A new uncertainty measure for belief networks with applications to optimal evidential inferencing

This paper is concerned with the problem of measuring the uncertainty in a broad class of belief networks, as encountered in evidential reasoning applications. In our discussion, we give an explicit account of the networks concerned, and coin them the Dempster-Shafer (D-S) belief networks. We examine the essence and the requirement of such an uncertainty measure based on well-defined discrete event dynamical systems concepts. Furthermore, we extend the notion of entropy for the D-S belief networks in order to obtain an improved optimal dynamical observer. The significance and generality of the proposed dynamical observer of measuring uncertainty for the D-S belief networks lie in that it can serve as a performance estimator as well as a feedback for improving both the efficiency and the quality of the D-S belief network-based evidential inferencing. We demonstrate, with Monte Carlo simulation, the implementation and the effectiveness of the proposed dynamical observer in solving the problem of evidential inferencing with optimal evidence node selection.