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Matroidal structure of covering-based rough sets through the upper approximation number
by Shiping Wang; William Zhu
International Journal of Granular Computing, Rough Sets and Intelligent Systems (IJGCRSIS), Vol. 2, No. 2, 2011
Abstract: Covering-based rough set theory is a generalisation of rough set theory. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. In this paper, we introduce matroid theory to covering-based rough sets, and explore the matroidal structure and properties of covering-based rough sets. Specifically, we define the upper approximation number to establish the matroidal structure of covering-based rough sets. So many important concepts and methods in matroid theory can be employed to investigate covering-based rough sets. The rank plays a very important role in a matrix, so we use the rank function of the matroid induced by a covering to measure the covering. With the rank function, a pair of approximation operators, namely, matroid approximation operators, are constructed. This type of approximation operators not only inherits the properties of those traditional ones which are defined from the perspective of set theory, but also presents some new properties. Finally, the matroid upper approximations are compared with the second upper approximations in covering-based rough sets.
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