Conditioning in possibility theory with strict order norms
Fuzzy Sets and Systems
Independence concepts in possibility theory: part I
Fuzzy Sets and Systems
Supremum preserving upper probabilities
Information Sciences: an International Journal
Conditional independence relations in possibility theory
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on models for imprecise probabilities and partial knowledge
Conditional Plausibility Measures and Bayesian Networks
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Conditional Independence and Markov Properties in Possibility Theory
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
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Markov properties and factorization are powerful tools allowing the expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several years, the demand for analogous tools in possibility theory seems quite natural. This paper is intended to be a promotion of De Cooman's measure-theoretic approach to possibility theory, as this approach allows us to find analogies to many important results obtained in a probabilistic framework.First we recall our definition of conditional possibilistic independence, parameterized by a continuous it-norm, and its properties. Then we introduce Markov properties, based on this conditional independence notion, and factorization of possibility distributions (again parameterized by a continuous it-norm) and we find the relationships between them. Our results are accompanied by a number of counterexamples, which show that the assumptions of particular theorems are substantial.