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Variable Precision Fuzzy Rough Sets

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Transactions on Rough Sets I

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3100))

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Abstract

In this paper the variable precision fuzzy rough sets (VPFRS) concept will be considered. The notions of the fuzzy inclusion set and the α-inclusion error based on the residual implicators will be introduced. The level of misclassification will be expressed by means of α-cuts of the fuzzy inclusion set. Next, the use of the mean fuzzy rough approximations will be postulated and discussed. The concept of VPFRS will be defined using the extended version of the variable precision rough sets (VPRS) model, which utilises a general allowance for levels of misclassification expressed by two parameters: lower (l) and upper (u) limit. Remarks concerning the variable precision rough fuzzy sets (VPRFS) idea will be given. An example will illustrate the proposed VPFRS model.

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Author information

Authors and Affiliations

  1. Department of Avionics and Control, Rzeszów University of Technology, ul. W. Pola 2, 35-959, Rzeszów, Poland

    Alicja Mieszkowicz-Rolka & Leszek Rolka

Authors
  1. Alicja Mieszkowicz-Rolka
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  2. Leszek Rolka
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

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

    Andrzej Skowron  & Marcin S. Szczuka  & 

  3. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

  4. Multimedia Systems Department, Gdańsk University of Technology, Narutowicza 11/12, 80-952, Gdańsk, Poland

    Bożena Kostek

  5. Department of Mathematical and Computer Sciences, San Diego State University, 5500 Campanile Drive, CA 92182, San Diego, USA

    Roman W. Świniarski

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© 2004 Springer-Verlag Berlin Heidelberg

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Mieszkowicz-Rolka, A., Rolka, L. (2004). Variable Precision Fuzzy Rough Sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds) Transactions on Rough Sets I. Lecture Notes in Computer Science, vol 3100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27794-1_6

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  • DOI: https://doi.org/10.1007/978-3-540-27794-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22374-0

  • Online ISBN: 978-3-540-27794-1

  • eBook Packages: Springer Book Archive

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