Geometry of relative plausibility and relative belief of singletons
Geometry of relative plausibility and relative belief of singletons
复制标题
单例的相对合理性和相对信念的几何
DOI：
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发表时间：
2010
影响因子：
1.2
通讯作者：
Fabio Cuzzolin
中科院分区：
文献类型：
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作者：
Fabio Cuzzolin
对信念和概率之间相互作用的研究可以在一个几何框架中进行，在这个框架中，信念和似然函数被表示为笛卡尔空间中的简化点。信念函数的概率近似形成两个齐次群，我们称之为“仿射”和“认知”族。在这篇文章中，我们关注的是独生子女这个“认知型”家庭的相对可信性、信任度和概率的不确定性。它们根据邓普斯特组合规则的行为形成了一个连贯的概率变换集合。在这里，我们研究了它们在所有伪信任函数空间和概率单纯形中的几何，并与仿射族的几何进行了比较。我们给出了两族概率重合的充分条件。
The study of the interplay between belief and probability can be posed in a geometric framework, in which belief and plausibility functions are represented as points of simplices in a Cartesian space. Probability approximations of belief functions form two homogeneous groups, which we call “affine” and “epistemic” families. In this paper we focus on relative plausibility, belief, and uncertainty of probabilities of singletons, the “epistemic” family. They form a coherent collection of probability transformations in terms of their behavior with respect to Dempster’s rule of combination. We investigate here their geometry in both the space of all pseudo belief functions and the probability simplex, and compare it with that of the affine family. We provide sufficient conditions under which probabilities of both families coincide.