Testing fuzzy hypotheses with crisp data

In this paper an approach is presented how statistical tests originally constructed to examine crisp hypotheses can also be applied to fuzzily formulated hypotheses. In particular, criterions alpha and beta are proposed generalizing the probabilities of the errors of type I and type II, respectively. The general approach is applied to one-and two-sided GauB tests. Here, diagrams are given to determine the critical values in the most popular cases of alpha = 0.01 and alpha = 0.05. If, in addition, the value of beta is fixed in advance the sample size of a one-or two-sided GauB test can be obtained using supplementary graphs. (C) 1998 Elsevier Science B.V.