IEEE Trans Cybern. 2016 Jan;46(1):109-22. doi: 10.1109/TCYB.2015.2395877. Epub 2015 Feb 6.
As part of the theory of belief functions, we address the problem of appraising the similarity between bodies of evidence in a relevant way using metrics. Such metrics are called evidential distances and must be computed from mathematical objects depicting the information inside bodies of evidence. Specialization matrices are such objects and, therefore, an evidential distance can be obtained by computing the norm of the difference of these matrices. Any matrix norm can be thus used to define a full metric. In this paper, we show that other matrices can be used to obtain new evidential distances. These are the α -specialization and α -generalization matrices and are closely related to the α -junctive combination rules. We prove that any L(1) norm-based distance thus defined is consistent with its corresponding α -junction. If α > 0 , these distances have in addition relevant variations induced by the poset structure of the belief function domain. Furthermore, α -junctions are meta-data dependent combination rules. The meta-data involved in α -junctions deals with the truthfulness of information sources. Consequently, the behavior of such evidential distances is analyzed in situations involving uncertain or partial meta-knowledge about information source truthfulness.
作为信任函数理论的一部分，我们使用度量标准来解决以相关方式评估证据体之间相似性的问题。这种度量标准被称为证据距离，必须从描述证据体内部信息的数学对象计算得到。专门化矩阵就是这样的对象，因此，证据距离可以通过计算这些矩阵之间的差异的范数来获得。因此，可以使用任何矩阵范数来定义完整的度量标准。在本文中，我们展示了可以使用其他矩阵来获得新的证据距离。这些是 α -专门化和 α -广义矩阵，它们与 α -合取组合规则密切相关。我们证明了由此定义的任何基于 L(1)范数的距离都与其相应的 α -合取一致。如果 α > 0 ，则这些距离由于信任函数域的偏序结构而具有相关的变化。此外，α -合取是元数据依赖的组合规则。α -合取中涉及的元数据涉及信息源真实性的可信性。因此，在涉及关于信息源真实性的不确定或部分元知识的情况下，分析了这些证据距离的行为。
