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Probabilistic Rough Sets Characterized by Fuzzy Sets

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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2639))

Abstract

In this paper, fuzziness in probabilistic rough set is studied by fuzzy sets. we show that the variable precision approximation of a probabilistic rough set can be generalized from the vantage point of the cuts of a fuzzy set which is determined by the rough membership function. As a result, the fuzzy set can be used conveniently to describe the feature of rough set. Moreover we give a measure of fuzziness, fuzzy entropy, induced by roughness in a probabilistic rough set and make some characterizations of this measure. For three well-known entropy functions, we show that the finer the information granulation is, the less the fuzziness in a rough set. The superiority of fuzzy entropy to Pawlak’s accuracy measure is illustrated with examples. Finally, the fuzzy entropy of a rough classification is defined by the fuzzy entropy of corresponding rough sets, and show that one possible application of it is to measure the inconsistency in a decision table.

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Author information

Authors and Affiliations

  1. Institute of Information and System Science, Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Li-Li Wei & Wen-Xiu Zhang

Authors
  1. Li-Li Wei
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  2. Wen-Xiu Zhang
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Editor information

Editors and Affiliations

  1. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, P.R. China

    Guoyin Wang

  2. Department of Computer Science, Nanchang University, Nanchang, 330029, P.R. China

    Qing Liu

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

    Yiyu Yao

  4. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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© 2003 Springer-Verlag Berlin Heidelberg

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Wei, LL., Zhang, WX. (2003). Probabilistic Rough Sets Characterized by Fuzzy Sets. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2003. Lecture Notes in Computer Science(), vol 2639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39205-X_22

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  • DOI: https://doi.org/10.1007/3-540-39205-X_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14040-5

  • Online ISBN: 978-3-540-39205-7

  • eBook Packages: Springer Book Archive

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