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Is Fuzzy Number the Right Result of Arithmetic Operations on Fuzzy Numbers?

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 643))

Abstract

Present versions of fuzzy arithmetic (FA) are not ideal. For some computational problems they deliver credible results. However for many other problems the results are less credible or sometimes clearly incredible. Reason of this state of matter is the fact that present FA-versions partially or fully (depending on a method) do not possess mathematical properties that are necessary for achieving correct calculation results as: distributivity law, cancellation law, neutral elements of addition and multiplication, property of restoration, possibility of decomposition of calculation in parts, ability of credible equations’ solving, property of delivering universal algebraic solutions, possibility of formula transformation, and other. Lack of above properties is, in the authors’ opinion, caused by incorrect assumption of all existing FA-versions that result of arithmetic operations on unidimensional fuzzy intervals is also a unidimensional fuzzy interval. In the paper authors show that the correct result is a multidimensional fuzzy set and present a fuzzy arithmetic based on this proposition, which possess all necessary mathematical properties and delivers credible results.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science and Information Systems, West Pomeranian University of Technology, Zolnierska Street 49, 71-210, Szczecin, Poland

    Andrzej Piegat

  2. Department of Mathematical Methods, Maritime University of Szczecin, Waly Chrobrego 1-2, 70-500, Szczecin, Poland

    Marek Landowski

Authors
  1. Andrzej Piegat
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  2. Marek Landowski
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Corresponding author

Correspondence to Marek Landowski .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Institute of Biophysics and Biomedical Engineering, Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Piegat, A., Landowski, M. (2018). Is Fuzzy Number the Right Result of Arithmetic Operations on Fuzzy Numbers?. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 643. Springer, Cham. https://doi.org/10.1007/978-3-319-66827-7_17

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  • DOI: https://doi.org/10.1007/978-3-319-66827-7_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

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