A fuzzy decision problem based on the generalized Neyman-Pearson criterion

Abstract A reformulation of the generalized Neyman-Pearson lemma is attempted using fuzzy set theory. Based on the result, we define a locally optimum (or locally most powerful) fuzzy test and derive the locally optimum fuzzy test function. As a practical application of the locally optimum fuzzy test, detection of weak deterministic signals corrupted by purely-additive noise is considered, which is an important problem in statistical signal processing. Comparisons between the locally optimum and the locally optimum fuzzy tests are also made in the example.