Metric spaces of fuzzy variables

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• 作者：Wansheng Tang ; Xiaozhong Li ; Ruiqing Zhao
• 关键词：Fuzzy variable ; Credibility theory ; Distances ; Metric space ; Fuzzy random variable
• 刊名：Computers and Industrial Engineering
• 出版年：2009
• 出版时间：November 2009
• 年：2009
• 卷：57
• 期：4
• 页码：1268-1273
• 全文大小：210 K

文摘

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.