We generalize the idea of (∈, ∈ ∨q k )-fuzzy ordered semigroup and give the concept of (∈, ∈ ∨q k )-fuzzy ordered LA-semigroup. We show that (∈, ∈ ∨q k )-fuzzy left (right, two-sided) ideals, (∈, ∈ ∨q k )-fuzzy (generalized) bi-ideals, (∈, ∈ ∨q k )-fuzzy interior ideals and (∈, ∈ ∨q k )-fuzzy (1, 2)-ideals need not to be coincide in an ordered LA-semigroup but on the other hand, we prove that all these (∈, ∈ ∨q k )-fuzzy ideals coincide in a left regular class of an ordered LA-semigroup.

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... we investigate some useful conditions for an ordered LA-semigroup to become a left regular ordered LAsemigroup and characterize a left regular ordered LA-semigroup in terms of (∈, ∈ ∨q k )-fuzzy one-sided ideals. Finally we connect an ideal theory with an (∈, ∈ ∨q k )-fuzzy ideal theory by using the notions of duo and (∈, ∈ ∨q k )-fuzzy duo.