Object-oriented algorithm for combining dichotomic belief functions

Abstract

The problem of combining dichotomic belief functions over a hierarchical structure of propositions can be viewed as a problem of updating local data in objects and exchanging messages among objects. Such approach is proposed in this paper. A set of propositions is given in a hierarchical structure so that each node represents a proposition. Nodes in the same level represent disjunctive propositions. A node proposition is given by the union of its node proposition children. Evidences for and against propositions in the hierarchy are translated into dichotomic belief functions. In this form they are combined and propagated to and over nodes of the hierarchy. In this approach, each node is an object. There are three classes of objects: root, internal and external nodes. The objects can receive message, update their local data and send messages to their father and children. For each piece of evidence, the effort to combine and propagate has time complexity linearly proportional to the number of propositions and to the branch factor of the hierarchical tree.