Devaney chaotic fuzzy discrete dynamical systems

This paper is a contribution to the theoretical foundations of the theory of fuzzy discrete dynamical systems. We study relations between a given discrete dynamical system and its fuzzy extension — namely, a dynamical system induced by the Zadeh´s extension principle. Results contained in this contribution are related to the most common definition of chaos, i.e., Devaney´s one, and provide almost complete answer to the problem introduced in [H. Roma´n-Flores, Y. Chalco-Cano, Some chaotic properties of Zadeh´s extension, Chaos, Solitons & Fractals, Volume 35, Issue 3, February 2008, Pages 452–459].