Some kinds of (∈γ , ∈γ ∨qδ)-fuzzy ideals of BCI-algebras

The concepts of (∈γ , ∈γ ∨qδ)-fuzzy (positive implicative, implicative and commutative) ideals and (∈γ , ∈γ ∨qδ)-fuzzy (positive implicative, implicative and commutative) ideals in BCI-algebras are introduced. Some new characterizations are investigated. In particular, we prove that a fuzzy set μ of a BCI-algebra X is an (∈γ , ∈γ ∨qδ)-fuzzy implicative ideal of X if and only if it is both an (∈γ , ∈γ ∨qδ)-fuzzy positive implicative ideal and an (∈γ , ∈γ ∨qδ)- fuzzy commutative ideal. Finally, we give some characterizations of three particular classes of BCI-algebras by these generalized fuzzy ideals.