Abstract: Puri and Ralescu [10] given, recently, an embedding of the class E of fuzzy sets u with the level application a Lou Lipschitzian on C([0,1] x S1). In this work we extend the above result to the class E of the continuous level applications. Moreover, we prove that E is a complete metric space while at the E is not, and that E E. Also, we deduce some properties in the fuzzy random variables Ver menos