Fuzzy Bayesian inference

In standard Bayesian inference, a-priori distributions are assumed to be classical probability distributions. This is a topic of critical discussions because, in reality, a-priori information is usually more or less non-precise, i.e. fuzzy. Hence, a more general form of a-priori distributions (so-called fuzzy a-priori densities) is more suitable to model such a-priori information. Moreover, data from continuous quantities are always more or less fuzzy. As a result, Bayes' theorem has to be generalized to capture this situation. This is possible and will be explained in the paper. In addition, the concepts of HPD-regions and predictive distributions are generalized to the situation of fuzzy a-priori information and fuzzy data.