Maxitive functions with respect to general orders
Statistics Theory
2025-03-05 v3 Statistics Theory
Abstract
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 functions. 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.
Cite
@article{arxiv.2403.06613,
title = {Maxitive functions with respect to general orders},
author = {M. Kupper and J. M. Zapata},
journal= {arXiv preprint arXiv:2403.06613},
year = {2025}
}