Inference in Possibilistic Hypergraphs

In order to obivate soundness problems in the local treatment of uncertainty in knowledge-based systems, it has been recently proposed to represent dependencies by means of hypergraphs and Markov trees. It has been shown that a unified algorithmic treatment of uncertainties via local propagation is possible on such structures, both for belief functions and Bayesian probabilities, while preserving the soundness and the completeness of the obtained results. This paper points out that the same analysis applies to approximate reasoning based on possibility theory, and discusses the usefulness of the idempotence property for combining possibility distributions, a property not satisfied in probabilistic reasoning. The second part analyzes a previously proposed technique for handling dependencies, by relating it to the hypergraph approach.