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On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones

Author

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  • Jiří Kupka

    (Centre of Excellence IT4Innovations (CE IT4I), Institute for Research and Applications of Fuzzy Modeling (IRAFM), University of Ostrava, 70103 Ostrava, Czech Republic)

  • Nicole Škorupová

    (Centre of Excellence IT4Innovations (CE IT4I), Institute for Research and Applications of Fuzzy Modeling (IRAFM), University of Ostrava, 70103 Ostrava, Czech Republic)

Abstract

Zadeh’s extension principle is one of the elementary tools in fuzzy set theory, and among other things, it provides a natural extension of a real-valued continuous self-map to a self-map having fuzzy sets as its arguments. The purpose of this paper is to introduce a new algorithm that can be used for simulations of fuzzy dynamical systems induced by interval maps. The core of the proposed algorithm is based on calculations including piecewise linear maps, and consequently, an implementation of an optimization algorithm (in our case, particle swarm optimization) was prepared to obtain necessary piecewise linear approximations. For all parts of this algorithm, we provide detailed testing and numerous examples.

Suggested Citation

  • Jiří Kupka & Nicole Škorupová, 2021. "On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones," Mathematics, MDPI, vol. 9(21), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2737-:d:666831
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    References listed on IDEAS

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    1. Stefanini, Luciano & Sorini, Laerte & Guerra, Maria Letizia, 2006. "Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 638-652.
    2. Daniel Jardón & Iván Sánchez & Manuel Sanchis, 2020. "Transitivity in Fuzzy Hyperspaces," Mathematics, MDPI, vol. 8(11), pages 1-9, October.
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    Cited by:

    1. Nicole Škorupová & Petr Raunigr & Petr Bujok, 2022. "Usage of Selected Swarm Intelligence Algorithms for Piecewise Linearization," Mathematics, MDPI, vol. 10(5), pages 1-24, March.

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