The notion of a rough set was originally proposed by Pawlak (1982). Later on, there is a fast growing interest in this theory. In this paper we present a more general approach to the generalization of rough sets. Specifically, generalized formulation has been studied by using a binary relation on two universes without any restriction on the car- dinality. The algebraic properties of generalized rough sets are given, and the extension principle for crisp sets is ex- plained as the upper approximations of rough sets. The re- lationship between the extension principle for fuzzy sets and the upper approximations of fuzzy rough sets is investigated.