Abstract The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray's representation theorem for his linear utility theory for belief functions. We illustrate our representation theorem using some examples discussed in the literature, and we propose a simple model for assessing utilities based on an interval-valued pessimism index representing a decision-maker's attitude to ambiguity and indeterminacy. Finally, we compare our decision theory with those proposed by Jaffray, Smets, Dubois et al., Giang and Shenoy, and Shafer.

中文翻译：

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用于决策的区间值效用理论与 Dempster-Shafer 信念函数

摘要 本文的主要目标是描述 Dempster-Shafer 信念函数彩票的公理效用理论。所使用的公理框架类似于 Luce 和 Raiffa 所描述的 von Neumann-Morgenstern 的概率彩票效用理论。与概率情况不同，我们的公理框架导致区间值效用，因此，导致所有信念函数彩票的集合上的部分（不完整）偏好顺序。如果我们使用的信念函数参考彩票是贝叶斯信念函数，那么我们的表示定理与 Jaffray 的信念函数线性效用理论的表示定理是一致的。我们使用文献中讨论的一些例子来说明我们的表示定理，我们提出了一个基于区间值悲观指数的简单模型来评估效用，该指数代表决策者对模糊性和不确定性的态度。最后，我们将我们的决策理论与 Jaffray、Smets、Dubois 等人、Giang 和 Shenoy 以及 Shafer 提出的决策理论进行比较。