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Flexible and Simple Methods of Calculations on Fuzzy Numbers with the Ordered Fuzzy Numbers Model

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Artificial Intelligence and Soft Computing (ICAISC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7894))

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Abstract

The publication shows the way of implementing arithmetic operations on fuzzy numbers based on Ordered Fuzzy Numbers calculation model [12], [13], [14]. This model allows to perform calculations on fuzzy numbers in a way that the outcomes meet the same criteria as the outcomes of calculations on real numbers. In this text, to the four basic operations with Ordered Fuzzy Numbers, a logarithm and exponentiation was added. Several examples of the calculations are included, the results of which are obvious and typical of real numbers but not achievable with the use of conventional computational methods for fuzzy numbers. From these examples one can see that the use of Ordered Fuzzy Numbers allows to obtain outcomes for real numbers in spite of using the fuzzy values.

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Authors and Affiliations

  1. Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, Bydgoszcz, Poland

    Piotr Prokopowicz

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  1. Piotr Prokopowicz
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Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Michiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Department of Electrical Engineering and Computer Sciences, University of California, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

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Prokopowicz, P. (2013). Flexible and Simple Methods of Calculations on Fuzzy Numbers with the Ordered Fuzzy Numbers Model. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_33

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  • DOI: https://doi.org/10.1007/978-3-642-38658-9_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38657-2

  • Online ISBN: 978-3-642-38658-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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