Effects of membership functions on fuzzy signal detection

Fuzzy logic can be used to construct signal detection systems that, unlike Bayesian classifiers, can explicitly describe the degree of uncertainty in the detection decision. Use of piece-wise linear membership functions produced a detector with a small number (approximately 25%) of waveforms classified as uncertain and corresponding decreases in the number of waveforms correctly and incorrectly classified as signal-absent or signal-present (compared to a Bayesian detector). Detection performance was relatively insensitive to the parameters used for the membership function, as long as it was piece-wise linear. These results are in contrast to those found for continuous nonlinear membership functions. In the latter case, over 60% of the waveforms were classified as uncertain. The number of classification errors was reduced to almost zero, but performance was very sensitive to the parameters used for the membership function. In both cases, approximately one-third of the waveforms classified as uncertain were waveforms that were incorrectly classified by the Bayesian detector, and the remaining two-thirds were waveforms that were correctly classified by the Bayesian detector