Abstract
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.
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Since the research projects given in the original manuscript have concluded, we present our new research projects. The marked expression should be replaced by the following statement: This work was supported by the National Natural Science Foundation of China (Grant No. 61073121), and the Fundamental Research Funds for the Central Universities (Grant No. 11ML65).
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Tian, J. Inequalities and mathematical properties of uncertain variables. Fuzzy Optim Decis Making 10, 357–368 (2011). https://doi.org/10.1007/s10700-011-9110-9
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DOI: https://doi.org/10.1007/s10700-011-9110-9