共查询到15条相似文献,搜索用时 187 毫秒
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K-积分模意义下折线模糊神经网络的泛逼近性 总被引:1,自引:0,他引:1
为克服模糊数运算的复杂性引入折线模糊数的定义,利用折线模糊数的优良性质获得了两个重要不等式,并给出实例说明折线模糊数的逼近能力有效.其次,引进K-拟可加积分和K-积分模概念,在折线模糊数空间满足可分性的基础上,借助于模糊值简单函数和模糊值Bernstein多项式研究了若干函数空间的稠密性问题,获得了可积有界模糊值函数类依K-积分模构成完备可分的度量空间.最后,在K-积分模意义下讨论了四层正则折线模糊神经网络对模糊值简单函数的泛逼近性,进而得到该网络对可积有界函数类也具有泛逼近性.该结果表明正则折线模糊神经网络对连续模糊系统的逼近能力可以推广为对一般可积系统的逼近能力. 相似文献
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广义分层混合模糊系统及其泛逼近性 总被引:1,自引:0,他引:1
为避免广义模糊系统出现规则爆炸现象, 引进实参数将Mamdani模糊系统和T--S模糊系统统一起来建立广义分层混合模糊系统, 进而给出了广义分层混合模糊系统的数学表示. 此外, 应用方形分片线性函数的优良性质获得该广义分层混合模糊系统在积分模意义下仍具有泛逼近性, 并通过实例及仿真说明该分层混合模糊系统能够避免模糊规则爆炸问题. 相似文献
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首先, 引入后件直联型分层方法及其推理规则, 以对广义混合模糊系统的输入变量实施分层, 获得分层广义混合模糊系统的输入输出表达式和推理规则数的计算公式; 然后, 基于??- 积分模(度量) 和分片线性函数证明分层后广义混合模糊系统对一类可积函数具有逼近性; 最后, 通过模拟实例给出后件直联型分层广义混合模糊系统对可积函数的逼近过程. 模拟结果表明, 所提出的方法不仅能使原系统模糊规则总数大大减少, 而且能使分层后系统仍具有逼近性.
相似文献4.
广义递阶Mamdani模糊系统及其泛逼近性 总被引:1,自引:1,他引:1
从解决模糊系统的“规则爆炸”问题出发,本文首先给出广义递阶M amdan i模糊系统的定义,然后证明其与具有中间变量的广义M amdan i模糊系统等价,并借助方形分片线性函数构造性的证明了在最大模和积分模意义下该系统是泛逼近器.最后仿真实例证实了该系统的有效性. 相似文献
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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。 相似文献
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本文提出模糊系统中基于泛逻辑的泛蕴涵推理机,给出其在描绘函数图形时的应用,同时比较了它与Mamdani型和Lasen型两种模糊系统在描绘函数图形时的误差。分析和比较表明,在相同规则下含有泛蕴涵推理机的模糊系统产生的误差最低。 相似文献
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Necessary conditions on minimal system configuration for general MISO Mamdani fuzzy systems as universal approximators 总被引:3,自引:0,他引:3
Yongsheng Ding Hao Ying Shihuang Shao 《IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics》2000,30(6):857-864
Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators with as minimal system configuration as possible. The general MISO fuzzy systems employ almost arbitrary continuous input fuzzy sets, arbitrary singleton output fuzzy sets, arbitrary fuzzy rules, product fuzzy logic AND, and the generalized defuzzifier containing the popular centroid defuzzifier as a special case. Our necessary conditions are developed under the practically sensible assumption that only a finite set of extrema of the multivariate continuous function to be approximated is available. We have first revealed a decomposition property of the general fuzzy systems: A r-input fuzzy system can always be decomposed to the sum of r simpler fuzzy systems where the first system has only one input variable, the second one two input variables, and the last one r input variables. Utilizing this property, we have derived some necessary conditions for the fuzzy systems to be universal approximators with minimal system configuration. The conditions expose the strength as well as limitation of the fuzzy approximation: (1) only a small number of fuzzy rules may be needed to uniformly approximate multivariate continuous functions that have a complicated formulation but a relatively small number of extrema; and (2) the number of fuzzy rules must be large in order to approximate highly oscillatory continuous functions. A numerical example is given to demonstrate our new results. 相似文献
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Puyin Liu 《Fuzzy Systems, IEEE Transactions on》2002,10(6):756-766
The issue of fuzzy systems as universal approximators has drawn significant attention, but all results obtained are restricted to deterministic input-output (I/O) relationships. It should be noted that, in practice, many I/O systems, including fuzzy systems, operate in the environment which is essentially stochastic. In this paper, the Mamdani fuzzy systems are generalized as stochastic systems. By proving the Mamdani systems as universal approximators with L/sup 2/-norm, the approximation capability of the stochastic Mamdani systems to a class of random processes is systematically analyzed. In the mean square sense, such stochastic fuzzy systems are capable of approximating the prescribed random processes with arbitrary accuracy. Further, an efficient learning algorithm for the stochastic Mamdani systems is developed. Finally, a simulation example is employed to demonstrate our results. 相似文献