This paper suggests an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. This approximation method involves the construction of Lipschitz fuzzy sets using the supmin convolution of a compact fuzzy set with a fuzzy zero. Considering a similar procedure, we present the approximation of a trapezoidal type fuzzy interval by a sequence of differentiable fuzzy intervals. We show some important properties of both approximations and we give some numerical examples illustrating the results. © 2010 Elsevier Ltd. All rights reserved.