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
Consonant approximation of belief functions
International Journal of Approximate Reasoning
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
Coarsening Approximations of Belief Functions
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
A Comparison of Bayesian and Belief Function Reasoning
Information Systems Frontiers
On transformations of belief functions to probabilities: Research Articles
International Journal of Intelligent Systems - Uncertainty Processing
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
The Intersection Probability and Its Properties
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
The canonical decomposition of a weighted belief
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Decision making in the TBM: the necessity of the pignistic transformation
International Journal of Approximate Reasoning
Three alternative combinatorial formulations of the theory of evidence
Intelligent Data Analysis - Artificial Intelligence
Theoretical foundations for abstraction-based probabilistic planning
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
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The study of the interplay between belief and probability can be posed in a geometric framework, in which belief and plausibility functions are represented as points of simplices in a Cartesian space. Probability approximations of belief functions form two homogeneous groups, which we call "affine" and "epistemic" families. In this paper we focus on relative plausibility, belief, and uncertainty of probabilities of singletons, the "epistemic" family. They form a coherent collection of probability transformations in terms of their behavior with respect to Dempster's rule of combination. We investigate here their geometry in both the space of all pseudo belief functions and the probability simplex, and compare it with that of the affine family. We provide sufficient conditions under which probabilities of both families coincide.