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Some Chaotic Properties of Discrete Fuzzy Dynamical Systems

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Listed:
  • Yaoyao Lan
  • Qingguo Li
  • Chunlai Mu
  • Hua Huang

Abstract

Letting (X, d) be a metric space, f : X → X a continuous map, and (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 f∧:ℱ(X)→ℱ(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.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:875381
DOI: 10.1155/2012/875381
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