<p>The concepts of Hom-groups and fuzzy Hom-groups have been generalized in recent research. In this paper, we further develop the notion of fuzzy (normal) Hom-groups by extending the notion of fuzzy (normal) groups into the setting of Hom-algebraic structures. We introduce and construct new fuzzy Hom-groups by integrating a twisting map into the fuzzy group framework. We investigate the most important properties of fuzzy Hom-subgroups, paying particular attention to the behavior of level sets associated with fuzzy Hom-subgroups, as well as to the notions of fuzzy normal Hom-subgroups and fuzzy characteristic Hom-subgroups, highlighting their roles within the broader algebraic context. Additionally, we study the effect of a Hom-group homomorphism on the image (resp. preimage) of a given fuzzy Hom-subgroup. Finally, we define the direct product of fuzzy Hom-subgroups and explore its algebraic implications. The results presented in this work contribute to the growing theory of fuzzy algebraic systems by establishing a foundation for future investigations into fuzzy structures within non-classical algebraic frameworks.</p>