THE COMPACTNESS OF E(X)

Let X be a metric space and E(X) the class of fuzzy compact sets on X, equipped with the generalized Hausdorff metric D which take the supre mum on the Hausdorff distances between the corresponding alpha-level s ets. The aim of this paper is, on the one hand, to analyze the compact ness and separability of E(X) with respect to the compactness and sepa rability of X, and on the other, to study these properties on the subc lass E-c(X) of level-continuous fuzzy sets.