A purely topological characterization of relatively compact sets is given for the metric space (K(Y),D) of upper semicontinuous, compact-supported, normal fuzzy subsets of a metric space Y . The considered metric D is that of the distance between fuzzy subsets, which is the supremum of the Hausdorff distances of the corresponding level sets. In the given proof the compactness of a variational convergence which was introduced by De Giorgi and Franzoni is fundamental.
A characterization of relatively compact sets of fuzzy sets
Greco, Gabriele Hans
2006-01-01
Abstract
A purely topological characterization of relatively compact sets is given for the metric space (K(Y),D) of upper semicontinuous, compact-supported, normal fuzzy subsets of a metric space Y . The considered metric D is that of the distance between fuzzy subsets, which is the supremum of the Hausdorff distances of the corresponding level sets. In the given proof the compactness of a variational convergence which was introduced by De Giorgi and Franzoni is fundamental.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
