| 多层前向正则模糊神经网络的逼近能力 |
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| 引用本文： | 刘普寅. 多层前向正则模糊神经网络的逼近能力[J]. 高校应用数学学报(英文版), 2001, 16(1): 45-57. DOI: 10.1007/s11766-001-0036-9 |
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| 作者姓名： | 刘普寅 |
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| 作者单位： | Liu PuyinDept. of Math.，National Univ. of Defence Technology，Changsha 410073;Dept. of Math.，Beijing Normal Univ.，Beijing 100875. |
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| 基金项目： | This work was supported by National Natural Science Foundation(699740 4 1，699740 0 6) |
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| 摘 要： | Abstract. Four-layer feedforward regular fuzzy neural networks are constructed. Universal ap-proximations to some continuous fuzzy functions defined on (R)“ by the four-layer fuzzyneural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzyvalued functions are empolyed to approximate continuous fuzzy valued functions defined on eachcompact set of R“. Secondly,by introducing cut-preserving fuzzy mapping,the equivalent condi-tions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzyneural networks are shown. Finally a few of sufficient and necessary conditions for characteriz-ing approximation capabilities of regular fuzzy neural networks are obtained. And some concretefuzzy functions demonstrate our conclusions.
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| 关 键 词： | 多层前向正则模糊神经网络 逼近能力 模糊值函数 多变量Bernstein多项式 |
| 收稿时间： | 1999-08-13 |
Approximation capabilities of multilayer feedforward regular fuzzy neural networks |
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| Liu Puyin. Approximation capabilities of multilayer feedforward regular fuzzy neural networks[J]. Applied Mathematics A Journal of Chinese Universities, 2001, 16(1): 45-57. DOI: 10.1007/s11766-001-0036-9 |
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| Authors: | Liu Puyin |
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| Affiliation: | (1) Dept. of Math., National Univ. of Defence Technology, 410073 Changsha;(2) Dept. of Math., Beijing Normal Univ., 100875 Beijing |
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| Abstract: | Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions. |
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| Keywords: | Regular fuzzy neural networks cut preserving fuzzy mappings universal approximators fuzzy valued Bernstein polynomials. |
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