Abstract. In this article, the concept of (∈γ, ∈γ ∨ q δ )-fuzzy LAsubsemigroups, (∈γ, ∈γ ∨ q δ )-fuzzy left(right) ideals, (∈γ, ∈γ ∨ q δ )-fuzzy generalized bi-ideals and (∈γ, ∈γ ∨ q δ )-fuzzy bi-ideals of an LA-semigroup are introduced. The given concept is a generalization of (∈, ∈ ∨ q)-fuzzy LA-subsemigroups, (∈, ∈ ∨ q)-fuzzy left(right) ideals, (∈, ∈ ∨ q)-fuzzy generalized bi-ideals and (∈, ∈ ∨ q)-fuzzy bi-ideals of an LA-semigroup. We also give some examples of (∈γ, ∈γ ∨ q δ )-fuzzy LA-subsemigroups ( left, right, generalized bi-and bi) ideals of an LA-semigroup. We prove some fundamental results of these ideals. We characterize (∈ γ , ∈γ ∨ q δ )-fuzzy left(right) ideals, (∈γ, ∈γ ∨ q δ )-fuzzy generalized bi-ideals and (∈γ, ∈γ ∨ q δ )-fuzzy bi-ideals of an LA-semigroup by the properties of level sets
