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Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets

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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

Rough set theory has become well-established as a mechanism for uncertainty management in a wide variety of applications. This paper studies the measurement of uncertainty in generalized fuzzy rough sets determined by a triangular norm. Based on information theory, the entropy of a generalized fuzzy approximation space is introduced, which is similar to Shannon’s entropy. To measure uncertainty in generalized fuzzy rough sets, a notion of fuzziness is introduced. Some basic properties of this measure are examined. For a special triangular norm T =  min , it is proved that the measure of fuzziness of a generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable.

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Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, 050016, P.R. China

    Ju-Sheng Mi & Hui-Yin Zhao

  2. College of Science, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, P.R. China

    Xiu-Min Li & Tao Feng

  3. College of Science, Hebei College of Industry and Technology, Shijiazhuang, Hebei, 050091, P.R. China

    Hui-Yin Zhao

Authors
  1. Ju-Sheng Mi
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  2. Xiu-Min Li
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  3. Hui-Yin Zhao
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  4. Tao Feng
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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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Mi, JS., Li, XM., Zhao, HY., Feng, T. (2007). Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets. 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_7

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  • DOI: https://doi.org/10.1007/978-3-540-72530-5_7

  • 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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