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2012 Matroidal Structure of Rough Sets Based on Serial and Transitive Relations
Yanfang Liu, William Zhu
J. Appl. Math. 2012: 1-16 (2012). DOI: 10.1155/2012/429737


The theory of rough sets is concerned with the lower and upper approximations of objects through a binary relation on a universe. It has been applied to machine learning, knowledge discovery, and data mining. The theory of matroids is a generalization of linear independence in vector spaces. It has been used in combinatorial optimization and algorithm design. In order to take advantages of both rough sets and matroids, in this paper we propose a matroidal structure of rough sets based on a serial and transitive relation on a universe. We define the family of all minimal neighborhoods of a relation on a universe and prove it satisfies the circuit axioms of matroids when the relation is serial and transitive. In order to further study this matroidal structure, we investigate the inverse of this construction: inducing a relation by a matroid. The relationships between the upper approximation operators of rough sets based on relations and the closure operators of matroids in the above two constructions are studied. Moreover, we investigate the connections between the above two constructions.


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Yanfang Liu. William Zhu. "Matroidal Structure of Rough Sets Based on Serial and Transitive Relations." J. Appl. Math. 2012 1 - 16, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1264.05028
MathSciNet: MR3000284
Digital Object Identifier: 10.1155/2012/429737

Rights: Copyright © 2012 Hindawi


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