On the Rao-Blackwell theorem for fuzzy random variables

In a previous paper, conditions have been given to compute iterated expecta tions of fuzzy random variables, irrespectively of the order of integration . In another previous paper, a generalized real-valued measure to quantify the absolute variation of a fuzzy random variable with respect to its expec ted value have been introduced and analyzed. In the present paper we combin e the conditions and generalized measure above to state an extension of the basic Rao-Blackwell Theorem. An application of this extension is carried o ut to construct a proper unbiased estimator of the expected value of a fuzz y random variable in the random sampling with replacement from a finite pop ulation.