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Intelligent Information Processing and Web Mining pp 353–362Cite as

On Algebraic Operations on Fuzzy Numbers

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Part of the Advances in Soft Computing book series (AINSC,volume 22)

Abstract

New definition of the fuzzy counterpart of real number is presented. An extra feature, called the orientation of the membership curve is introduced. It leads to a novel concept of an ordered fuzzy number, represented by the ordered pair of real continuous functions. Four algebraic operations on ordered fuzzy numbers are defined; they enable to avoid some drawbacks of the classical approach.

  • fuzzy numbers
  • quasi-convexity
  • orientation
  • algebraic operations

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  • DOI: 10.1007/978-3-540-36562-4_37
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Author information

Affiliations

  1. Research Center, Polish—Japanese Institute of Information Technology, ul. Koszykowa 86, 02-008, Warsaw, Poland

    Witold Kosiński & Dominik Ślęzak

  2. Institute of Environmental Mechanics and Applied Computer Science, The University of Bydgoszcz, ul. Chodkiewicza 30, 85-064, Bydgoszcz, Poland

    Piotr Prokopowicz

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

    Dominik Ślęzak

Authors
  1. Witold Kosiński
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  2. Piotr Prokopowicz
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  3. Dominik Ślęzak
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© 2003 Springer-Verlag Berlin Heidelberg

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Kosiński, W., Prokopowicz, P., Ślęzak, D. (2003). On Algebraic Operations on Fuzzy Numbers. In: Kłopotek, M.A., Wierzchoń, S.T., Trojanowski, K. (eds) Intelligent Information Processing and Web Mining. Advances in Soft Computing, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36562-4_37

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  • DOI: https://doi.org/10.1007/978-3-540-36562-4_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00843-9

  • Online ISBN: 978-3-540-36562-4

  • eBook Packages: Springer Book Archive