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小波分析与模糊系统分析的联系
引用本文:陈永义.小波分析与模糊系统分析的联系[J].模糊系统与数学,2002,16(3):38-43.
作者姓名:陈永义
作者单位:北京气象学院,计算机系,北京,100081
基金项目:国家自然科学基金资助项目 (6 0 0 72 0 0 6 )
摘    要:讨论小波基函数与模糊集隶属函数之间的联系 ,证明模糊系统研究与应用中的隶属函数都可以由称之为简单小波的母函数表出 ,反之每一简单小波也可以由某一隶属函数表出 ,从而验证简单小波类与某一隶属函数类的一一对应关系。该结果进一步揭示模糊推理和模糊控制的实质 ,为在模糊系统辨识、模糊控制和模糊数据分析等诸多领域充分利用近代小波分析的成果提供新思路

关 键 词:模糊控制  隶属函数  小波  简单小波
文章编号:1001-7402(2002)03-0038-06
修稿时间:2001年4月30日

The Relationship between Wavelets and Analysis of Fuzzy Systems
CHEN Yong-yi.The Relationship between Wavelets and Analysis of Fuzzy Systems[J].Fuzzy Systems and Mathematics,2002,16(3):38-43.
Authors:CHEN Yong-yi
Abstract:In this paper, we discuss the relationship between the wavelets base functions and the membership functions of fuzzy sets. Based on it, we proved that all the commonly used membership functions can be described by what is called simple mother wavelets. Moreover, every simple wavelet can be derived from certain membership function. Thus, the one-to-one relationship between simple wavelet classes and membership function classes is verified. In addition, this depicts the essence of fuzzy inference and control, and provides a new approach of applying wavelet analysis method to the areas of fuzzy system identification, fuzzy control, and fuzzy data analysis, etc.
Keywords:Fuzzy Control  Membership Functions  Wavelets  Simple Wavelets
本文献已被 CNKI 维普 万方数据 等数据库收录!
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