On distance between fuzzy variables

摘要

Distance between fuzzy variables has been defined in many ways, for example, Hausdorff-like distance and Hamming distance. This paper discusses the properties of a new distance between fuzzy variables defined by expected value operator. Furthermore, a metric space of fuzzy variables is defined and the completeness of this space is proved. Finally, the distances between fuzzy vectors, fuzzy random vectors, and random fuzzy vectors are given.