Abstract This paper presents an axiomatic framework for influence diagram computation, which allows reasoning with partially ordered values of utility. We show how an algorithm based on sequential variable elimination can be used to compute the set of maximal values of expected utility (up to an equivalence relation). Formalisms subsumed by the framework include decision making under uncertainty based on multi-objective utility, or on interval-valued utilities, as well as a more qualitative decision theory based on order of magnitude probabilities and utilities. Consequently, we also introduce the order of magnitude influence diagram to model and solve partially specified sequential decision problems when only qualitative (or imprecise) information is available.

中文翻译：

---

具有偏序偏好的影响图计算的公理化框架

摘要 本文提出了一个用于影响图计算的公理框架，它允许使用部分有序的效用值进行推理。我们展示了如何使用基于顺序变量消除的算法来计算期望效用的最大值集（直到等价关系）。该框架包含的形式主义包括基于多目标效用或区间值效用的不确定性下的决策，以及基于数量级概率和效用的更定性的决策理论。因此，当只有定性（或不精确）信息可用时，我们还引入了数量级影响图来建模和解决部分指定的顺序决策问题。