitionistic fuzzy hom-subgroups

This study introduces and investigates intuitionistic fuzzy Homsubgroups, 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 Homgroup 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.