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International Conference on Artificial Intelligence and Soft Computing

ICAISC 2013: Artificial Intelligence and Soft Computing pp 365–375Cite as

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

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

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.

Keywords

  • fuzzy number
  • Ordered Fuzzy Numbers
  • arithmetic calculations on fuzzy numbers
  • logarithm of fuzzy numbers
  • exponent of fuzzy numbers

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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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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

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