A certain conception of the calculus of rough sets.
Zbigniew Bonikowski · Notre Dame Journal of Formal Logic · 1992
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.