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\(\mathbb{B}\)-fuzzy probabilities. (English) Zbl 0868.03023
Summary: We treat \(\mathbb{B}\)-fuzzy probabilities in nonstandard frameworks by methods based on Boolean-valued models and especially Boolean powers. These formal methods, apart from the difficulties associated with the formal model itself, give a simple and powerful theory of fuzzy probability spaces and fuzzy random variables. Essentially everything is reduced to a transfer principle. However, one can also work using classical methods of proof. We first give the necessary background on nonstandard frameworks. Within these frameworks we develop Boolean fuzzy probabilities and fuzzy random variables.

MSC:
03E72 Theory of fuzzy sets, etc.
60B99 Probability theory on algebraic and topological structures
03H05 Nonstandard models in mathematics
03E40 Other aspects of forcing and Boolean-valued models
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