一致选择函数的一种基于意愿的公理化
A Desirability-Based Axiomatisation for Coherent Choice Functions
摘要：
选择函数构成了一个简单，直接和非常普遍的数学框架，在不确定性下的选择建模。特别是，他们能够代表集值的选择，通常产生于应用决策规则不精确的概率不确定性模型。我们为他们提供了一个明确的解释，在赌博的态度，借用的想法，从理论上的套可取的赌博，我们用这种解释来获得一套基本公理。我们表明，这些公理导致一个完整的理论连贯的选择功能，其中包括一个代表性的理想赌博集，和保守的推理方法。
英文摘要：
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules to imprecise-probabilistic uncertainty models. We provide them with a clear interpretation in terms of attitudes towards gambling, borrowing ideas from the theory of sets of desirable gambles, and we use this interpretation to derive a set of basic axioms. We show that these axioms lead to a full-fledged theory of coherent choice functions, which includes a representation in terms of sets of desirable gambles, and a conservative inference method.
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