On the Credal Structure of Consistent Probabilities
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
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
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
An Evidential Measure of Risk in Evidential Markov Chains
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
On generalized fuzzy belief functions in infinite spaces
IEEE Transactions on Fuzzy Systems
The geometry of consonant belief functions: Simplicial complexes of necessity measures
Fuzzy Sets and Systems
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
Dampster-Shafer evidence theory based multi-characteristics fusion for clustering evaluation
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
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
Distances in evidence theory: Comprehensive survey and generalizations
International Journal of Approximate Reasoning
On the relative belief transform
International Journal of Approximate Reasoning
A proof for the positive definiteness of the Jaccard index matrix
International Journal of Approximate Reasoning
Integrating textual analysis and evidential reasoning for decision making in Engineering design
Knowledge-Based Systems
Information-based dissimilarity assessment in Dempster-Shafer theory
Knowledge-Based Systems
Engineering Applications of Artificial Intelligence
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In this paper, we propose a geometric approach to the theory of evidence based on convex geometric interpretations of its two key notions of belief function (b.f.) and Dempster's sum. On one side, we analyze the geometry of b.f.'s as points of a polytope in the Cartesian space called belief space, and discuss the intimate relationship between basic probability assignment and convex combination. On the other side, we study the global geometry of Dempster's rule by describing its action on those convex combinations. By proving that Dempster's sum and convex closure commute, we are able to depict the geometric structure of conditional subspaces, i.e., sets of b.f.'s conditioned by a given function b. Natural applications of these geometric methods to classical problems such as probabilistic approximation and canonical decomposition are outlined.