AbstractIn this paper, the notions of (∈, ∈ ∨(k ∗, qk))-fuzzy left Γ-ideals, (∈, ∈ ∨(k ∗, qk))-fuzzy right Γ-ideals and (∈, ∈ ∨(k ∗, qk))-fuzzy Γ-ideals in ordered Γ-semigroups are introduced and their related properties are investigated. Furthermore, (k ∗, k)-lower parts of (∈, ∈ ∨(k ∗, qk))-fuzzy left Γ-ideals, (∈, ∈ ∨(k ∗, qk))-fuzzy right Γ-ideals and (∈, ∈ ∨(k ∗, qk))-fuzzy Γ-ideals are also defined. Finally, left regular, right regular and regular ordered Γ-semigroups in terms of (∈, ∈ ∨(k ∗, qk))-fuzzy left Γ-ideals and (∈, ∈ ∨(k ∗, qk))-fuzzy right Γ-ideals are characterized.