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Zbl 1129.68088
Zhu, William
Generalized rough sets based on relations. (English)
[J] Inf. Sci. 177, No. 22, 4997-5011 (2007). ISSN 0020-0255

Summary: Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations. This paper studies arbitrary binary relation based generalized rough sets. In this setting, a binary relation can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a relation under which these properties hold for the relation based lower and upper approximation operations.This paper also explores the relationships between the lower or the upper approximation operation generated by the intersection of two binary relations and those generated by these two binary relations, respectively. Through these relationships, we prove that two different binary relations will certainly generate two different lower approximation operations and two different upper approximation operations.

MSC 2000:: *68T30 Knowledge representation
68T37 Reasoning under uncertainty

Keywords: Rough set; lower approximation; upper approximation; binary relation; fuzzy set; granular computing

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