## Abstract and Applied Analysis

### Some Chaotic Properties of Discrete Fuzzy Dynamical Systems

#### Abstract

Letting $(X,d)$ be a metric space, $f:X\to X$ a continuous map, and $({\scr F}(X),D)$ the space of nonempty fuzzy compact subsets of $X$ with the Hausdorff metric, one may study the dynamical properties of the Zadeh's extension $\stackrel{̂}{f}:{\scr F}(X)\to {\scr F}(X):u\mapsto\stackrel{̂}{f}u$. 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 $\stackrel{̂}{f}$. 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

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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