In this paper, using the notion of ðk; qÞ-quasi-coincident of an ordered fuzzy point with a fuzzy set of the support, the concept of ð2; 2 _ðκ; qκÞÞ-fuzzy bi-Γ-ideals in ordered Γ-semigroups is defined. We prove that intersection of ð2; 2 _ðκ; qκÞÞ-fuzzy bi-Γ-ideals of S is an ð2; 2 _ðκ; qkÞÞ-fuzzy bi-Γ-ideal but the statement does not hold for union, and in this aim an example is provided. Moreover, we present correspondence between bi-Γ-ideals and ð2; 2 _ðκ; qκÞÞ-fuzzy bi-Γ-ideals of ordered Γ-semigroups based on level subset and ð2 _ðκ; qκÞÞ-level subset of fuzzy sets.