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

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 fo...

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Autores principales:	Jiří Kupka, Nicole Škorupová
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Zadeh’s extension principle particle swarm optimization fuzzy dynamical systems piecewise linearization simulations approximation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6b1f6634889240edbc00e2929988c77a
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spelling	oai:doaj.org-article:6b1f6634889240edbc00e2929988c77a2021-11-11T18:17:16ZOn PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones10.3390/math92127372227-7390https://doaj.org/article/6b1f6634889240edbc00e2929988c77a2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2737https://doaj.org/toc/2227-7390Zadeh’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.Jiří KupkaNicole ŠkorupováMDPI AGarticleZadeh’s extension principleparticle swarm optimizationfuzzy dynamical systemspiecewise linearizationsimulationsapproximationMathematicsQA1-939ENMathematics, Vol 9, Iss 2737, p 2737 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Zadeh’s extension principle particle swarm optimization fuzzy dynamical systems piecewise linearization simulations approximation Mathematics QA1-939
spellingShingle	Zadeh’s extension principle particle swarm optimization fuzzy dynamical systems piecewise linearization simulations approximation Mathematics QA1-939 Jiří Kupka Nicole Škorupová On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones
description	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.
format	article
author	Jiří Kupka Nicole Škorupová
author_facet	Jiří Kupka Nicole Škorupová
author_sort	Jiří Kupka
title	On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones
title_short	On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones
title_full	On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones
title_fullStr	On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones
title_full_unstemmed	On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones
title_sort	on pso-based simulations of fuzzy dynamical systems induced by one-dimensional ones
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/6b1f6634889240edbc00e2929988c77a
work_keys_str_mv	AT jirikupka onpsobasedsimulationsoffuzzydynamicalsystemsinducedbyonedimensionalones AT nicoleskorupova onpsobasedsimulationsoffuzzydynamicalsystemsinducedbyonedimensionalones
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On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones

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