On fuzzy Bayesian inference

Abstract The paper combines methods from Bayesian statistics with ideas from fuzzy set theory to generalize Bayesian methods both for samples of fuzzy data and for prior distributions with non-precise parameters. Applying the principle of propagation of fuzziness we introduce a fuzzy valued likelihood function, Bayes' theorem for both fuzzy data and fuzzy priors, a fuzzy Bayes' estimator, fuzzy predictive densities and distributions, and fuzzy H.P.D.-regions.