Some Chaotic Properties of Discrete Fuzzy Dynamical Systems

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) over cap : F(X) -> F(X) : u bar right arrow (f) over capu. In this paper, we present, as a response to the question proposed by Roman-Flores and Chalco-Cano 2008, some chaotic relations between f and (f) over cap . 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.