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Piecewise Linear Approximation of Fuzzy Numbers Preserving the Support and Core

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 443))

Abstract

A reasonable approximation of a fuzzy number should have a simple membership function, be close to the input fuzzy number, and should preserve some of its important characteristics. In this paper we suggest to approximate a fuzzy number by a piecewise linear 1-knot fuzzy number which is the closest one to the input fuzzy number among all piecewise linear 1-knot fuzzy numbers having the same core and the same support as the input. We discuss the existence of the approximation operator, show algorithms ready for the practical use and illustrate the considered concepts by examples. It turns out that such an approximation task may be problematic.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Oradea, 1 Universitatii Street, 410087, Oradea, Romania

    Lucian Coroianu

  2. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Marek Gagolewski & Przemyslaw Grzegorzewski

  3. Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

    Marek Gagolewski & Przemyslaw Grzegorzewski

  4. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Iran

    M. Adabitabar Firozja

  5. School of Mathematics and Computer Sciences, Damghan University, Iran

    Tahereh Houlari

Authors
  1. Lucian Coroianu
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  2. Marek Gagolewski
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  3. Przemyslaw Grzegorzewski
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  4. M. Adabitabar Firozja
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  5. Tahereh Houlari
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Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. LIRMM, UMR CNRS/Universite Montpellier II, 161 rue Ada, 34392, Montpellier cedex 5, France

    Olivier Strauss

  3. UPMC Univ. Paris 06, CNRS UMR 7606, LIP6, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2014 Springer International Publishing Switzerland

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Coroianu, L., Gagolewski, M., Grzegorzewski, P., Firozja, M.A., Houlari, T. (2014). Piecewise Linear Approximation of Fuzzy Numbers Preserving the Support and Core. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-08855-6_25

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  • DOI: https://doi.org/10.1007/978-3-319-08855-6_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08854-9

  • Online ISBN: 978-3-319-08855-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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