论文标题
与较低概率的信用集相对应的普通锥
Normal cones corresponding to credal sets of lower probabilities
论文作者
论文摘要
信用集是描述概率不确定性的最重要模型之一。它们通常是作为概率模型的凸组集合，与相干较低的预防或更具体的模型（例如相干较低的概率或概率间隔）相兼容。在有限的空间中，信用集通常采用凸多型的形式。凸多属的许多特性可以从其正常锥体中得出，这些锥形成了称为正常风扇的多面体复合物。我们分析了对应于相干较低概率的信用集的正常锥体的特性。对于两种重要类的相干较低概率，2-单酮较低的概率和概率间隔，我们提供了对正常风扇结构的详细描述。这些结构与信用集的极端点的结构有关。为了得出我们的主要结果，我们为凸多面体的三角态粉丝及其邻接结构提供了一些普遍的结果。
Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific models such as coherent lower probabilities or probability intervals. In finite spaces, credal sets usually take the form of convex polytopes. Many properties of convex polytopes can be derived from their normal cones, which form polyhedral complexes called normal fans. We analyze the properties of normal cones corresponding to credal sets of coherent lower probabilities. For two important classes of coherent lower probabilities, 2-monotone lower probabilities and probability intervals, we provide a detailed description of the normal fan structure. These structures are related to the structure of the extreme points of the credal sets. To arrive at our main results, we provide some general results on triangulated normal fans of convex polyhedra and their adjacency structure.
