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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (4): 397-402    DOI: 10.3785/j.issn.1008-9497.2017.04.003
数学与计算机科学     
高维分层混合模糊系统的规则缩减及逼近性假设检验
王贵君1, 段晨霞2, 张德利3
1. 天津师范大学 数学科学学院, 天津 300387;
2. 天津市南开区咸阳路小学, 天津 300110;
3. 吉林省教育学院 信息中心, 吉林 长春 130022
Reduction of the number of rules of high-dimensional hybrid fuzzy system and its hypothesis test of the approximation
WANG Guijun1, DUAN Chenxia2, ZHANG Deli3
1. School of Mathematics Science, Tianjin Normal University, Tianjin 300387, China;
2. Xianyang Road Primary School, Nankai District, Tianjin 300110, China;
3. Information Center, Jilin Provincial Institute of Education, Changchun 130022, China
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摘要： 混合模糊系统，即通过调控参数将Mamdani和T-S合并建立的一种新型系统模型.混合模糊系统不仅能保持各自模糊系统的优良特性，还可大大缩减系统内部的模糊规则总数.为避免因增加输入变量引发高维混合模糊系统规则爆炸，基于混合模糊系统的分层表示，给出了分层混合模糊系统对连续函数的逼近算法.对比发现，高维分层混合模糊系统的规则总数可被大幅度削减.此外，通过实例模拟了一个三维混合模糊系统分层后的实际输出，并用统计学的t-假设检验方法检验了该分层混合模糊系统的逼近性能.
关键词： 调控参数;  分层混合模糊系统;  规则数;  逼近性;  t-假设检验    
Abstract: The hybrid fuzzy system is a new system model combining Mamdani fuzzy system and T-S fuzzy system by the control parameters. It retains the excellent characteristics of each system, meanwhile greatly reducing the total number of fuzzy rules. To avoid the rule explosion in high-dimensional mixed fuzzy system under increasing input variables, this article proposes an approximation algorithm for a continuous function based on the layered representation of the hybrid fuzzy system. The total number of rules of high-dimensional layered hybrid fuzzy system can be greatly reduced according to the comparison results. In addition, we simulate the actual output of a three-dimensional hybrid fuzzy system through a practical example, and apply the statistical t-hypothesis test to examine the approximation performance of the three-dimensional mixed fuzzy system.
Key words: control parameter    layered hybrid fuzzy system    the number of rules    approximation    t-hypothesis test
收稿日期: 2016-05-26 出版日期: 2017-12-09
CLC:  O159  
基金资助: 国家自然科学基金资助项目（61374009）；吉林省自然科学基金资助项目（201215190）.
通讯作者: 张德利,ORCID:http://orcid.org/0000-0002-2043-2797,E-mail:zhangdl64@126.com.     E-mail: zhangdl64@126.com
作者简介: 王贵君(1962-),ORCID:http://orcid.org/0000-0002-2337-5951,男,教授,主要从事模糊系统、模糊神经网络和模糊积分理论研究,E-mail:tjwgj@126.com.
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引用本文:

王贵君, 段晨霞, 张德利. 高维分层混合模糊系统的规则缩减及逼近性假设检验[J]. 浙江大学学报（理学版）, 2017, 44(4): 397-402.

WANG Guijun, DUAN Chenxia, ZHANG Deli. Reduction of the number of rules of high-dimensional hybrid fuzzy system and its hypothesis test of the approximation. Journal of Zhejiang University (Science Edition), 2017, 44(4): 397-402.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.04.003    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I4/397

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