Uncertainty, fuzzy logic, and signal processing

In this paper we focus on model-based statistical signal processing and how some problems that are associated with it can be solved using fuzzy logic. We explain how uncertainty (which is prevalent in statistical signal proce ssing applications) can be handled within the framework of fuzzy logic. Typ e-1 singleton and non-singleton fuzzy logic systems (FLSs) are reviewed. Ty pe-2 FLSs, which are relatively new, and are very appropriate for signal pr ocessing problems, because they can handle linguistic and numerical uncerta inties, are overviewed in some detail. The output of a type-2 FLS is a type -2 fuzzy set. Using a new operation called type-reduction, the type-2 set c an be reduced to a type-1 set - the type-reduced set - which plays the role of a confidence interval for linguistic uncertainties. No such result can be obtained for a type-1 FLS. We demonstrate, by means of examples, that a type-2 FLS can outperform a type-1 FLS for one-step prediction of a Mackey- Glass chaotic time series whose measurements are corrupted by additive nois e, and equalization of a nonlinear time-varying channel. (C) 2000 Elsevier Science B.V. All rights reserved.