[Show abstract][Hide abstract] ABSTRACT: The Dempster-Shafer theory of evidence accumulation is one of the main tools
for combining data obtained from multiple sources. In this paper a special case
of combination of two bodies of evidence with non-zero conflict coefficient is
considered. It is shown that application of the Dempster-Shafer rule of
combination in this case leads to an evaluation of masses of the combined
bodies that is different from the evaluation of the corresponding probabilities
obtained by application of the law of total probability. This finding supports
the view that probabilistic interpretation of results of the Dempster-Shafer
analysis in the general case is not appropriate.
[Show abstract][Hide abstract] ABSTRACT: Dempster-Shafer theory is one of the main tools for reasoning about data obtained from multiple sources, subject to uncertain information. In this work abstract algebraic properties of the Dempster-Shafer set of mass assignments are investigated and compared with the properties of the Bayes set of probabilities. The Bayes set is a special case of the Dempster-Shafer set, where all non-singleton masses are fixed at zero. The language of semigroups is used, as appropriate subsets of the Dempster-Shafer set, including the Bayes set and the singleton Dempster-Shafer set, under either a mild restriction or a slight extension, are semigroups with respect to the Dempster-Shafer evidence combination operation. These two semigroups are shown to be related by a semigroup homomorphism, with elements of the Bayes set acting as images of disjoint subsets of the Dempster-Shafer set. Subsequently, an inverse mapping from the Bayes set onto the set of these subsets is identified and a procedure for computing certain elements of these subsets, acting as subset generators, is obtained. The algebraic relationship between the Dempster-Shafer and Bayes evidence accumulation schemes revealed in the investigation elucidates the role of uncertainty in the Dempster-Shafer theory and enables direct comparison of results of the two analyses.
IEEE Transactions on Information Theory 12/2009; · 2.62 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this work we focus on the relationship between the Dempster-Shafer (DS) and Bayesian evidence accumulation. While it is accepted that the DS theory is, in a certain sense, a generalization of the probability theory, the approaches vary in several important respects, including the treatment of uncertain information and the way the evidence is combined, making direct comparison of results of the two analyses difficult. In this work we ameliorate these difficulties by proposing a mathematical framework within which the relationship between the two methods can be made precise. The findings of the investigation elucidate the role uncertainty plays in the DS theory and enable evaluation of relative fitness of the two techniques for practical data fusion scenarios.