(A) fuzzy set theoretic reformulation of classical decision criteria and signal detection

Abstract

In this thesis, fuzzy statistical techniques are introduced into the optimum signal detection problems. For the hypotheses testing with fuzzy information we reformulate conventional decision criteria based on the fuzzy set theory and show that conventional decision criteria is also applicable in fuzzy signal detection area. The likelihood ratio for fuzzy detection of known signals is obtained. As a special case of the fuzzy signal detector, a fuzzy set theoretic approach to sign detection of known signals is considered. The test statistic of the fuzzy sign detector for known signals is obtained. Some properties of the fuzzy sign nonlinearity, which constitutes the fuzzy sign detectors, are also described. Finally the performance characteristics of the fuzzy sign detector are investigated and compared to those of the crisp sign detector.