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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing pp 90–101Cite as

A Comparison of Two Types of Covering-Based Rough Sets Through the Complement of Coverings

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9437))

Abstract

In recent years, many types of covering-based rough set models were established and the study of their relationships was a hot research topic. Covering-based rough sets defined by Zhu and ones defined by Xu and Zhang were compared with each other through binary relations. And the relationships between these two types were further explored by introducing a concept of complementary neighborhood. However, the essential connections between these two types have not been revealed. In this paper, we consider these two types of covering-based rough sets by introducing a notion of the complement of coverings. In fact, these two types are expressed by each other through the complement of coverings. Based on the above results, we analyze a notion of the extension of a covering, which is introduced on the basis of the complement of the covering. Finally, we further explore the structure of these types of covering-based rough set models. This study suggests some internal connections between covering-based rough sets and demonstrates a new research tendency of them.

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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.

Author information

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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Corresponding authors

Correspondence to Yanfang Liu or William Zhu .

Editor information

Editors and Affiliations

  1. University of Regina, Regina, SK, Canada

    Yiyu Yao

  2. Tianjin University, Tianjin, China

    Qinghua Hu

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

    Hong Yu

  4. University of Kansas, Lawrence, KS, USA

    Jerzy W. Grzymala-Busse

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Liu, Y., Zhu, W. (2015). A Comparison of Two Types of Covering-Based Rough Sets Through the Complement of Coverings. In: Yao, Y., Hu, Q., Yu, H., Grzymala-Busse, J.W. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Lecture Notes in Computer Science(), vol 9437. Springer, Cham. https://doi.org/10.1007/978-3-319-25783-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-25783-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

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