The structure of ordered Γ-semigroup is a generalization of ordered semigroup. The purpose of this paper is to introduce the notion of (∈,∈ vq_k)-fuzzy bi Γ-ideals in ordered Γ-semigroup. This new concept is the generalization of fuzzy bi-ideals of ordered semigroup. Further we explore some classifications of different classes such as regular, right regular in terms of (∈,∈ vq_k)-fuzzy bi Γ-ideals. Particularly, we examine that the concepts of (∈,∈vq_k)-fuzzy bi Γ-ideals and (∈,∈vq_k)-fuzzy generalized bi Γ-ideals coincide in right regular ordered Γ-semigroup and regular ordered Tsemigroup.
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