Determining the parameters of statistical tests by fuzzy constraints

In this paper an approach is presented how to determine the parameters of statistical tests by means of fuzzy constraints on the probabilities of the errors of type I and of type II and on the sample size; here the case of single sampling is considered. A general upper bound for the sample size of an optimal test is derived. Furthermore, the approach is illustrated by two applications: the determination of an optimal one-sided normal test and the determination of an optimal test on a fraction particularly important in acceptance sampling.