On the Orthogonal Projection of a Belief Function
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
A Generalization of the Pignistic Transform for Partial Bet
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
The Intersection Probability and Its Properties
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Credal semantics of Bayesian transformations in terms of probability intervals
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Three alternative combinatorial formulations of the theory of evidence
Intelligent Data Analysis - Artificial Intelligence
Geometry of relative plausibility and relative belief of singletons
Annals of Mathematics and Artificial Intelligence
Belief functions combination without the assumption of independence of the information sources
International Journal of Approximate Reasoning
On consistent approximations of belief functions in the mass space
ECSQARU'11 Proceedings of the 11th 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
Distances in evidence theory: Comprehensive survey and generalizations
International Journal of Approximate Reasoning
On the relative belief transform
International Journal of Approximate Reasoning
How to preserve the conflict as an alarm in the combination of belief functions?
Decision Support Systems
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In this paper, we analyze from a geometric perspective the meaningful relations taking place between belief and probability functions in the framework of the geometric approach to the theory of evidence. Starting from the case of binary domains, we identify and study three major geometric entities relating a generic belief function (b.f.) to the set of probabilities P: 1) the dual line connecting belief and plausibility functions; 2) the orthogonal complement of P; and 3) the simplex of consistent probabilities. Each of them is in turn associated with a different probability measure that depends on the original b.f. We focus in particular on the geometry and properties of the orthogonal projection of a b.f. onto P and its intersection probability, provide their interpretations in terms of degrees of belief, and discuss their behavior with respect to affine combination.