For many practical problems, the information concerning the system under study is often represented in two forms: one is a set of input-output data pairs, and, the other is a set of linguistic descriptions about the system, often in the form of IF-THEN fuzzy rules. Traditional system identification methods and classification methods, even including the (model-free) neural network approaches, can only utilize the input-output data pairs. This research will continue to develop general methods to combine both input-output data pairs and linguistic IF-THEN rules into signal - processing systems designs. The new direction that this research is taking is the handling of uncertainty by using fuzzification in a fuzzy logic signal processor. The nonsingleton FLSs will be applied to a variety of important signal processing problems including fuzzy classification. The objectives are to: (1) establish a measure of uncertainty for the output of a nonsingleton FLS, in accordance with estimation theory practice; (2) develop a nonsingleton FLS state estimator for nonlinear dynamical systems; (3) extend fuzzy logic classifiers to include imprecise training samples and noisy measurements, using nonsingleton FLSs; (4) extend backpropagation and orthogonal least squares parameter training procedures to nonsingleton FLSs and classifiers; (5) apply nonsingleton FLSs to the forecasting of multiple time series and to adaptive filtering problems of noise cancellation and blind equalization; and, (6) apply nonsingleton fuzzy logic classifiers to modulation classification.
