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The Scientific World Journal - Volume 2014 2014, Article ID 243070, 7 pages -

Research ArticleLaboratory of Granular Computing, Minnan Normal University, Zhangzhou 363000, China

Received 15 June 2014; Accepted 23 July 2014; Published 5 August 2014

Academic Editor: Yunqiang Yin

Copyright © 2014 Hui Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as combinatorial optimization and rough sets. In this paper, we construct a matroidal structure of the generalized rough set based on a tolerance relation. First, a family of sets are constructed through the lower approximation of a tolerance relation and they are proved to satisfy the circuit axioms of matroids. Thus we establish a matroid with the family of sets as its circuits. Second, we study the properties of the matroid including the base and the rank function. Moreover, we investigate the relationship between the upper approximation operator based on a tolerance relation and the closure operator of the matroid induced by the tolerance relation. Finally, from a tolerance relation, we can get a matroidof the generalized rough set based on the tolerance relation. The matroid can also induce a new relation. We investigate the connection between the original tolerance relation and the induced relation.

Author: Hui Li, Yanfang Liu, and William Zhu



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