Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As mul-tidimensional possibilistic models have been studied for several years, the demand for analogous tools in possibility theory seems to be 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 prob-abilistic framework. First we recall semi-graphoid properties of conditional possibilis-tic independence, parameterized by a contin-uous t-norm, and find sufficient conditions for a class of Archimedean t-norms to have the graphoid property. Then we introduce Markov properties and factorization of possi-bility distributions (again parameterized by a continuous t-norm) and find the relation-ships between them. These results are ac-companied by a number of counterexamples, which show that the assumptions of specific theorems are substantial.
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