Rough Sets

We study properties of rough sets, that is, approximations to sets of records in a database or, more formally, to subsets of the universe of an information system. A rough set is a pair hL; U i such that L; U are de nable in the information system and L U . In the paper, we introduce a language, called the language of inclusion-exclusion, to describe incomplete speci cations of (unknown) sets. We use rough sets in order to de ne a semantics for theories in the inclusion-exclusion language. We argue that our concept of a rough set is closely related to that introduced by Pawlak. We show that rough sets can be ordered by the knowledge ordering (denoted kn). We prove that Pawlak's rough sets are characterized as kn-greatest approximations. We show that for any consistent (that is, satis able) theory T in the language of inclusion-exclusion there exists a kn-greatest rough set approximating all sets X that satisfy T . For some classes of theories in the language of inclusion-exclusion...

• Type: Conference
• Year: 1995
• Where: ACM
• Authors: Zdzislaw Pawlak
• Keywords: ACM 1995, Information System, Pawlak's Rough Sets, Rough Set, Theoretical Computer Science