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| Universal Approximation of Fuzzy Functions by Polygonal Fuzzy Neural Networks with General Inputs |
| HE Chun-Mei1, YE You-Pei1, LI Jian1, XU Wei-Hong2 |
1.College of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094
2.College of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410077 |
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Abstract Firstly, a class of feedforward fuzzy neural networks (FNNs), polygonal FNNs, is proposed based on a redefined extension principle and fuzzy arithmetic.Then, while the inputs are general fuzzy numbers and the active functions are monotone continuous sigmoid functions, the topologic structure and the related properties of the polygonal FNNs are analyzed systemically. Some theorems for the continuous fuzzy function can be approximated to any degree of accuracy by polygonal FNN and they are proved. Finally, the equivalent conditions are presented. Thus the problem whether the polygonal FNNs with general inputting fuzzy numbers is the universal approximator to the class of continuously increasing fuzzy function is solved, and consequently the application areas of polygonal fuzzy neural networks are extended.
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Received: 22 September 2008
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[1] Stinchcombe M B. Neural Network Approximation of Continuous Functionals and Continuous Functions on Compactifications. Neural Networks, 1999, 12(3): 467-477
[2] Scarselli F, Tsoi A C. Universal Approximation Using Feedforward Neural Networks: A Survey of Some Existing Methods and New Results. Neural Networks, 1998, 11(1): 15-37
[3] Chen Tianping, Chen Hong, Liu R W. Approximation Using Capability in 公式 by Multilayer Feedforward Networks and Related Problems. IEEE Trans on Neural Networks,1995, 6(1): 25-30
[4] Buckley J J, Hayashi Y. Can Fuzzy Neural Nets Approximate Continuous Fuzzy Functions? Fuzzy Sets and Systems, 1994, 61(1): 43-51
[5] Buckley J J, Hayashi Y. Can Neural Nets Be Universal Approximators for Fuzzy Functions? Fuzzy Sets and Systems, 1999, 101(3): 323-330
[6] Liu Puyin. Analyses of Regular Fuzzy Neural Networks for Approximation Capabilities. Fuzzy Sets and Systems, 2000, 114(2): 329-338
[7] Liu Puyin,Wang Hao. Research of Regular Fuzzy Neural Networks for Approximation Capabilities. Science in China: Series E, 1999, 29(1): 54-60 (in Chinese)
(刘普寅,汪 浩.正则模糊神经网络对连续模糊函数的近似逼近能力研究.中国科学:E辑, 1999, 29(1): 54-60)
[8] Liu Puyin. Universal Approximation of Continuous Fuzzy-Valued Functions by Multi-Layer Regular Fuzzy Neural Networks. Fuzzy Sets and Systems, 2001, 119(2): 313-320
[9] Liu Puyin. Regular Fuzzy Neural Network as Universal Approximator of Fuzzy Valued Function. Control and Decision, 2003, 18(1): 19-28 (in Chinese)
(刘普寅.正则模糊神经网络是模糊值函数的泛逼近器.控制与决策, 2003, 18(1): 19-28)
[10] Liu Puyin, Li Hongxing. Approximation Analysis of Feedforward Regular Fuzzy Neural Networks with Two Hidden Layers. Fuzzy Sets and Systems, 2005, 150(2): 373-396
[11] Liu Puyin. A New Fuzzy Neural Network and Its Approximation Capabilities. Science in China: Series E, 2002, 32(1): 76-86 (in Chinese)
(刘普寅.一种新的模糊神经网络及其逼近性能.中国科学:E辑, 2002, 32(1): 76-86)
[12] Liu Puyin. Fuzzy Neural Networks Theory and Application Research. Ph.D Dissertation. Beijing, China: Beijing Normal University. Mathematics Research Institute, 2002: 59-95 (in Chinese)
(刘普寅.模糊神经网络理论及应用研究.博士学位论文.北京:北京师范大学.数学与数学教育研究所, 2002: 59-95)
[13] He Chunmei, Ye Youpei, Xu Weihong. Universal Approximation of Fuzzy Functions by Polygonal Fuzzy Neural Networks. Computer Applications, 2008, 28(6): 1555-1558 (in Chinese)
(何春梅,叶有培,徐蔚鸿.折线模糊神经网络对模糊函数的通用逼近.计算机应用, 2008, 28(6): 1555-1558)
[14] Diamond P, Kloeden P. Metric Space of Fuzzy Sets. Singapore, Singapore: World Scientific Press, 1994
[15]Gerla G, Scarpati L. Extension Principles for Fuzzy Set Theory. Information Sciences—Informatics and Computer Science: An International Journal, 1998, 106(1/2): 49-69 |
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2009, Vol. 22 
