Applications of Fuzzy Systems to Signal Processing

在许多实际问题中，关于系统的信息通常以两种形式表示：一种是输入输出数据对的集合，另一种是关于系统的语言描述的集合，通常以IF-THEN模糊规则的形式。 传统的系统辨识方法和分类方法，甚至包括（无模型）神经网络方法，只能利用输入输出数据对。 本研究将继续开发通用方法，将输入输出数据对和语言IF-THEN规则结合到信号处理系统设计中。 新的方向，这项研究正在采取的是不确定性的处理，使用模糊化的模糊逻辑信号处理器。 非单点FLS将被应用到各种重要的信号处理问题，包括模糊分类。 其目标是：（1）根据估计理论实践，建立非单值FLS输出的不确定性度量;（2）开发非线性动力系统的非单值FLS状态估计器;（3）使用非单值FLS，扩展模糊逻辑分类器以包括不精确的训练样本和有噪测量;（4）将反向传播和正交最小二乘参数训练过程扩展到非单点FLS和分类器;（5）将非单点FLS应用于多时间序列的预测以及噪声抵消和盲均衡的自适应滤波问题;（6）将非单点模糊逻辑分类器应用于调制分类。

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.