The fuzzy characterizing function of the distribution of a random fuzzy number

Abstract Characterizing the distribution of random elements is valuable for different purposes. Among them, inferential conclusions about the population distribution can be drawn on the basis of the sample one. When one deals with real-valued random variables this characterization is usually made through the distribution function or other ones, like the moment-generating or the characteristic functions. In case of dealing with random elements taking on fuzzy number values, the distribution function cannot be adequately defined in terms of a total ordering since there is no universally acceptable one for fuzzy numbers. This paper introduces a characterization of the distribution of these random elements by extending the moment-generating function. Properties of this extension are examined, and the notion is illustrated by means of some examples.