In this paper, two new operators are introduced for the rough set theory. Using them, two inequalities well known in the rough set theory can now be modified to become equalities. With this change, no information will be lost in the new expressions. Hence, many properties in rough set theory can be improved and in particular, the union, the intersection, and the complement operations can be redefined based on the two equalities. Furthermore, the collection of rough sets of an approximation space forms a Boolean algebra under these new operators. Finally, roughness properties of fuzzy sets are analyzed using the new operations.