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arXiv · 1209.5470

Matroidal structure of generalized rough sets based on symmetric and transitive relations

Bin Yang·William Zhu
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Abstract

Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and transitive relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and transitive relations, and provide an approach to study the matroid induced by a symmetric and transitive relation. Secondly, this paper establishes a close relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and transitive relation can be constructed by a matroid with some special properties.

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Bin Yang, William Zhu. 2012-12-17. Matroidal structure of generalized rough sets based on symmetric and transitive relations. https://arxiv.org/abs/1209.5470

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