Hybrid covered bi-ideals in semigroups

Hybrid structures provide a unifying framework for the study of fuzzy and soft sets. In this paper, we introduce the concepts and terminology of hybrid covered bi-ideals. Within the framework of semigroups, we investigate several fundamental properties and present illustrative examples. Furthermore, we show that the class of hybrid covered bi-ideals is closed under intersection, though not necessarily under union. Finally, the concept of covered bi-ideals is generalized to the broader setting of generalized bi-ideals.