Fundamentals of fuzzy probability theory

The canonical classical extension of quantum mechanics studied recently by E. G. Beltrametti and S. Bugajski opens a new way toward generalizing the standard probability theory. The emerging fuzzy probability theory is able to give a full account of both classical and quantal probabilities, and—like the standard probability theory—could be of universal use, far outside the borders of physics. A specific feature of this hypothetical theory of probability is its mixed, classical-quanta character: classical as well as quantal random variables are described on an equal footing in a unified framework. Some new features of the fuzzy probability theory are shown on simple examples.