Let I = [a, b] a real compact interval and f : I → I a continuous function. Define Kc([a, b]) the class of all non empty compact subinterval of [a, b] and let fc the natural extension of f to Kc([a, b]), that is to say, fc(J) = f(J) for all J ∈ Kc([a, b]). Also, let Fc([a, b]) the class of all fuzzy-intervals with support contained in [a, b] and consider fcc the Zadeh's extension of f to Fc([a, b]). The aim of this paper is to show some dynamical properties of fc and fcc in relation to the Devaney's conditions for complexity of functions and, in particular, to show the surprising difference between the dynamics on the base space X = [a, b] compared with the dynamics of the interval extension Kc([a, b]) and fuzzy-interval extension Fc([a, b]), which could be useful in the mathematical modelling of real problems.