On the Partial Approximation of Sets

Abstract

1 According to Pawlak's classic rough set theory the vagueness of a subset of a finite universe U is defined by the difference of its upper and lower approximations with respect to an equivalence relation on U . A natural way of the generalization of this idea is that the equivalence relation is replaced by either any other type of binary relations on U or an arbitrary covering of the universe. In this paper, our starting point will be an arbitrary family of subsets of an arbitrary universe U . Within this framework, we shall investigate a possible generalization of Pawlak's idea. Both Pawlak's rough set theory and our approach can extensively be applied in medical informatics.