Inequalities of uncertain set with its applications

Journal of inequalities and applications

Yufu Ning¹ 

关键词: uncertain set;    membership function;    inequality;    uncertainty theory;   

DOI  :  10.1186/1029-242X-2014-169

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

An uncertain set, as a generalization of the uncertain variable, is a set-valued function on an uncertainty space. It provides theoretical foundations for uncertain inference and uncertain logic. This paper aims at providing some inequalities in the framework of uncertain set theory, including the Markov inequality, the Chebyshev inequality, the Jensen inequality, the Hölder inequality, and the Minkowski inequality. In addition, this paper applies these inequalities to the area of incomplete uncertain knowledge representation.

【 授权许可】

CC BY