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In this paper, we introduce a considerable machinery that permits us to characterize a number of special (fuzzy) subsets in ordered semigroups. In this regard, we generalize (Davvaz and Khan in Inform Sci 181:1759–1770 2011) and define ()-fuzzy generalized bi-ideals in ordered semigroups, which is a generalization of the concept of an (α, β)-fuzzy generalized bi-ideal in an ordered semigroup. We also define ()-fuzzy left (resp. right)-ideals. Using these concept, some characterization theorems of regular, left (resp. right) regular, completely regular and weakly regular ordered semigroups are provided. The upper/lower parts of an ()-fuzzy generalized bi-ideal and ()-fuzzy left (resp. right)-ideal are given, and some characterizations are provided.