Abstract
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.
The first author is in part supported by the New Economy Research Fund of New Zealand and this work is also in part supported by two 973 projects (2004CB318103) and (2002CB312200) from the Ministry of Science and Technology of China.
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Zhu, W., Wang, FY. (2006). Binary Relation Based Rough Sets. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2006. Lecture Notes in Computer Science(), vol 4223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881599_31
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DOI: https://doi.org/10.1007/11881599_31
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