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Markov Properties and Factorization of Possibility Distributions

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Abstract

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.

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Authors and Affiliations

  1. Laboratory for Intelligent Systems, University of Economics, Prague and Institute of Information Theory and Automation, Academy of Sciences, Czech Republic

    Jiřina Vejnarová

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  1. Jiřina Vejnarová
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Vejnarová, J. Markov Properties and Factorization of Possibility Distributions. Annals of Mathematics and Artificial Intelligence 35, 357–377 (2002). https://doi.org/10.1023/A:1014568208202

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