Metric spaces of fuzzy variables

Authors:
Wansheng Tang;Xiaozhong Li;Ruiqing Zhao
Affiliations:
Institute of Systems Engineering, Tianjin University, Tianjin 300072, China;Institute of Systems Engineering, Tianjin University, Tianjin 300072, China and College of Computer Science and Information Engineering, Tianjin University of Science and Technology, Tianjin 30022 ...;Institute of Systems Engineering, Tianjin University, Tianjin 300072, China
Venue:
Computers and Industrial Engineering
Year:
2009

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Abstract

Distance between fuzzy variables has played an important role in fuzzy theory and has been defined in many ways, for example, Hausdorff-like distance, Hamming distance and the distance based on expected value operator of fuzzy variable. This paper proposes a new kind of distances between fuzzy variables, fuzzy random variables and random fuzzy variables and these distances completely satisfy the mathematical axioms of a metric. Furthermore, a metric space of fuzzy variables is defined, the completeness of this space is proved and the properties of new distances are discussed. Finally, the distances between fuzzy vectors, fuzzy random vectors and random fuzzy vectors are also given.