Fuzzy Hv-ideals in Γ –Hv-rings

In this paper, by means of a kind of new idea, we consider the (∈, ∈ ∨q)-fuzzy Hv-ideals of a Γ –Hv-ring. The concept of Γ –Hv-rings, which is a generalization of Γ -rings and Hv-rings, is introduced. The notion of (∈, ∈ ∨q)-fuzzy Hv-ideals of a Γ –Hv-ring is provided and some related properties are investigated. The concept of implication-based fuzzy Hv-ideals of a Γ –Hv-ring is studied, in particular, the implication operators in the Lukasiewicz system of continuous-valued logic are discussed. Finally, the homomorphism of (∈, ∈ ∨q)-fuzzy Hv-ideals of a Γ –Hv-ring is explored.