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Advances in Intelligent Modelling and Simulation pp 25–41Cite as

Step Fuzzy Numbers and Neural Networks in Defuzzification Functional Approximation

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 422))

Abstract

Ordered fuzzy numbers as generalization of convex fuzzy numbers are defined together with four algebraic operations. For defuzzification operators, that play the main role when dealing with fuzzy controllers and fuzzy inference systems, new representation formulae are given. Step ordered fuzzy numbers are considered. Approximation method based on forward neural networks is presented for determining defuzzification functionals when training sets of data are given. Results of approximation are given.

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Author information

Authors and Affiliations

  1. Polish-Japanese Institute of Information Technology, Warsaw, Poland

    Witold Kosiński

  2. Kazimierz-Wielki University, Bydgoszcz, Poland

    Witold Kosiński

  3. École Supérieure d’Ingénieurs en Informatique et Génie de Télécommunication (ESIGETEL), Avon, France

    Katarzyna Węgrzyn-Wolska

Authors
  1. Witold Kosiński
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  2. Katarzyna Węgrzyn-Wolska
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, Cracow University of Technology, ul. Warszawska 24, Cracow, 31-155, Poland

    Joanna Kołodziej

  2. , Department of Electrical and Computer, North Dakota State University, Fargo, 58108-6050, USA

    Samee Ullah Khan

  3. Department of Computer Science, Cracow University of Technology, ul. Warszawska 24, Cracow, 31-155, Poland

    Tadeusz Burczy´nski

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Kosiński, W., Węgrzyn-Wolska, K. (2012). Step Fuzzy Numbers and Neural Networks in Defuzzification Functional Approximation. In: Kołodziej, J., Khan, S., Burczy´nski, T. (eds) Advances in Intelligent Modelling and Simulation. Studies in Computational Intelligence, vol 422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30154-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-30154-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30153-7

  • Online ISBN: 978-3-642-30154-4

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