Rough equivalence and algebraic properties of rough sets

Abstract

Rough sets are used as an effective model to deal with imprecise knowledge, since its inception by Pawlak (1982). Rough equalities, introduced and studied by Novotny and Pawlak (1985a, 1985b, 1985c) as methods for comparison of rough sets, were generalised to the notions of rough equivalences by Tripathy et al. (2008), where they have shown their superiority over rough equalities. In this paper, we establish the rough equivalence of some of the algebraic properties, which occur frequently in the study of crisp sets. These new properties can be used in the study of rough logic.