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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing pp 149–160Cite as

Connectedness of Graph and Matroid by Covering-Based Rough Sets

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

Abstract

Covering-based rough sets provide an efficient theory to process information in data mining. Matroid theory is a generalization of both linear algebra and graph theory, and has a variety of applications in many fields, such as covering-based rough sets. In this paper, we study the connectedness of graphs and matroids through covering-based rough sets. First, we present an approach to induce a covering by a graph. Then we use the covering upper approximation operator and the rank of matrix representation of the covering to study the connectedness of the graph. Moreover, we give the expression of the number of the connected components of a graph. Second, we establish a matroid based on the covering induced by a graph and study the connectedness of this matroid.

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Acknowledgments

This work is in part supported by The National Nature Science Foundation of China under Grant Nos. 61170128, 61379049 and 61379089, the Key Project of Education Department of Fujian Province under Grant No. JA13192, and the Science and Technology Key Project of Fujian Province, China Grant No. 2012H0043.

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Authors and Affiliations

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

    Hui Li & William Zhu

Authors
  1. Hui Li
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  2. William Zhu
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Corresponding author

Correspondence to Hui Li .

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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Li, H., Zhu, W. (2015). Connectedness of Graph and Matroid by Covering-Based Rough Sets. 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_14

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  • DOI: https://doi.org/10.1007/978-3-319-25783-9_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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