Inference in directed evidential networks based on the transferable belief model

Inference algorithms in directed evidential networks (DEVN) obtain their efficiency by making use of the represented independencies between variables in the model. This can be done using the disjunctive rule of combination (DRC) and the generalized Bayesian theorem (GBT), both proposed by Smets [Ph. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning 9 (1993) 1–35]. These rules make possible the use of conditional belief functions for reasoning in directed evidential networks, avoiding the computations of joint belief function on the product space. In this paper, new algorithms based on these two rules are proposed for the propagation of belief functions in singly and multiply directed evidential networks.