On the relative belief transform

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• 作者：Fabio Cuzzolin ^{fabio.cuzzolin@brookes.ac.uk}
• 关键词：Theory of evidence ; Probability transformation ; Relative plausibility and belief of singletons ; Duality ; Dempster&rsquo ; s combination ; Commutativity
• 刊名：International Journal of Approximate Reasoning
• 出版年：2012
• 期刊代码：76_0888613x
• 类别：et
• 出版时间：July, 2012
• 卷：53
• 期：5
• 页码：786-804
• 文件大小：600 K

摘要

In this paper we discuss the semantics and properties of the relative belief transform, a probability transformation of belief functions closely related to the classical plausibility transform. We discuss its rationale in both the probability-bound and Shafer鈥檚 interpretations of belief functions. Even though the resulting probability (as it is the case for the plausibility transform) is not consistent with the original belief function, an interesting rationale in terms of optimal strategies in a non-cooperative game can be given in the probability-bound interpretation to both relative belief and plausibility of singletons. On the other hand, we prove that relative belief commutes with Dempster鈥檚 orthogonal sum, meets a number of properties which are the duals of those met by the relative plausibility of singletons, and commutes with convex closure in a similar way to Dempster鈥檚 rule. This supports the argument that relative plausibility and belief transform are indeed naturally associated with the D-S framework, and highlights a classification of probability transformations into two families, according to the operator they relate to. Finally, we point out that relative belief is only a member of a class of 鈥渞elative mass鈥?mappings, which can be interpreted as low-cost proxies for both plausibility and pignistic transforms.