Evidential Matrix Metrics as Distances Between Meta-Data Dependent Bodies of Evidence

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.