Advances in the Dempster-Shafer theory of evidence
Advances in the Dempster-Shafer theory of evidence
On the evidence inference theory
Information Sciences: an International Journal
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Combining ambiguous evidence with respect to ambiguous a priori knowledge. I. Boolean logic
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Information combination operators for data fusion: a comparative review with classification
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
The modified Dempster-Shafer approach to classification
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Target identification based on the transferable belief model interpretation of dempster-shafer model
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Generalization of the Dempster-Shafer theory: a fuzzy-valued measure
IEEE Transactions on Fuzzy Systems
Connectionist-based Dempster-Shafer evidential reasoning for data fusion
IEEE Transactions on Neural Networks
A skin detection approach based on the Dempster--Shafer theory of evidence
International Journal of Approximate Reasoning
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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.