Bayesian inference based upon fuzzy events

The purpose of the paper is to show that, contrary to the claims of some probabilists of the Bayesian trade, probability theory relates to fuzzy set theory in a similar way as it relates to classical set theory. Examining the well known proof by R.T. Cox (1946), whose aim is to justify the rules of classical Bayesian inference, we point to some weaknesses of the proof and show that it does not exclude the possibility of alternative rules of Bayesian inference based on fuzzy events.