Inequalities of uncertain set with its applications. (English) Zbl 1326.46065
Summary: An uncertain set, as a generalization of an 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.
MSC:
| 46S40 | Fuzzy functional analysis |
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