Approximation Relation for Rough Sets

Rough set theory has the ability of deduction, reduction and common sense reasoning. First, this paper proposes the definition of the approximation relation; then, a kind of measurement method based on the approximation relation is proposed to judge whether any two sets are approximate with each other and then we can mine all of the sets that are approximate with a certain set by the measurement method in any approximation space; finally, this paper discusses algebraic properties for the measurement method, furthermore, we give its algebraic structure, which is proved a new standard boolean algebra for Rough sets.