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∨q¯δ)-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 μμ of a BCI-algebra XX is an (∈γ,∈γ∨qδ)-fuzzy implicative ideal of XX 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.