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
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International Journal of Man-Machine Studies
Perspectives on the theory and practice of belief functions
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UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
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Artificial Intelligence
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Dual Properties of the Relative Belief of Singletons
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
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IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
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IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2
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IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
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Information Sciences: an International Journal
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IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Two New Bayesian Approximations of Belief Functions Based on Convex Geometry
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Geometry of relative plausibility and relative belief of singletons
Annals of Mathematics and Artificial Intelligence
On the relative belief transform
International Journal of Approximate Reasoning
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In this paper we introduce three alternative combinatorial formulations of the theory of evidence (ToE), by proving that both plausibility and commonality functions share the structure of "sum function" with belief functions. We compute their Moebius inverses, which we call basic plausibility and commonality assignments. In the framework of the geometric approach to uncertainty measures the equivalence of the associated formulations of the ToE is mirrored by the geometric congruence of the related simplices. We can therefore describe the point-wise geometry of these sum functions in terms of rigid transformations mapping them onto each other. Combination rules can be applied to plausibility and commonality functions through their Moebius inverses, leading to interesting applications of such inverses to the probabilistic transformation problem.