[1]孙富春,杨 晋,刘华平.SISO Mamdani模糊系统作为函数逼近器的必要条件[J].智能系统学报,2009,4(4):288-294.
　SUN Fu-chun,YANG Jin,LIU Hua-ping.Preconditions for SISO Mamdani fuzzy systems to perform as function approximators[J].CAAI Transactions on Intelligent Systems,2009,4(4):288-294.
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SISO Mamdani模糊系统作为函数逼近器的必要条件

《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷: 4 期数: 2009年第4期 页码: 288-294 栏目: 学术论文—人工智能基础 出版日期: 2009-08-25
Title:
Preconditions for SISO Mamdani fuzzy systems to perform as function approximators
文章编号:
1673-4785(2009)04-0288-07
作者:
孙富春，杨 晋，刘华平
清华大学智能技术与系统国家重点实验室，北京100084
Author(s):
SUN Fu-chun, YANG Jin, LIU Hua-ping
State Key Laboratory of Intelligent Technology and System, Tsinghua University, Beijing 100084, China
关键词:
模糊系统; 必要条件; 模糊规则; 逼近精度
Keywords:
fuzzy systems;  necessary conditions;  fuzzy rules;  approximation accuracy
分类号:
TP18
文献标志码:
A
摘要:
模糊系统已被证明是通用逼近器，但实现高精度通常需要大量规则.模糊系统满足给定精度的必要条件能指导最优系统的构造，如输入输出模糊集、模糊规则的选取.研究了单输入单输出（SISO）Mamdani模糊系统在给定逼近精度下作为函数逼近器的必要条件.由于通用型SISO Mamdani模糊系统在划分子区间单调，所以模糊系统的最优配置是输入域的划分数至少为系统输出的单调性变化次数.当模糊系统满足给定逼近精度时，通过分析目标函数的局部特性，基于目标函数的极点，建立了SISO Mamdani模糊系统的必要条件.更重要的是证明了现有的必要条件仅仅是该文结论的一种特例.最后，使用数值实例来验证该文的结论，分析模糊系统作为函数逼近器的优劣.
Abstract:
It has been proven that fuzzy systems are universal approximators. However, a large number of rules are usually needed for high accuracy. Knowledge of conditions necessary for a fuzzy system to have a given level of accuracy can provide guidance for design of an optimal system, such as selection of optimal input/output fuzzy sets and fuzzy rules. The necessary conditions for a singleinput singleoutput (SISO) Mamdani fuzzy system to operate as a function approximator subject to a given precision were discussed. Since the general SISO Mamdani fuzzy system is monotonic at subintervals, its optimal configuration is when the number of division points is not less than the number of times its monotonicity changes. Thus by analyzing the local characteristics of the object function under the fuzzy system, necessary conditions for a SISO Mamdani fuzzy systems were obtained in accordance with the extrema of the object function. Furthermore, it was shown that the necessary conditions found in prior documents are only a special case of those described here. Finally, simulation examples were given to verify our conclusions and analyze the performance as well as the limitations of a fuzzy system as a function approximator. 
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相似文献/References:
[1]刘福才,陈 超,邵 慧,等.模糊系统万能逼近理论研究综述[J].智能系统学报,2007,2(1):25.
　LIU Fu cai,CHEN Chao,SHAO Hui,et al.Researches for universal approximation of fuzzy syste ms: a survey[J].CAAI Transactions on Intelligent Systems,2007,2():25.

备注/Memo

收稿日期：2009-01-01.
基金项目：国家自然科学基金资助项目（90716021，60621062）.
通信作者：杨 晋.E-mail:yangjin06@mails.tsinghua.edu.cn.
作者简介：
孙富春，男，1964年生，教授，博士生导师，主要研究方向为模糊神经系统、变结构控制、网络控制系统和机器人.2000年获得全国优秀博士论文奖，2003年获韩国第十八届ChoonGang 国际学术奖一等奖第一名.发表学术论文120余篇，其中在国际重要刊物发表论文50余篇.
杨 晋，男，1983年生，硕士研究生，主要研究方向为模糊系统逼近、行人视频检测和跟踪.
刘华平，男，1976年生，副教授，主要研究方向为智能控制与机器人、行人视频跟踪与检测、智能交通等.

更新日期/Last Update: 2009-11-16
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