On the propagation of fuzziness of data

The object of this paper is to discuss how fuzziness of data is propagated when statistical inference for samples of non-precise data is carried out.

The method of propagation of fuzziness as introduced by Schnatter (1989) is reviewed. This method may be applied to any statistical method which leads to a result that may be expressed as a function f(x1,...,xn) of the data x1,...,xn. It is outlined that practical application of this method is equal to determining the images of a family of compact subsets of the sample space under the function f(·).

An illustrative example from environmetrics is discussed. The general approach is used to formulate a fuzzy sample mean and a fuzzy valued empirical distribution function.