Roughness in vector spaces

Rough set theory proposed by Pawlak, is a complementary generalization of classical set theory. The relations between rough sets and algebraic systems endowed with two binary operations such as rings, groups and semigroups have been already considered. Wu, Xie and Cao defined a pair of rough approximation operators based on a sub-space. In this paper we do the further study about the upper (lower)approximations. We propose concepts of W-upper(lower) rough subspaces in an approximation space and give some properties of the upper(lower) and rough subspaces. Some characterizations of the upper(lower) rough subspace are expressed with addition and intersection operations of subspaces. At the same time, some counterexamples are offered to illustrate the relevant results.