In this paper, we introduce two new aggregation operators of q-rung orthopair fuzzy (q-ROF) sets based on generalized Dombi operations within the framework of fuzzy rough set theory. The aggregations are composed of those of lower and upper approximations in a q-ROF approximation space. That is, the actual aggregated data are not q-ROF sets but their corresponding q-ROF rough sets, and the aggregated results are ordered pairs of q-ROF values. The developed operators are generalizations of those induced by Dombi operations and Hamacher operations. Moreover, it is proved that the traditional q-ROF aggregation is bounded by lower and upper bounds of the new aggregation in a q-ROF reflexive approximation space. These conceptual arguments are illustrated by a numerical example, in which an analysis of parameter variations is also provided.