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广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程

王贵君 李晓萍 隋晓琳

王贵君, 李晓萍, 隋晓琳. 广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程. 自动化学报, 2014, 40(1): 143-148. doi: 10.3724/SP.J.1004.2014.00143
引用本文: 王贵君, 李晓萍, 隋晓琳. 广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程. 自动化学报, 2014, 40(1): 143-148. doi: 10.3724/SP.J.1004.2014.00143
WANG Gui-Jun, LI Xiao-Ping, SUI Xiao-Lin. Universal Approximation and Its Realization of Generalized Mamdani Fuzzy System Based on K-integral Norms. ACTA AUTOMATICA SINICA, 2014, 40(1): 143-148. doi: 10.3724/SP.J.1004.2014.00143
Citation: WANG Gui-Jun, LI Xiao-Ping, SUI Xiao-Lin. Universal Approximation and Its Realization of Generalized Mamdani Fuzzy System Based on K-integral Norms. ACTA AUTOMATICA SINICA, 2014, 40(1): 143-148. doi: 10.3724/SP.J.1004.2014.00143

广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程

doi: 10.3724/SP.J.1004.2014.00143
基金项目: 

国家自然科学基金(61374009)资助

详细信息
    作者简介:

    王贵君 天津师范大学数学科学学院教授. 1994 年获得东北师范大学数学系硕士学位. 主要研究方向为模糊测度与模糊积分,模糊神经网络,模糊系统分析. 本文通信作者. E-mail:tjwgj@126.com

Universal Approximation and Its Realization of Generalized Mamdani Fuzzy System Based on K-integral Norms

Funds: 

Supported by National Natural Science Foundation of China (61374009)

  • 摘要: 首先,通过引入拟减法算子给出K-积分模定义,并针对广义Mamdani模糊系统实施等距剖分其输入空间. 其次,应用分片线性函数(Piecewise linear function,PLF)的性质构造性地证明了广义Mamdani模糊系统在K-积分模意义下具有泛逼近性,从而将该模糊系统对连续函数空间的逼近能力扩展到一类可积函数类空间上. 最后,通过模拟实例给出该广义Mamdani模糊系统对给定可积函数的泛逼近及实现过程.
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    [12] Wang Gui-Jun, Li Dan. Capability of universal approximation of feedforward regular fuzzy neural networks in K-integral norm. Acta Mathematicae Applicatae Sinica, 2013, 36(1): 141-152(王贵君, 李丹. 前向正则模糊神经网络依K-积分模的泛逼近能力. 应用数学学报, 2013, 36(1): 141-152)
    [13] Wang Gui-Jun, Duan Chen-Xia. Generalized hierarchical hybrid fuzzy system and its universal approximation. Control Theory and Application, 2012, 29(5): 673-680(王贵君, 段晨霞. 广义分层混合模糊系统及其泛逼近性. 控制理论与应用, 2012, 29(5): 673-680)
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    [16] Duan Chen-Xia, Wang Gui-Jun. Universal approximation of square pricewise linear functions in K-integral norms in fuzzy system. Journal of Tianjin Normal University (Natural Science Edition), 2012, 32(3): 13-16(段晨霞, 王贵君. 模糊系统中方形分片线性函数依K-积分模的泛逼近性. 天津师范大学学报(自然科学版), 2012, 32(3): 13-16)
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出版历程
  • 收稿日期:  2012-09-21
  • 修回日期:  2013-04-02
  • 刊出日期:  2014-01-20

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