On Fuzzy Bayesian Inference

Abstract

Bayesian inference deals with a-priori information in statistical analysis. However, usually Bayesians assume that all kind of uncertainty can be modeled by probability. Unfortunately, this is not always true due to how uncertainties are defined. The uncertainty of measurement results of continuous quantities differs from probabilistic uncertainty. Individual measurement results also contain another kind of uncertainty, which is called fuzziness. The combination of fuzziness and stochastic uncertainty calls for a generalization of Bayesian inference, i.e. fuzzy Bayesian inference. This chapter explains the generalized Bayes’ theorem in handling fuzzy a-priori information and fuzzy data.