| 基于神经网络的模糊关系方程极小解求解算法 |
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| 引用本文： | 冯霜,李金权,温永川. 基于神经网络的模糊关系方程极小解求解算法[J]. 北京师范大学学报(自然科学版), 2012, 48(2): 111-114 |
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| 作者姓名： | 冯霜 李金权 温永川 |
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| 作者单位： | 北京师范大学珠海分校应用数学学院,广东珠海,519085;北京师范大学珠海分校应用数学学院,广东珠海,519085;北京师范大学珠海分校应用数学学院,广东珠海,519085 |
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| 摘 要： | 利用神经网络求解有限论域上模糊关系方程的极小解,将未知的模糊关系作为神经网络的权重参数进行学习,并设计了相应的网络训练算法Ⅰ.证明了该训练算法将收敛到模糊关系方程的极小解,并通过2个数值实例来验证算法的有效性.
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| 关 键 词： | 模糊关系方程 极小解 神经网络 极大解 |
A NOVEL ALGORITHM FOR OBTAINING MINIMAL SOLUTIONS OF FUZZY RELATION EQUATIONS BASED ON NEURAL NETWORKS |
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| FENG Shuang,LI Jinquan,WEN Yongchuan. A NOVEL ALGORITHM FOR OBTAINING MINIMAL SOLUTIONS OF FUZZY RELATION EQUATIONS BASED ON NEURAL NETWORKS[J]. Journal of Beijing Normal University(Natural Science), 2012, 48(2): 111-114 |
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| Authors: | FENG Shuang LI Jinquan WEN Yongchuan |
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| Affiliation: | (School of Applied Mathematics,Beijing Normal University(Zhuhai),519085,Zhuhai,Guangdong,China) |
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| Abstract: | A novel algorithm(training algorithm I) using neural networks was proposed to solve fuzzy relation equations on finite universe.Unknown fuzzy relation was treated as weight parameters in neural networks.It was found that the proposed training algorithm was convergent on a minimal solution of given fuzzy relation equation.Two numerical examples were given to demonstrate the efficiency of this algorithm. |
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| Keywords: | fuzzy relation equations minimal solutions neural networks maximal solutions |
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