Overview on the development of fuzzy random variables (Q853426)

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.