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Intuitionistic fuzzy generalized bi-ideals play an important role in the study of ordered semigroups. In this paper, we try obtain more general form of intuitionistic fuzzy generalized bi-ideal of an ordered semigroup. The concept of (∈, ∈ ∨qk)-intuitionistic fuzzy generalized bi-ideal is introduced and several related properties are investigated. We show that in regular and left weakly regular ordered semigroups the concepts of (∈, ∈ ∨qk)-intuitionistic fuzzy generalized biideal and (∈, ∈ ∨qk)-intuitionistic fuzzy bi-ideal coincide.