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Fuzzy Approximation Operators Based on Coverings

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Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4482))

Abstract

This paper presents a general framework for the study of covering-based fuzzy approximation operators in which a fuzzy set can be approximated by some elements in a crisp or a fuzzy covering of the universe of discourse. Two types of approximation operators, crisp-covering-based rough fuzzy approximation operators and fuzzy-covering-based fuzzy rough approximation operators, are defined, their properties are examined in detail. Finally, the comparison of these new approximation operators is done, a sufficient and necessary condition is given under which some operators are equivalent, and approximation operator characterization of fuzzy partitions of the universe is obtained.

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Author information

Authors and Affiliations

  1. Mathematics, Physics and Information College, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, P.R. China

    Tongjun Li

  2. Institute for Information and System Sciences, Faculty of Science, Xi’an Jiaotong University, Xi’an, Shaan’xi, 710049, P.R. China

    Tongjun Li & Jianmin Ma

Authors
  1. Tongjun Li
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  2. Jianmin Ma
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, York University, M3J 1P3, Toronto, Ontario, Canada

    Aijun An

  2. Institute of Computing Sciences, Poznań University of Technology, ul. Piotrowo 2, 60–965, Poznań, Poland

    Jerzy Stefanowski

  3. Department of Applied Computer Science, University of Winnipeg, R3B 2E9, Winnipeg, Manitoba, Canada

    Sheela Ramanna

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Cory J. Butz

  5. Department of Electrical and Computer Engineering, University of Alberta, T6G 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

  6. Institute of Compuer Science and Technology, Chongqing University of Posts and Telecommunications, 40065, Chongqing, P.R. China

    Guoyin Wang

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© 2007 Springer-Verlag Berlin Heidelberg

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Li, T., Ma, J. (2007). Fuzzy Approximation Operators Based on Coverings. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2007. Lecture Notes in Computer Science(), vol 4482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72530-5_6

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  • DOI: https://doi.org/10.1007/978-3-540-72530-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72529-9

  • Online ISBN: 978-3-540-72530-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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