Abstract and Applied Analysis

Some Chaotic Properties of Discrete Fuzzy Dynamical Systems

Yaoyao Lan, Qingguo Li, Chunlai Mu, and Hua Huang

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Abstract

Letting ( X , d ) be a metric space, f : X X a continuous map, and ( ( 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 f ̂ : ( X ) ( X ) : u f ̂ u . In this paper, we present, as a response to the question proposed by Román-Flores and Chalco-Cano 2008, some chaotic relations between f and 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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 875381, 9 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168225

Digital Object Identifier
doi:10.1155/2012/875381

Mathematical Reviews number (MathSciNet)
MR3004896

Zentralblatt MATH identifier
1263.37031

Citation

Lan, Yaoyao; Li, Qingguo; Mu, Chunlai; Huang, Hua. Some Chaotic Properties of Discrete Fuzzy Dynamical Systems. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 875381, 9 pages. doi:10.1155/2012/875381. https://projecteuclid.org/euclid.aaa/1365168225


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