Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem (Q1308975)

Belief functions of evidence theory based on basic probability assignments with not necessarily zero values for the empty set are considered. The usual Dempster's rule of combination is defined from the conjunction of two pieces of evidence. In the paper a disjunctive rule of combination, i.e., based on the disjunction of two pieces of evidence, is discussed. Also, the Bayes' rule is extended by replacement of conditional probabilities by belief functions. Properties of both operations and their use for belief propagation in directed belief networks are discussed.