Abstract and Applied Analysis
Volume 2012 (2012), Article ID 875381, 9 pages
http://dx.doi.org/10.1155/2012/875381
Research Article

Some Chaotic Properties of Discrete Fuzzy Dynamical Systems

Yaoyao Lan,1,2 Qingguo Li,2 Chunlai Mu,1 and Hua Huang3

1College of Computer Science, Chongqing University, Chongqing 401331, China
2College of Applied Mathematics, Hunan University, Changsha 410082, Hunan, China
3Department of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan 402160, China

Received 16 September 2012; Revised 21 November 2012; Accepted 21 November 2012

Academic Editor: Gani Stamov

Copyright © 2012 Yaoyao Lan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Letting be a metric space, a continuous map, and the space of nonempty fuzzy compact subsets of with the Hausdorff metric, one may study the dynamical properties of the Zadeh's extension . In this paper, we present, as a response to the question proposed by Román-Flores and Chalco-Cano 2008, some chaotic relations between and . More specifically, we study the transitivity, weakly mixing, periodic density in system , and its connections with the same ones in its fuzzified system.