Testing fuzzy linear hypotheses in linear regression models

In this paper statistical tests with fuzzily formulated hypotheses are discussed, i.e., hypotheses H <Subscript>0</Subscript> and H <Subscript>1</Subscript> 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 H <Subscript>0</Subscript> against the omnibus alternative H <Subscript>1</Subscript>: -H <Subscript>0</Subscript>. This is completely different from the classical case of testing crisp complementary hypotheses. Copyright Springer-Verlag 2003