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Overview on the development of fuzzy random variables. (English) Zbl 1108.60006
The paper presents a brief overview on probability theory and statistics for fuzzy random variables (FRV). Two main approaches are discussed: the Kwakernaak approach where an FRV is considered as a fuzzy perception of a real random variable, and the Puri-Ralescu approach where an FRV is considered as a variable with fuzzy set-valued outcomes. From the large number of special results on FRV’s the authors discuss in some detail a law of large numbers, a central limit theorem and a special result on testing hypotheses for the Aumann expectation.
60B99Probability theory on general structures
03E72Fuzzy set theory
26E50Fuzzy real analysis
60D05Geometric probability and stochastic geometry