Directed belief networks

摘要

In this paper, we present directed belief networks when uncertainty is expressed inform of belief functions. For this purpose, we explain how to represent belief function in directed acyclic graphs (DAGs). We suppose that the networks we are working with do not have loops. In order to evaluate these belief networks, we apply the disjunctive rule of combination and the generalised Bayesian theorem (Smets [1993J). Based on the work of Cano et al. [1993] in which they have presented an axiomatic framework for propagating valuations in directed acyclic graph, we show how the belief functions theory fits in this framework. Then, we present a propagation algorithm in directed belief networks.