In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with respect to general preorders and provide a representation theorem for such functionals. The results are illustrated for different stochastic orders in the literature, including the usual stochastic order, the increasing convex/concave order, and the dispersive order.

翻译：在决策理论中，极大性函数被用于最坏情况与最好情况的评估。极大性产生了一个丰富的结构，该结构在逐点序的背景下已得到充分研究。本文探讨了关于一般预序的极大性，并为此类泛函提供了一个表示定理。研究结果通过文献中不同的随机序进行了例证，包括通常随机序、递增凸/凹序以及分散序。