The validity of Dempster-Shafer belief functions

The validity of Dempster-Shafer belief functions

This reply to papers by Pearl and Shafer focuses on two issues underlying the debate on the validity o f using Dempster-Shafer theory, namely the requirement of a process-independent semantics and the a priori need for multiple uncertainty calculi. Pearl shows deficiencies of Dempster-Shafer theory in dealing with several instances o f commonsense reasoning in a process-independent manner. Alth...

Classic Works of the Dempster-Shafer Theory of Belief Functions

Independence, Conditionality and Structure of Dempster-Shafer Belief Functions

Several approaches of structuring (factorization, decomposition) of Dempster-Shafer joint belief functions from literature are reviewed with special emphasis on their capability to capture independence from the point of view of the claim that belief functions generalize bayes notion of probability. It is demonstrated that Zhu and Lee's {Zhu:93} logical networks and Smets' {Smets:93} directed ac...

Fast-Division Architecture for Dempster-Shafer Belief Functions

Given a number of Dempster-Shafer belief functions there are different architectures which allow to do a compilation of the given knowledge. These architectures are the Shenoy-Shafer Architecture, the Lauritzen-Spiegelhalter Architecture and the HUGIN Architecture. We propose a new architecture called ”Fast-Division Architecture” which is similar to the former two. But there are two important a...

An Alternative to Outward Propagation for Dempster-Shafer Belief Functions

Given several Dempster-Shafer belief functions, the framework of valuation networks describes an efficient method for computing the marginal of the combined belief function. The computation is based on a message passing scheme in a Markov tree where after the selection of a root node an inward and an outward propagation can be distinguished. In this paper it will be shown that outward propagati...