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The λ-average value and the fuzzy expectation of a fuzzy random variable. (English) Zbl 0941.60030
Summary: The concepts of fuzzy random variable, and the associated fuzzy expected value, have been introduced by M. L. Puri and D. A. Ralescu [J. Math. Anal. Appl. 114, 409-422 (1986; Zbl 0592.60004)] as an extension of measurable set-valued functions (random sets), and of the Aumann integral of these functions, respectively. On the other hand, the λ-average function has been suggested by L. M. de Campos Ibáñez and A. González Muñoz [Fuzzy Sets Syst. 29, No. 2, 145-153 (1989; Zbl 0672.90001)] as an appropriate function to rank fuzzy numbers. We are going to analyze some useful properties concerning the λ-average value of the expectation of a fuzzy random variable, and some practical implications of these properties are also commented on.
60D05Geometric probability and stochastic geometry
60A99Foundations of probability theory