Chaos in iterated fuzzy systems
type: Item
instance of: scholarly article
title: Chaos in iterated fuzzy systems
zbMATH Open document ID: 0830.54006
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-09-08T00:00:00Z
review text: This paper can be considered as a natural continuation of previous works [e.g., the author and \textit{P. E. Kloeden}, Fuzzy Sets Syst. 29, No. 3, 341-348 (1989; Zbl 0661.54011); \textit{P. E. Kloeden} and \textit{A. I. Mees}, Bull. Math. Biol. 47, 697-738 (1985; Zbl 0586.92002)]. Using the well known principle of G. Darbo, the author gives a fixed point theorem in a suitable metric space of fuzzy sets. Sufficient conditions for chaos of fuzzy mappings are presented relaxing the hypothesis of compactness. Indeed an example of a noncompact chaotic mapping is given in the last section.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 635940
zbMATH Keywords: metric space of fuzzy sets
zbMATH Keywords: chaos of fuzzy mappings
zbMATH Keywords: noncompact chaotic mapping
author: Phil Diamond
reviewed by: Salvatore Sessa
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1216
OpenAlex ID: W2011315275
DOI: 10.1006/JMAA.1994.1216
description: scientific article; zbMATH DE number 635940