The quality of consequences in a decision making problem under (severe) uncertainty must often be compared among different targets (goals, objectives) simultaneously. In addition, the evaluations of a consequence's performance under the various targets often differ in their scale of measurement, classically being either purely ordinal or perfectly cardinal. In this paper, we transfer recent developments from abstract decision theory with incomplete preferential and probabilistic information to this multi-target setting and show how -- by exploiting the (potentially) partial cardinal and partial probabilistic information -- more informative orders for comparing decisions can be given than the Pareto order. We discuss some interesting properties of the proposed orders between decision options and show how they can be concretely computed by linear optimization. We conclude the paper by demonstrating our framework in an artificial (but quite real-world) example in the context of comparing algorithms under different performance measures.
翻译:在(严重)不确定性下,决策问题的后果质量往往必须同时在不同的目标(目标、目标)之间进行比较。此外,对不同目标下的结果绩效的评价在衡量规模上往往不同,通常不是纯粹的或完全的,就是完全的;在本文件中,我们将抽象决定理论的最新发展变化与不完整的优惠和概率信息转移到这一多目标设定中,并表明如何通过利用(可能)部分基本和部分概率信息,提供比Pareto命令更多的比较决定的信息命令。我们讨论了各种决定选项之间拟议命令的一些有趣的属性,并表明如何通过线性优化具体计算这些属性。我们通过在人造(但相当真实的)框架内比较不同性措施下的算法,在人造(但相当真实的)框架内展示我们的框架。