Chaotic properties; Devaney chaotic; Discrete dynamical systems; Fuzzy extension; Theoretical foundations; Zadeh's extension principles

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. Román-Flores, Y. Chalco-Cano, Some chaotic properties of Zadeh's extension, Chaos, Solitons & Fractals, Volume 35, Issue 3, February 2008, Pages 452-459].