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浙江大学学报(理学版)  2018, Vol. 45 Issue (4): 394-399    DOI: 10.3785/j.issn.1008-9497.2018.04.002
数学与计算机科学     
以Bernstein多项式为规则后件的模糊系统构造及算法
周洁, 王贵君
天津师范大学 数学科学学院, 天津 300387
Construction and algorithm of fuzzy systems based on Bernstein polynomials as a rule's consequence.
ZHOU Jie, WANG Guijun
School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
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摘要: 以多元多项式为规则后件的模糊系统是区别于Mamdani型和T-S型的一类模糊系统,在模糊控制器及其应用中具有重要的理论价值.首先,以Bernstein多项式为规则后件建立了一类新的多输入单输出模糊系统,进而证明了该模糊系统对n维单位正方体上的连续函数具有逼近性.其次,利用随机剖分数所确定的Bernstein多项式给出了这类模糊系统的输出算法,并通过实例说明该算法是有效的.
关键词: Bernstein多项式模糊规则模糊系统随机剖分数输出算法    
Abstract: The fuzzy system based on multivariate polynomial as a rule's consequence is different from Mamdani and T-S fuzzy systems. This system has important theoretical value in fuzzy controller and its applications. In this paper, a new fuzzy system with multiple input and single output is firstly established as a rule's consequence by the Bernstein polynomials, and then we prove that the fuzzy system can approximate a continuous function on n-dimensional unit cube. Secondly, the output algorithm of the fuzzy system is given by the Bernstein polynomial determined with some random subdivision numbers, and the effectiveness of the algorithm is illustrated by an example.
Key words: Bernstein polynomial    fuzzy rule    fuzzy system    random subdivision number    output algorithm
收稿日期: 2017-11-02 出版日期: 2018-07-12
CLC:  O159  
基金资助: 国家自然科学基金资助项目(61374009)
通讯作者: 王贵君,通信作者,ORCID:http://orcid.org/0000-0002-2337-5951,E-mail:tjwgj@126.com.     E-mail: tjwgj@126.com
作者简介: 周洁(1992-),ORCID:http://orcid.org/0000-0001-5376-7350,女,硕士研究生,主要从事模糊系统与神经网络研究,E-mail:tjnuzhou@163.com.
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引用本文:

周洁, 王贵君. 以Bernstein多项式为规则后件的模糊系统构造及算法[J]. 浙江大学学报(理学版), 2018, 45(4): 394-399.

ZHOU Jie, WANG Guijun. Construction and algorithm of fuzzy systems based on Bernstein polynomials as a rule's consequence.. Journal of Zhejiang University (Science Edition), 2018, 45(4): 394-399.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.04.002        https://www.zjujournals.com/sci/CN/Y2018/V45/I4/394

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