对应于较低概率的置信集的Normal cones
Normal cones corresponding to credal sets of lower probabilities
摘要：
信用集是描述概率不确定性的重要模型之一。它们通常作为概率模型的凸集出现，与根据相干较低预测或更具体的模型（如相干较低概率或概率区间）提供的判断兼容。在有限空间中，信任集通常采用凸多胞体的形式。凸多胞体的许多性质都可以从它们的法锥导出，法锥形成多面体复形，称为法扇。我们分析了对应于相干下概率置信集的正规锥的性质。对于两类重要的相干下概率，2-单调下概率和概率区间，我们给出了正规扇形结构的详细描述。这些结构与置信集的极值点的结构有关。为了得到我们的主要结果，我们给出了关于凸多面体的三角剖分法扇及其邻接结构的一些一般性结果。
英文摘要：
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.
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