Effects of membership function parameters on the performance of a fuzzy signal detector

Abstract

This paper describes a signal-detection algorithm based on fuzzy logic. The detector combines evidence provided by two waveform features and explicitly considers uncertainty in the detection decision. The detector classifies waveforms including a signal, not including a signal, or being uncertain, in which case no conclusion regarding presence or absence of a signal is drawn. Piecewise linear membership functions are used, and a method to describe the membership functions in terms of two parameters is developed. The performance of the detector is compared to a Bayesian maximum likelihood detector, using brainstem auditory evoked potential signals in simulated noise, and the effects of the steepness (slope) and overlap of the membership functions on detector performance are evaluated. By varying the membership function steepness and overlap, the fuzzy detector can almost completely eliminate classification errors at the cost of a large number of uncertain classifications or it can be made to perform similarly to the Bayesian detector.