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Comparative Study between Extension of Covering Approximation Space and Its Induction through Transversal Matroid

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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8170))

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Abstract

Extension of a covering approximation space has been successfully applied to attribute reduction of covering-based rough sets. While the algorithms to solve attribute reduction are almost greedy ones. As a generalization of linear algebra and graph theory, matroids provide well-established platforms for greedy algorithms. In this paper, we introduce induction of a covering approximation space through transversal matroids, and then study its relationship with extension of the covering approximation space. Generally, the induced space of a covering approximation space generates more exact approximations than itself. Based on this, we investigate the relationship between induction of a covering approximation space and its extension. In fact, the induced space of a covering approximation space generates a bigger covering lower approximation and smaller covering upper approximation than the extended space. These interesting results demonstrate the potential for studying attribute reduction of covering-based rough sets by matroidal approaches.

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Author information

Authors and Affiliations

  1. Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China

    Yanfang Liu & William Zhu

Authors
  1. Yanfang Liu
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  2. William Zhu
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Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, viale Sarca 336/14, 20126, Milano, Italy

    Davide Ciucci

  2. Osaka University, 560-8531, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

  3. University of Regina, S4S 0A2, Regina, SK, Canada

    Yiyu Yao

  4. University of Warsaw, ul. Banacha, 2, 02-097, Warsaw, Poland

    Dominik Ślęzak

  5. Chongqing Institute of Green and Intelligent Technology, CAS, 401122, Chongqing, China

    Guoyin Wang

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Liu, Y., Zhu, W. (2013). Comparative Study between Extension of Covering Approximation Space and Its Induction through Transversal Matroid. In: Ciucci, D., Inuiguchi, M., Yao, Y., Ślęzak, D., Wang, G. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2013. Lecture Notes in Computer Science(), vol 8170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41218-9_24

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  • DOI: https://doi.org/10.1007/978-3-642-41218-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41217-2

  • Online ISBN: 978-3-642-41218-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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