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International Journal of Machine Learning and Cybernetics
Published in: International Journal of Machine Learning and Cybernetics 4/2011

01-12-2011 | Original Article

Matroidal approaches to generalized rough sets based on relations

Authors: William Zhu, Shiping Wang

Published in: International Journal of Machine Learning and Cybernetics | Issue 4/2011

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Abstract

Rough set theory is a useful tool for dealing with the vagueness, granularity and uncertainty in information systems. This paper connects generalized rough sets based on relations with matroid theory. We define the upper approximation number to induce a matroid from a relation. Therefore, many matroidal approaches can be used to study generalized rough sets based on relations. Specifically, with the rank function of the matroid induced by a relation, we construct a pair of approximation operators, namely, matroid approximation operators. The matroid approximation operators present some unique properties which do not exist in the existing approximation operators. On the other hand, we present an approach to induce a relation from a matroid. Moreover, the relationship between two inductions is studied.
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Metadata
Title
Matroidal approaches to generalized rough sets based on relations
Authors
William Zhu
Shiping Wang
Publication date
01-12-2011
Publisher
Springer-Verlag
Published in
International Journal of Machine Learning and Cybernetics / Issue 4/2011
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-011-0027-y

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