On the Dempster-Shafer evidence theory and non-hierarchical aggregation of belief structures

The Dempster´s rule of combination is a widely used technique to integrate evidence collected from different sources. In this paper, it is shown that the values of certain functions defined on a family of belief structures decrease (by scale factors depending on the degree of conflict) when the belief structures are combined according to the Dempster´s rule. Similar results also hold when an arbitrary belief structure is prioritized while computing the combination. Furthermore, the length of the belief-plausibility interval is decreased during a nonhierarchical aggregation of belief structures. Several types of inheritance networks are also proposed each of which allows considerable flexibility in the choice of prioritization