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Published in:
2006 | OriginalPaper | Chapter
Binary Relation Based Rough Sets
Authors : William Zhu, Fei-Yue Wang
Published in: Fuzzy Systems and Knowledge Discovery
Publisher: Springer Berlin Heidelberg
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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. We prove that such a binary relation is unique, since two different binary relations will generate two different lower approximation operations and two different upper approximation operations. This paper also explores the relationships between the lower or upper approximation operation generated by the intersection of two binary relations and those generated by these two binary relations, respectively.