Belief functions versus probability functions
Proceedings of the 2nd International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems on Uncertainty and intelligent systems
A computationally efficient approximation of Dempster-Shafer theory
International Journal of Man-Machine Studies
Approximations for efficient computation in the theory of evidence
Artificial Intelligence
Artificial Intelligence
Inner and outer approximation of belief structures using a hierarchical clustering approach
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Constructing the Pignistic Probability Function in a Context of Uncertainty
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
A Comparison of Bayesian and Belief Function Reasoning
Information Systems Frontiers
Updating beliefs with incomplete observations
Artificial Intelligence
Decision making in the TBM: the necessity of the pignistic transformation
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Approximations for decision making in the Dempster-Shafer theory of evidence
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
A Geometric Approach to the Theory of Evidence
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Two New Bayesian Approximations of Belief Functions Based on Convex Geometry
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Transferable belief model for decision making in the valuation-based systems
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
The Intersection Probability and Its Properties
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Towards an alarm for opposition conflict in a conjunctive combination of belief functions
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
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In this paper, we propose a credal representation of the interval probability associated with a belief function (b.f.) and show how it relates to several classical Bayesian transformations of b.f.'s through the notion of "focus" of a pair of simplices. While a b.f. corresponds to a polytope of probabilities consistent with it, the related interval probability is geometrically represented by a pair of upper and lower simplices. Starting from the interpretation of the pignistic function as the center of mass of the credal set of consistent probabilities, we prove that the relative belief of singletons, the relative plausibility of singletons, and the intersection probability can all be described as the foci of different pairs of simplices in the region of all probability measures. The formulation of frameworks similar to the transferable beliefmodel for such Bayesian transformations appears then at hand.