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：在决策过程中，极大函数用于最坏情况和最佳情况的评估。极大性产生了一种丰富的结构，该结构在逐点序的背景下已得到充分研究。本文研究了关于一般预序的极大性，并为这类泛函提供了表示定理。相关结果通过文献中的不同随机序进行了说明，包括通常随机序、递增凸/凹序以及离散序。