Teacher:In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Teacher: Now, understand the problem? Solve this instance: Conditional independence and Markov prop erties 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.
Student:
Conditional Independence and Markov Properties in Possibility Theory