关于共单调极大化泛函的函子
On the functor of comonotonically maxitive functionals
AI总结：
本文引入保持共单调函数最大值和常数加法的泛函函子，证明其与容量函子同构（通过模糊极大加积分），该结果是里斯定理的幂等类似物。
摘要：
我们引入了一个保持共单调函数最大值和常数加法的泛函函子。该函子是保序泛函函子的子函子，且包含幂等测度函子作为其子函子。本文的主要目的是证明该函子与容量函子同构。我们利用模糊极大加积分建立了这种同构关系。事实上，我们可将该结果视为里斯定理的幂等类似物，后者涉及σ-可加正则博雷尔测度集与线性正定泛函集之间的对应关系。
英文摘要：
We introduce a functor of functionals which preserve maximum of comonotone functions and addition of constants. This functor is a subfunctor of the functor of order-preserving functionals and contains the idempotent measure functor as subfunctor. The main aim of this paper is to show that this functor is isomorphic to the capacity functor. We establish such isomorphism using the fuzzy max-plus integral. In fact, we can consider this result as an idempotent analogue of Riesz Theorem about a correspondence between the set of $σ$-additive regular Borel measures and the set of linear positively defined functionals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
