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Inequalities and mathematical properties of uncertain variables. (English) Zbl 1254.28020
Summary: Uncertain variables are measurable functions from uncertainty spaces to the set of real numbers. In this paper, some important inequalities of uncertain variables, for example, extension of Jensen’s inequality, Liapounov’s inequality, and refined Markov inequalities are presented. In addition, some mathematical properties of uncertain variables are also given and proven.
MSC:
28E10Fuzzy measure theory
60E15Inequalities in probability theory; stochastic orderings
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