Separability for graph convergence of sequences of fuzzy-valued random variables

Abstract

We prove that the graph convergence in Hausdorff metric or Kuratowski-Mosco topology of a sequence of fuzzy sets follows from the convergence of the sequences of the level sets for countable dense levels. As an application, we give a strong law of large numbers for fuzzy-valued random variables, including the case when the level sets may not be bounded. © 2001 Elsevier Science B.V. All rights reserved.