Applications of Fuzzy Systems to Signal Processing

孟德尔在许多实际信号处理问题中，信息常常以两种形式表示：一种是一组输入输出数据对，通过测量一些典型输入信号的系统输出而获得；另一种是一组输入输出数据对，通过测量系统对一些典型输入信号的输出而获得。另一个是关于系统的一组语言描述，通常采用 IF-THEN 模糊规则的形式，来自非常熟悉系统行为的人类专家。本研究正在开发一种通用方法，将数字输入/输出对和语言 IF-THEN 规则结合到模糊系统理论框架内的信号处理系统设计中。 目标是： 1. 从理论上证明模糊系统的实际成功； 2. 开发使用数字和语言信息的模糊系统的综合方法； 3.将这些综合方法应用于信号处理问题，例如时间序列预测，并对这些方法进行理论性能分析。 模糊系统的优化设计方法也正在开发中，它将给定的输入输出对匹配到任意精度。

Mendel In many practical signal processing problems, information is often represented in two forms: one is a set of input-output data pairs, obtained by measuring the outputs of the system for some typical input signals; and, the other is a set of linguistic descriptions about the system, often in the form of IF-THEN fuzzy rules, from human experts who are very familiar with the behavior of the system. This research is developing a general method to combine both numerical input/output pairs and linguistic IF-THEN rules into signal processing system design within the framework of fuzzy system theory. The objectives are to: 1. theoretically justify the practical successes of fuzzy systems; 2. develop synthesis methods for fuzzy systems which use both numerical and linguistic information; and 3. apply these synthesis methods to signal processing problems, such as time-series prediction, and subject these methods to theoretical performance analyses. An optimal design method for fuzzy systems which will match given input-output pairs to arbitrary accuracy is also being developed.