A computationally efficient approximation of Dempster-Shafer theory
International Journal of Man-Machine Studies
The nature of the unnormalized beliefs encountered in the transferable belief model
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
Mathematical foundations of evidence theory: a theory of reasoning with uncertain arguments
Mathematical models for handling partial knowledge in artificial intelligence
Uncertainty, belief, and probability
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Decision making in the TBM: the necessity of the pignistic transformation
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
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
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In this paper we introduce indeed two alternative formulations of the theory of evidence by proving that both plausibility and commonality functions share the same combinatorial structure of sum function of belief functions, and computing their Moebius inverses called basic plausibility and commonality assignments. The equivalence of the associated formulations of the ToE is mirrored by the geometric congruence of the related simplices. Applications to the probabilistic approximation problem are briefly presented.