Efficient reasoning for uncertainty management in expert systems

Bayesian statistics assigns basic probabilities to singletons. By assigning basic probabilities to subsets, the Dempster Shafer theory significantly generalizes Bayesian statistics to represent evidence and to develop evidential reasoning. But the computation of probabilities on subsets is exponentially complex. J.A. Barnett (1981) presented a linear time computational technique. G. Shafer and R. Logan (1987) gave an algorithm for the exact implementation of Dempster Shafer´s rule in the case of hierarchical evidence. Earlier, we improved the algorithm (for the second propagation) to make the algorithm more attractive for embodiment in working systems (J.W. Guan and D.A. Bell, 1991). The paper compliments that earlier paper by giving details and examples of our improved algorithm