标题： 关于单调性和共单调最大泛函的单调性 显示英文标题

标题： On monotonicity of comonotonically maxitive functional

摘要： 共单调极大性性质在基于最大运算的模糊积分特征化中经常出现。在某些特殊情况下，共单调极大性意味着泛函的单调性。T. Radul (2023)提出了这个蕴涵是否在一般情况下成立的问题。该文证明了这个蕴涵对于有限紧集是有效的。本文给出了这个问题的一般情况下的否定回答，并讨论了需要额外施加的性质以确保这个蕴涵成立。 显示英文摘要

摘要： The comonotonic maxitivity property of functionals frequently appears in the characterization of fuzzy integrals based on the maximum operation. In some special cases, comonotonic maxitivity implies monotonicity of functionals. The question of whether this implication holds in general was posed by T. Radul (2023). It was shown in that paper that the implication is valid for finite compacta. In this article, we provide a negative answer to the general problem and discuss additional properties that need to be imposed to ensure the implication holds.