Almost Bayesian Assignments and Conditional Independence (a contribution to Dempster-Shafer theory of evidence)

In the paper we introduce a family of almost Bayesian basic assignments, which slightly extends Bayesian basic assignments. This extension incorporates all the distributions that can be created from lowdimensional Bayesian basic assignments by application of the operator of composition, and simultaneously preserves the property of Bayesian basic assignments concerning the number of focal elements: it does not exceed cardinality of the frame of discernment. The other goal of the paper is to propagate a new way of definition of conditional independence relation in D-S theory. It follows ideas of P. P. Shenoy from [7], where the author defines the notion of conditional independence for valuation-based system based on his operation of “combination”. Here we do the same but using the operator of “composition”. The notion of independence we get in this way seems to meet better the general requirements on conditional independence relation for basic assignments.