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 sup-min 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. (C) 2010 Elsevier Ltd. All rights reserved.612412420Dipog-UTA [4730-09]Ministerio de Ciencia e Innovacion, Spain [MTM2008-00018]Conicyt-Chile [1080438]Dipog-UTA [4730-09]Ministerio de Ciencia e Innovacion, Spain [MTM2008-00018]Conicyt-Chile [1080438]