阿基米德选择函数：不精确决策的公理化基础
Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making
摘要：
如果不确定性是由概率度量建模的，则通常通过选择具有最高预期效用的选项来做出决策。如果使用一个不精确的概率模型来代替，这个决策规则可以通过几种方式来推广。在这里，我们集中在两个这样的推广，适用于概率测度集：E-容许性和极大性。它们都可以被视为所谓的选择函数的特殊实例，选择函数是一个非常通用的决策数学框架。对于这两个决策规则中的每一个，我们提供了一组选择功能的必要和充分条件，唯一的特点，这条规则，从而提供了一个公理化的基础不精确的决策与概率集。阿基米德选择函数在相干下预视方面的表示定理是在这两个结果的基础上。
英文摘要：
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.
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