On distance between fuzzy variables

Authors:
Xiang Li;Baoding Liu
Affiliations:
(Correspd. E-mail: xiang-li04@mails.tsinghua.edu.cn) Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China;Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2008

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Abstract

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.