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

Jiří Kupka and Nicole Škorupová
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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

Mathematics, 2021, vol. 9, issue 21, 1-26

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.

Keywords: Zadeh’s extension principle; particle swarm optimization; fuzzy dynamical systems; piecewise linearization; simulations; approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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