In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzied algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (${in},{in}{vee}ar{q}_k$)-fuzzy subsystems of ordered semigroups namely (${in},{in}{vee}ar{q}_k$)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (${in},{in}{vee}ar{q}_k$)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (${in},{in}{vee}ar{q}_k$)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.