| 以Bernstein多项式为规则后件的模糊系统构造及算法 |
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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. DOI: 10.3785/j.issn.1008-9497.2018.04.002 |
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| 作者姓名： | 周洁 王贵君 |
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| 作者单位： | 天津师范大学 数学科学学院, 天津 300387 |
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| 基金项目： | 国家自然科学基金资助项目（61374009） |
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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.
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| 关 键 词： | Bernstein多项式 模糊规则 模糊系统 随机剖分数 输出算法 |
| 收稿时间： | 2017-11-02 |
Construction and algorithm of fuzzy systems based on Bernstein polynomials as a rule's consequence. |
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| ZHOU Jie,WANG Guijun. Construction and algorithm of fuzzy systems based on Bernstein polynomials as a rule's consequence.[J]. Journal of Zhejiang University(Sciences Edition), 2018, 45(4): 394-399. DOI: 10.3785/j.issn.1008-9497.2018.04.002 |
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| Authors: | ZHOU Jie WANG Guijun |
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| Affiliation: | School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China |
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| 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. |
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| Keywords: | Bernstein polynomial fuzzy rule fuzzy system random subdivision number output algorithm |
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