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A Lower Bound on the Differential Entropy of Log-Concave Random Vectors with Applications

Some Inequalities Combining Rough and Random Information

School of Management, Shanghai University, Shanghai 200444, China
Author to whom correspondence should be addressed.
Entropy 2018, 20(3), 211;
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.

AMA Style

Gu Y, Zhang Q, Yu L. Some Inequalities Combining Rough and Random Information. Entropy. 2018; 20(3):211.

Chicago/Turabian Style

Gu, Yujie, Qianyu Zhang, and Liying Yu. 2018. "Some Inequalities Combining Rough and Random Information" Entropy 20, no. 3: 211.

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