“…They proved that for a locally associative Γ -LA-semigroup S with a left identity, S/ρ is a maximal weakly separative homomorphic image of S, where ρ is a relation on S defined by: aρb if and only if aγ b n = b n+1 and bγ a n = a n+1 for some positive integer n and for all γ ∈ Γ , where a, b ∈ S. In 2014, Abdullah et al [3] introduced the concept of interval-valued (∈, ∈ ∨q)-fuzzy ideals, interval-valued (∈, ∈ ∨q)-fuzzy bi-ideals and interval-valued (∈, ∈ ∨q)-fuzzy quasi-ideals of an LA-semigroup. Nowadays many scholars have studied different aspects of fuzzy subsets on LA-semigroups and Γ -LA-semigroups see [9,11,12,15,20,30,31,36,38,41,45,50]. In 2015, Abbasi and Basar [1] studied quasi-ideals and bi-ideals of locally associative Γ -LA-semigroups, (m, n) simple Γ -LA-semigroups, minimal bi-Γ -ideal, semiprime Γ -ideal and quasi-regular Γ -LA-semigroups.…”