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Jensen's inequalities for set-valued and fuzzy set-valued functions

机译：Jensen对集合和模糊集合函数的不等式

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Being an important part of classical analysis, Jensen's inequality has drawn much attention recently. Due to its generality, the inequality based on non-additive integrals appears in many forms, such as Sugeno integrals, Choquet integrals and pseudo-integrals. As a well-known generalization of classical one, the set-valued analysis is frequently applied to the research of mathematical economy, control theory and so on. Thus, it is of great necessity to generalize the set-valued case. Motivated by the pioneering work of Costa's Jensen's fuzzy-interval-valued inequality and Strboja et al.'s Jensen's set-valued inequality based on Aumann integrals and pseudo-integrals respectively, this paper focuses particularly on proving certain kinds of Jensen's set-valued inequalities and fuzzy set-valued inequalities. These inequalities consist of two families: the related convex (or concave) function is a set-valued or fuzzy set-valued function and the integrand is a real-valued function; the related convex (or concave) function is a real-valued function and the integrand is a set-valued or fuzzy set-valued function. Particularly, Jensen's interval-valued and fuzzy-intervalvalued inequalities, including Costa's, are obtained as corollaries. (C) 2020 Elsevier B.V. All rights reserved.
机译：作为古典分析的重要组成部分，Jensen的不平等最近引起了很多关注。由于其一般性，基于非添加剂积分的不等式出现了许多形式，例如Sugeno积分，Choquet积分和伪积分。作为古典众所周知的众所周知的，设定值分析经常应用于数学经济，控制理论等的研究。因此，概括了所设定的案例是巨大的需要。 Costa的模糊间隔不等式和Strboja等人的开创性工作是基于Aumann积分和伪积分的Jensen的集价值不等式，特别是尤其是证明某些纪仁的集合价值不等式和模糊的设定值不等式。这些不等式由两个家庭组成：相关凸（或凹形）函数是一个集价值或模糊的设定值函数，Integrand是实值的函数;相关凸（或凹形）函数是一个真实值的函数，Integrand是一个设定值或模糊的设定值函数。特别是，Jensen的间隔值和模糊过度的不等式，包括哥斯达人，作为推论。 （c）2020 Elsevier B.v.保留所有权利。

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