Fuzzy random variables. (English) Zbl 0592.60004

Puri, Madan L.; Ralescu, Dan A.

J. Math. Anal. Appl. 114, 409-422 (1986).

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.

Keywords:

differentials for a fuzzy valued function; existence theorem for the expected value; Lebesgue dominated convergence theorem for fuzzy random variables

Citations:

Zbl 0528.54009; Zbl 0438.60004; Zbl 0467.60005

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