主观期望效用理论对人的决策的描述性效度一直受到怀疑，越来越多的实证研究表明与主观期望效用理论的公理相背离。
The descriptive validity of subjective expected utility theory has been doubted all the time, more and more empirical research violates from the axioms of subjective expected utility theory.
提出了灰效用函数的概念，给出了灰效用函数存在的公理体系。
The concept of the grey utility function is proposed and the axiomatics for the existence of grey utility function are given.
作者提出一组有理数概率下效用函数存在的公理，并证明该公理体系下的效用表示定理。
This paper puts forward a set of axioms and proves the existence and uniqueness of utility function with rational probabilities on the set of axioms.
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