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Some Inequalities Combining Rough and Random Information

School of Management, Shanghai University, Shanghai 200444, China
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Entropy 2018, 20(3), 211; https://doi.org/10.3390/e20030211
Received: 1 February 2018 / Revised: 18 March 2018 / Accepted: 18 March 2018 / Published: 20 March 2018
(This article belongs to the Special Issue Entropy and Information Inequalities)
Rough random theory, generally applied to statistics, decision-making, and so on, is an extension of rough set theory and probability theory, in which a rough random variable is described as a random variable taking “rough variable” values. In order to extend and enrich the research area of rough random theory, in this paper, the well-known probabilistic inequalities (Markov inequality, Chebyshev inequality, Holder’s inequality, Minkowski inequality and Jensen’s inequality) are proven for rough random variables, which gives a firm theoretical support to the further development of rough random theory. Besides, considering that the critical values always act as a vital tool in engineering, science and other application fields, some significant properties of the critical values of rough random variables involving the continuity and the monotonicity are investigated deeply to provide a novel analytical approach for dealing with the rough random optimization problems. View Full-Text
Keywords: rough random variable; inequalities; critical values rough random variable; inequalities; critical values
MDPI and ACS Style

Gu, Y.; Zhang, Q.; Yu, L. Some Inequalities Combining Rough and Random Information. Entropy 2018, 20, 211.

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