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Fundamentals of fuzzy probability theory. (English) Zbl 0872.60003
Summary: The canonical classical extension of quantum mechanics studied recently by E. G. Beltrametti and the author [J. Phys. A, Math. Gen. 28, No. 12, 3329-3343 (1995; Zbl 0859.46049) and ibid. (to appear)] 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.

MSC:
60A99 Foundations of probability theory
81P20 Stochastic mechanics (including stochastic electrodynamics)
03E72 Theory of fuzzy sets, etc.
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