On Inequalities and Critical Values of Fuzzy Random Variable

作     者：Lixing Yang Uncertain Theory Laboratory, Department of Mathematical Sciences Tsinghua University, Beijing 100084, China 

会议名称：《第二届不确定系统年会》

会议日期：2004年

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

关 键 词：Fuzzy Random Variable Expected Value Operator Chance Measure Critical Value 

摘      要：It is well-known that Holder’s inequality, Minkowski inequality, Markov inequality, Chebyshev inequality and Jensen’s inequality are important and useful results in probability theory. In this paper, in order to further discuss the mathematical properties of fuzzy random variable, the analogous inequalities for fuzzy random variable are first proved based on the chance measure and expected value operator. After that, the continuity of critical values of fuzzy random variable are also investigated. Finally, a conclusion is made in the end of this paper.