Abstract 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 α and β 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 Gauß tests. Here, diagrams are given to determine the critical values in the most popular cases of α = 0.01 and α = 0.05. If, in addition, the value of β is fixed in advance the sample size of a one- or two-sided Gauß test can be obtained using supplementary graphs.