Possibilistic Bayesian inference based on fuzzy data

Abstract

A Bayesian approach in the possibilistic environment is introduced, when the available data of the underlying statistical model are fuzzy. In this approach, based on a possibilistic model and a prior possibility distribution, the possibilistic posterior distribution is defined, when the available data are fuzzy. While the probabilistic Bayesian approach is suitable when we have stochastic uncertainty in the underlying model and available information, the proposed possibilistic Bayesian approach is proper when we come across the possibilistic uncertainty which is related to the notions of compatibility and consistency. A few numerical examples and a couple of applied examples in the field of concept learning are presented to illustrate the applicability of the proposed models.