Rough set theory proposes a new mathematical approach to model vagueness. In this paper, we introduce a new definition for rough approximations with respect to the subgroups of a group, which is called the left (right) lower and upper approximations. In fact, we prove that this definition is a generalization of definition in [5]. Then we give some properties of these rough approximations.

rough sets, rough groups, left (right) lower approximation, left (right) upper approximation.