Belief combination and propagation in a lattice-structured interference network

Belief propagation and belief combination procedures based on the Dempster-Shafer belief function for inference in rule-based systems is proposed. The belief combination procedure yields results identical to those of Dempster´s rule when pieces of evidence are independent. Dempster´s rule is shown to be nonrobust for combining evidence with a high degree of conflict. The cause of the nonrobustness is discussed, and an alternative belief combination procedure to remedy the deficiency is proposed. Although the proposed procedure yields results that are dependent on the interpretations of the rule, it is shown to be an interpolation between total ignorance and the uncertainty associated with the rule regardless of the interpretations. When the rule interpretation yields an associative belief propagation procedure, a corresponding chaining syllogism for it can be derived. The proposed inference procedures are applied to a lattice-structured inference network