Some chaotic properties of discrete fuzzy dynamical systems
type: Item
instance of: scholarly article
title: Some chaotic properties of discrete fuzzy dynamical systems
zbMATH Open document ID: 1263.37031
DOI: 10.1155/2012/875381
author: Yao Yao Lan
author: Hua Huang
author: Qingguo Li
author: Chunlai Mu
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: Letting \((X, d)\) be a metric space, \(f : X \rightarrow X\) a continuous map, and \((\mathcal F(X), D)\) the space of nonempty fuzzy compact subsets of \(X\) with the Hausdorff metric, one may study the dynamical properties of the Zadeh's extension \(\hat{f} : \mathcal F(X) \rightarrow \mathcal F(X) : u \mapsto \hat{f}u\). In this paper, we present, as a response to the question proposed by \textit{H. Román-Flores} and \textit{Y. Chalco-Cano} [Chaos Solitons Fractals 35, No. 3, 452--459 (2008; Zbl 1142.37308)], some chaotic relations between \(f\) and \(\hat{f}\). More specifically, we study the transitivity, weakly mixing, periodic density in system \((X, f)\), and its connections with the same ones in its fuzzified system.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 6134182
zbMATH Keywords: fuzzy dynamics
zbMATH Keywords: fuzzy systems
zbMATH Keywords: transitivity
zbMATH Keywords: weakly mixing
zbMATH Keywords: periodic density
Wikidata QID: Q58697013
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/875381
OpenAlex ID: W2072481055
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description: scientific article; zbMATH DE number 6134182