不精确概率论中的Goodman-Nguyen关系
The Goodman-Nguyen Relation within Imprecise Probability Theory
摘要：
Goodman-Nguyen关系是将蕴涵（包含）关系推广到条件事件的偏序。因此，精确的概率，它既诱导一个同意的概率排序，是一个关键的工具，在某些常见的扩展问题。大多数以前的工作涉及这种关系是关注的条件事件代数或精确的概率。我们在这里调查它的作用不精确的概率论，首先在框架内的条件事件，然后提出一个概括的古德曼-阮关系条件赌博。事实证明，这种关系诱导一致的顺序一致或C-凸条件不精确预测。在一个有条件事件的标准推理问题中，它让我们确定自然扩张以及上扩展。对于条件博弈，它在推导一些推论不等式时是有用的。
英文摘要：
The Goodman-Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain common extension problem. Most previous work involving this relation is concerned with either conditional event algebras or precise probabilities. We investigate here its role within imprecise probability theory, first in the framework of conditional events and then proposing a generalisation of the Goodman-Nguyen relation to conditional gambles. It turns out that this relation induces an agreeing ordering on coherent or C-convex conditional imprecise previsions. In a standard inferential problem with conditional events, it lets us determine the natural extension, as well as an upper extension. With conditional gambles, it is useful in deriving a number of inferential inequalities.
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