Markov properties and factorization of possibility distributions.

*(English)*Zbl 1014.68155Summary: 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 t-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 t-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.