Conditional Independence and Markov Properties in Possibility Theory
  Conditional independence and Markov properties are powerful tools allowing
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 to be quite natural. This paper is intended to be a promotion of de
Cooman's measure-theoretic approcah to possibility theory, as this approach
allows us to find analogies to many important results obtained in probabilistic
framework. First, we recall semi-graphoid properties of conditional
possibilistic independence, parameterized by a continuous 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 possibility
distrubtions (again parameterized by a continuous t-norm) and find the
relationships between them. These results are accompanied by a number of
conterexamples, which show that the assumptions of specific theorems are
substantial.
