Uncertainty, fuzzy logic, and signal processing.
type: Item
instance of: scholarly article
title: Uncertainty, fuzzy logic, and signal processing.
zbMATH Open document ID: 1034.94527
DOI: 10.1016/S0165-1684(00)00011-6
published in: Signal Processing
publication date: 2000-08-21T00:00:00Z
review text: 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 processing applications) can be handled within the framework of fuzzy logic. Type-1 singleton and non-singleton fuzzy logic systems (FLSs) are reviewed. Type-2 FLSs, which are relatively new and are very appropriate for signal processing problems because they can handle linguistic and numerical uncertainties, 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 can 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 noise, and equalization of a nonlinear time-varying channel.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 1493245
zbMATH Keywords: Uncertainty
zbMATH Keywords: Fuzzy logic
zbMATH Keywords: Type-2 fuzzy logic
zbMATH Keywords: Signal processing
zbMATH Keywords: Forecasting of time series
zbMATH Keywords: Equalization
author: Jerry M. Mendel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1493245