Let I = [a, b] be a real compact interval and f : I a continuous function. Define kappa(c)([a, b]) the class of all non empty compact subinterval of [a, b] and let (f) over bar the natural extension of f kappa(c) K( [a, that is to say, (f) over bar (J) = f (J) for all J is an element of I[([a, b]). Also, let F-c([a, b]) the class of all fuzzy-intervals with support contained in [a, b] and consider (f) over cap the Zadeh's extension of f to F-c ([a, b]). The aim of this paper is to show that f and f are not transitive for any arbitrary self continuous function f defined on I.