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Fuzzy random variables. (English) Zbl 0592.60004
In a previous paper [ibid. 91, 552-558 (1983; Zbl 0528.54009)] the authors defined differentials for a fuzzy valued function. In this clearly thought and well-written paper they define an integral, or an expected value, of a fuzzy valued random variable. The definition is based on the integral of a set-valued function. The authors give an existence theorem for the expected value and derive the Lebesgue dominated convergence theorem for fuzzy random variables.
A different kind of expected value is defined by H. Kwakernaak [Inf. Sci. 15, 1-29 (1978; Zbl 0438.60004)] and W. E. Stein and K. Talati [Fuzzy Sets Syst. 6, 271-283 (1981; Zbl 0467.60005)].
Reviewer: O.Kaleva

MSC:
60A99 Foundations of probability theory
60D05 Geometric probability and stochastic geometry
28B99 Set functions, measures and integrals with values in abstract spaces
03E72 Theory of fuzzy sets, etc.
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