Possibility theory in information fusion
Résumé
Possibility theory and the body of aggregation operations from fuzzy set theory provide some tools to address the problem of merging information coming from several sources. Possibility theory is a representation framework that can model various kinds of information items: numbers, intervals, consonant random sets, special kind of probabilities families, as well as linguistic information, and uncertain formulae in logical settings. The possibilistic approach to fusion is general enough to encompass logical modes of combination (conjunctive and disjunctive) as well as fusion modes used in staisitics. The choice of a fusion mode depends on assumptions on whether all sources are reliable or not, and can be based on conflict analysis. This general framework allows to import inconsistency handling methods, inherited from logic, into numerical fusion problems. Quantified, prioritized and weighted fusion rules are described, as well as fusion inder a priori knowledge. It is shown that the possibilisitic setting is compatible with the Bayesian approach to fusion, the main difference being the presupposed existence, or not, of prior knowledge. The approach applies to sensor fusion, aggregation of expert opinions as well as the merging of databases especially in cases of poor, qualitative information.