| 正则模糊神经网络是模糊值函数的泛逼近器 |
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| 引用本文： | 刘 普 寅. 正则模糊神经网络是模糊值函数的泛逼近器[J]. 控制与决策, 2003, 18(1): 19-23 |
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| 作者姓名： | 刘 普 寅 |
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| 作者单位： | 北京师范大学,数学系,北京,100875 |
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| 基金项目： | 国家自然科学基金资助项目 (6 99740 41,6 99740 0 6 ) |
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| 摘 要： | 通过分析多元模糊值Bernstein多项式的近似特性，证明了4层前向正则模糊神经网络（FNN）的逼近性能，该类网络构成了模糊值函数的一类泛逼近器，即在欧氏空间的任何紧集上，任意连续模糊值函数能被这类FNN逼近到任意精度，最后通过实例给出了实现这种近似的具体步骤。
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| 关 键 词： | 正则模糊神经网络 模糊值函数 泛逼近器 Bernstein多项式 |
| 文章编号： | 1001-0920(2003)01-0019-05 |
Regular fuzzy neural network as universal approximator of fuzzy valued function |
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| of fuzzy valued function$$$$ LIU Pu-yin. Regular fuzzy neural network as universal approximator of fuzzy valued function[J]. Control and Decision, 2003, 18(1): 19-23 |
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| Authors: | of fuzzy valued function$$$$ LIU Pu-yin |
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| Abstract: | The systematic analysis on approximation capability of four-layer feedforward regular fuzzy neural network(FNN) is presented. This is done by fuzzy valued multivariate Bernstein polynomial whoseapproximationtofuzzyvalued functions is guaranteed. Such a four-layer FNN constitutes a universal approximator of fuzzy valued function. That is, each continuous fuzzy valued function defined on any compact set of Euclidean space can be approximated by the FNN to any degree of accuracy. A numerical example shows the realization process of the approximation. |
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| Keywords: | Regular fuzzy neural network Fuzzy valued Bernstein polynomial Universal approximator |
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