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Some Inequalities Combining Rough and Random Information

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 ra...

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Detalles Bibliográficos
Autores principales: Gu, Yujie, Zhang, Qianyu, Yu, Liying
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512726/
https://www.ncbi.nlm.nih.gov/pubmed/33265302
http://dx.doi.org/10.3390/e20030211
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author Gu, Yujie
Zhang, Qianyu
Yu, Liying
author_facet Gu, Yujie
Zhang, Qianyu
Yu, Liying
author_sort Gu, Yujie
collection PubMed
description 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.
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spelling pubmed-75127262020-11-09 Some Inequalities Combining Rough and Random Information Gu, Yujie Zhang, Qianyu Yu, Liying Entropy (Basel) Article 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. MDPI 2018-03-20 /pmc/articles/PMC7512726/ /pubmed/33265302 http://dx.doi.org/10.3390/e20030211 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Gu, Yujie
Zhang, Qianyu
Yu, Liying
Some Inequalities Combining Rough and Random Information
title Some Inequalities Combining Rough and Random Information
title_full Some Inequalities Combining Rough and Random Information
title_fullStr Some Inequalities Combining Rough and Random Information
title_full_unstemmed Some Inequalities Combining Rough and Random Information
title_short Some Inequalities Combining Rough and Random Information
title_sort some inequalities combining rough and random information
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512726/
https://www.ncbi.nlm.nih.gov/pubmed/33265302
http://dx.doi.org/10.3390/e20030211
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