Conditioning in possibility theory with strict order norms
Fuzzy Sets and Systems
Independence concepts in possibility theory: part I
Fuzzy Sets and Systems
A theoretical framework for possibilistic independence in a weakly ordered setting
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
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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 approach 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 distributions (again parameterized by a continuous t-norm) and find the relationships between them. These results are accompanied by a number of counterexamples, which show that the assumptions of specific theorems are substantial.