A Certain Conception of the Calculus of Rough Sets

We consider the family of rough sets in the present paper. In this family we define, by means of a minimal upper sample, the operations of rough addition, rough multiplication, and pseudocomplement. We prove that the family of rough sets with the above operations is a complete atomic Stone algebra. We prove that the family of rough sets, determined by the unions of equivalence classes of the relation R with the operations of rough addition, rough multiplication, and complement, is a complete atomic Boolean algebra. If the relation R determines a partition of set U into one-element equivalence classes, then the family of rough sets with the above operations is a Boolean algebra that is isomorphic with a Boolean algebra of subsets of universum U.