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

$\lambda $-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

$\lambda $-average value of the expectation of a fuzzy random variable, and some practical implications of these properties are also commented on.