The compactness of E(X) Original Research Article

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 supremum on the Hausdorff distances between the corresponding α-level sets. The aim of this paper is, on the one hand, to analyze the compactness and separability of E(X) with respect to the compactness and separability of X, and on the other, to study these properties on the subclass Ec(X) of level-continuous fuzzy sets.