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Matroidal approaches to generalized rough sets based on relations

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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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Acknowledgements

This work is in part supported by National Nature Science Foundation of China under grant No.60873077/F020107.

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Authors and Affiliations

  1. Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou, China

    William Zhu

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Shiping Wang

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  1. William Zhu
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  2. Shiping Wang
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Correspondence to Shiping Wang.

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Zhu, W., Wang, S. Matroidal approaches to generalized rough sets based on relations. Int. J. Mach. Learn. & Cyber. 2, 273–279 (2011). https://doi.org/10.1007/s13042-011-0027-y

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  • DOI: https://doi.org/10.1007/s13042-011-0027-y

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