On distance between fuzzy variables

Article type: Research Article

Authors: Li, Xiang | Liu, Baoding

Affiliations: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China

Note: [] Corresponding author. E-mail: [email protected]

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.

Keywords: Fuzzy variable, distance, fuzzy random variable, random fuzzy variable

Journal: Journal of Intelligent & Fuzzy Systems, vol. 19, no. 3, pp. 197-204, 2008