Kp-积分模意义下广义Mamdani模糊系统的逼近性能及其实现

doi:10.3969/j.issn.0372-2112.2015.11.022

电子学报 ›› 2015, Vol. 43 ›› Issue (11): 2284-2291.DOI: 10.3969/j.issn.0372-2112.2015.11.022

Kp-积分模意义下广义Mamdani模糊系统的逼近性能及其实现

陶玉杰¹, 王宏志¹, 王贵君²

1. 通化师范学院数学学院, 吉林通化 134002;
2. 天津师范大学数学科学学院, 天津 300387

收稿日期:2014-07-15 修回日期:2014-10-20 出版日期:2015-11-25 发布日期:2015-11-25
通讯作者: 王贵君
作者简介:陶玉杰 女,1975年8月出生,副教授,吉林通化人.2004年获燕山大学理学硕士学位,现在通化师范学院数学学院任教.主要研究方向:模糊系统分析.E-mail:taotujie@126.com;王宏志 男,1975年6月出生,副教授,吉林梅河口人,2006年获吉林大学数学所理学硕士学位,现在通化师范学院数学学院任教.主要研究方向:模糊系统逼近分析.E-mail:whz-98@126.com
基金资助:
国家自然科学基金(No.61374009)

Approximation Ability and Its Realization of the Generalized Mamdani Fuzzy System in the Sense of Kp-Integral Norm

TAO Yu-jie¹, WANG Hong-zhi¹, WANG Gui-jun²

1. College of Mathematics, Tonghua Normal University, Tonghua, Jilin 134002, China;
2. College of Mathematics Sciences, Tianjin Normal University, Tianjin 300387, China

Received:2014-07-15 Revised:2014-10-20 Online:2015-11-25 Published:2015-11-25

摘要/Abstract

摘要：

利用积分模(度量)研究模糊系统对可积函数类的逼近性是人们普遍关注的方法,而基于K-拟算术运算诱导的Kp-积分模不仅是一维积分模的推广,而且是刻画p-次可积函数类的重要工具.本文通过引入拟减运算重新定义Kp-积分模,且在Kp-积分模意义下讨论分片线性函数对一类û_p-可积函数的逼近性,进而构造性地证明广义Mamdani模糊系统对û_p-可积函数类仍有逼近性.最后通过实例分析说明广义Mamdani模糊系统的逼近效果.结果表明广义Mamdani模糊系统可以按任意精度逼近一类û_p-可积函数.

关键词: K-拟算术运算, û_p-可积函数, Kp-积分模, 分片线性函数, 广义Mamdani模糊系统, 逼近性

Abstract:

Researching on the approximation of fuzzy system to integrable function class by means of the integral norm(a metric) is one method of common concern to the people.The Kp-integral norm induced by the K-quasi-arithmetic operations is not only a generalization for a one dimensional integral norm,but also an important tool to describe the p-integrable function classes.In this paper,the Kp-integral norm is redefined by introducing the quasi-subtraction operator.In the sense of the Kp-integral norm,the approximation of the piecewise linear functions to a kind of û_p-integrable functions is discussed.Then,we prove constructively that the generalized Mamdani fuzzy system has the approximation to a class of û_p-integrable functions.Finally,by a practical example the approximation effect of the generalized Mamdani fuzzy systems is illustrated.The results show that the generalized Mamdani fuzzy system can approximate a kind of û_p-integrable functions to arbitrary accuracy.

Key words: K-quasi-arithmetic operation, û_p-integrable function, Kp-integral norm, piecewise linear function, generalized Mamdani fuzzy systems, approximation

中图分类号:

TP183
O159

陶玉杰, 王宏志, 王贵君. Kp-积分模意义下广义Mamdani模糊系统的逼近性能及其实现[J]. 电子学报, 2015, 43(11): 2284-2291.

TAO Yu-jie, WANG Hong-zhi, WANG Gui-jun. Approximation Ability and Its Realization of the Generalized Mamdani Fuzzy System in the Sense of Kp-Integral Norm[J]. Acta Electronica Sinica, 2015, 43(11): 2284-2291.

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Kp-积分模意义下广义Mamdani模糊系统的逼近性能及其实现

Approximation Ability and Its Realization of the Generalized Mamdani Fuzzy System in the Sense of Kp-Integral Norm

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