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The Matroidal Structures of the Second Type of Covering-Based Rough Set

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Rough Sets and Knowledge Technology (RSKT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9436))

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Abstract

Rough set theory is a useful tool for data mining. In recent yeas, ones have combined it with matroid theory to construct an excellent set-theoretical framework for empirical machine learning methods. Hence, the study of its matroidal structure is an interesting research topic, and the structure is part of the foundation of rough set theory. Few people study the combinations the second type of covering-based rough sets with matroids. x On the one hand, we establish a closure system through the fixed point family of the second type of covering lower approximation operator, and then construct a corresponding closure operator. For a covering of a universe, this closure operator is a matroidal closure operator if and only if the reduct of the covering forms a partition of the universe. On the other hand, we present two sufficient and necessary conditions for the second type of covering upper approximation operator to form a matroidal closure operator through the indiscernible neighborhood and the covering upper approximation operator.

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Acknowledgments

This work is in part supported by the National Science Foundation of China under Grant Nos. 61170128, 61379049, 61379089 and 61440047.

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Authors and Affiliations

  1. Institute of Information Engineering, Longyan University, Longyan, 364000, China

    Yanfang Liu

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

    William Zhu

Authors
  1. Yanfang Liu
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  2. William Zhu
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Correspondence to William Zhu .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  2. Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  3. Indian Statistical Institute, Kolkata, India

    Sushmita Mitra

  4. Zhejiang Ocean University, Zhejiang, China

    Wei-Zhi Wu

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Liu, Y., Zhu, W. (2015). The Matroidal Structures of the Second Type of Covering-Based Rough Set. In: Ciucci, D., Wang, G., Mitra, S., Wu, WZ. (eds) Rough Sets and Knowledge Technology. RSKT 2015. Lecture Notes in Computer Science(), vol 9436. Springer, Cham. https://doi.org/10.1007/978-3-319-25754-9_21

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  • DOI: https://doi.org/10.1007/978-3-319-25754-9_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25753-2

  • Online ISBN: 978-3-319-25754-9

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