论文标题
Archimedean选择功能：不精确决策的公理基础
Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making
论文作者
论文摘要
如果不确定性是通过概率度量建模的，则通常通过选择具有最高预期效用的选项来做出决策。如果使用不精确的概率模型，则可以通过多种方式将该决策规则推广。我们在这里着重于两个适用于一组概率度量的概括：E-加入性和最大性。他们俩都可以视为所谓选择功能的特殊实例，这是决策的一个非常普遍的数学框架。对于这两个决策规则中的每一个，我们都为选择功能提供了一组必要和充分的条件，这些函数以唯一的特征来表征该规则，从而为不准确的决策提供了与概率集的不精确决策。 Archimedean选择功能的代表定理在相干较低的预期方面取决于两个结果。
If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several ways. We here focus on two such generalisations that apply to sets of probability measures: E-admissibility and maximality. Both of them can be regarded as special instances of so-called choice functions, a very general mathematical framework for decision making. For each of these two decision rules, we provide a set of necessary and sufficient conditions on choice functions that uniquely characterises this rule, thereby providing an axiomatic foundation for imprecise decision making with sets of probabilities. A representation theorem for Archimedean choice functions in terms of coherent lower previsions lies at the basis of both results.
