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Calculations of Zadeh’s Extension of Piecewise Linear Functions

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Fuzzy Techniques: Theory and Applications (IFSA/NAFIPS 2019 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1000))

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Abstract

Zadeh’s extension principle is one of the most classical techniques in fuzzy set theory. It is a tool which, for example, can naturally extend a real-valued continuous map to a map having fuzzy sets as its arguments. Theoretically, it is a nice mathematical tool used in many theories, e.g. in studies on fuzzy dynamical systems. However, concrete calculations or even approximations can be very difficult in general and, consequently, many approaches trying to solve this problem appeared. In this work we present a novel algorithm which can compute Zadeh’s extension of given continuous piecewise linear functions. Among other things, an advantage of this approach is that, unlike almost all former approaches, it can deal with discontinuities which naturally appear in simulations of fuzzy dynamical systems.

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Acknowledgements

The second author acknowledges funding from the project “Support of talented PhD students at the University of Ostrava” from the programme RRC/10/2018 “Support for Science and Research in the Moravian-Silesian Region 2018”.

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Authors and Affiliations

  1. Centre of Excellence IT4Innovations, Division University of Ostrava, IRAFM, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Jiří Kupka & Nicole Škorupová

Authors
  1. Jiří Kupka
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  2. Nicole Škorupová
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Corresponding author

Correspondence to Nicole Škorupová .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA

    Ralph Baker Kearfott

  2. Center for Computing Research (CIC), Instituto Politecnico Nacional, Ciudad de Mexico, Mexico

    Ildar Batyrshin

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Marek Reformat

  4. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  5. Department of Computer Science, University of Texas at El Paso , El Paso, TX, USA

    Vladik Kreinovich

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Kupka, J., Škorupová, N. (2019). Calculations of Zadeh’s Extension of Piecewise Linear Functions. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_54

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