On the Structure of Hybrid Subalgebras in Bd-Algebras

By combining the properties of fuzzy and soft set theories, hybrid structures provide a more flexible framework for handling uncertainty. In this work, we define hybrid subalgebras of Bd-algebras and investigate related properties. We examine the properties of some special sets with hybrid structures. More precisely, we investigate situations where we can describe these sets as Bd-subalgebras. We show that hybrid intersections of hybrid Bd-subalgebras are also hybrid Bd-subalgebras, but we give an example that the hybrid union of hybrid Bd-subalgebras may not be a hybrid Bd-subalgebra. Furthermore, we prove that every homomorphic preimage of a hybrid Bd-algebra is a hybrid Bd-subalgebra.