Effects of the shape of fuzzy membership functions on fuzzy inference

Abstract

The paper investigates the effect of the shapes of membership functions on a fuzzy inference system to detect a signal in a noisy waveform. The detector, which uses values of features derived from the waveform, can classify the waveform as signal or noise, or it can be uncertain, that is, it can decide that no conclusion regarding presence or absence of a signal can be drawn. Piecewise linear membership functions were used, and analytical expressions for the dependence of classification on the membership function parameters were obtained. These results were verified in a simulation, using sensory evoked potential signals and simulated noise. The performance of the system was compared to a Bayesian maximum likelihood detector. By varying membership function parameters, the fuzzy detector can be made comparable to the Bayesian detector or it can almost completely eliminate errors, at the cost of a large number of uncertain classifications.