Testing fuzzy linear hypotheses in linear regression models

In this paper statistical tests with fuzzily forumlated hypotheses are discussed, i.e., hypotheses H0 and H1 are fuzzy sets. The classical criteria of the errors of type I and type II are generalized, and this approach is applied to the linear hypothesis in the linear regression model. A sufficient condition to control both generalized criteria simultaneously is presented even in case of testing H0 against the omnibus alternative H1: ¬H0. This is completely different from the classical case of testing crisp complementary hypotheses.