Rough sets on atomic Boolean lattices

Abstract

In this paper, the lower and upper generalized rough approximation operators on complete atomic Boolean lattices are studied by means of constructive and axiomatic approaches. In constructive approach, a pair of lower and upper rough approximation operators is first defined. The connections between binary relations on complete atomic Boolean lattices and rough approximation operators are established. In axiomatic approach, the axiomatic characterization of various classes of approximation operators are given.