Fuzzy HvHv-ideals in ΓΓ–HvHv-rings

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