Is it Necessary to Develop a Fuzzy Bayesian Inference ?

Abstract

In applications data used for updating a-priori information are often fuzzy. These fuzzy data are usually not described by standard Bayesian inference. Statistical analysis has to take care of this fuzzyness which can be described by fuzzy numbers. Therefore the resulting fuzzyness of a-posteriori distributions has to be modelled and an analogue of predictive distributions under fuzzyness must be developed. Moreover for a fuzzy observation it is not always possible to decide if it is a member of a certain event. This kind of uncertainty states the following question: Is additivity for the measurement of uncertainty in general valid or a generalization of probability, postulating superadditivity, necessary.