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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.

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