Abstract：The concepts of the maximum perturbation error of polygonal fuzzy numbers and γ-perturbation of training pattern pairs are put forward, and the learning algorithm of connection weight is designed according to error-correction rules by introducing polygonal fuzzy numbers and their operations. Then the definition of the global stability of the polygonal fuzzy neural networks of the perturbation of training pattern pairs is introdued. Secondly, whenever the transfer function satisfies the Lipschitz condition and γ-perturbation occurs in the training pattern pairs,the stability of the connections of the three-layer polygonal fuzzy neural networks is proved by applying mathematical induction. Moreover, that the γ-perturbation of this network with respect to the training pattern pairs possesses the global stability is obtained. Finally, the influence of perturbations of training pattern pairs on the stability of polygonal fuzzy neural networks is explained by the simulative examples.
隋晓琳，王贵君. 训练模式对的摄动对折线模糊神经网络稳定性的影响[J]. 模式识别与人工智能, 2012, 25(6): 928-936.
SUI Xiao-Lin, WANG Gui-Jun. Influence of Perturbations of Training Pattern Pairs on Stability of Polygonal Fuzzy Neural Network. , 2012, 25(6): 928-936.
[1] Ishibuchi H,Fujioka A R,Tanaka H.Neural Networks That Learn from Fuzzy If-Then Rules.IEEE Trans on Fuzzy Systems,1993,1(2): 85-97 [2] Dunyak J,Wunsch D.Training Fuzzy Number Neural Networks with Alpha-Cut Refinements // Proc of the IEEE International Conference on Systems,Man and Cybernetics.Orlando,USA,1997: 189-194 [3] Hearst M,Hirsh H.AI’s Greatest Trends and Controversies.IEEE Intelligent Systems,2000,15(1): 8-17 [4] Ying M S.Perturbation of Fuzzy Reasoning.IEEE Trans on Fuzzy Systems,1999,7(5): 625-629 [5] Liu Puyin.A New Fuzzy Neural Network and Its Approximation Capabilities.Science in China: Series F,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) [6] Xu Weihong,Chen Guoping,Yang Jingyu,et al.Influence of Fuzzy Implication Operators on Robustness of Reasoning with Perturbations of Rules.Chinese Journal of Computers,2005,28(10): 1701-1707 (in Chinese) (徐蔚鸿,陈国平,杨静宇,等.规则摄动时模糊蕴涵算子对模糊推理的鲁棒性的影响.计算机学报,2005,28(10): 1701-1707) [7] Xu Weihong,Song Luanjiao,Li Aihua,et al.Influence and Control of Perturbation of Training Pattern Pairs on Fuzzy Bidirectional Associative Memories.Chinese Journal of Computers,2006,29(2): 337-344 (in Chinese) (徐蔚鸿,宋鸾姣,李爱华,等.训练模式对的摄动对模糊双向联想记忆网络的影响及其控制.计算机学报,2006,29(2): 337-344) [8] Zeng Shuiling,Xu Weihong,Yang Jingyu.Influences of Perturbations of Training Pattern Pairs on Fuzzy Morphological Associative Memory Networks.Pattern Recognition and Artificial Intelligence,2010,23(1): 91-96 (in Chinese) (曾水玲,徐蔚鸿,杨静宇.训练模式摄动对模糊形态学联想记忆网络的影响.模式识别与人工智能,2010,23(1): 91-96) [9] He Chunmei,Ye Youpei,Li Jian,et al.Universal Approximation of Fuzzy Functions by Polygonal Fuzzy Neural Networks with General Inputs.Pattern Recognition and Artificial Intelligence,2009,22(3): 481-487 (in Chinese) (何春梅,叶有培,李 健,等.一般输入的折线模糊神经网络对模糊函数的通用逼近.模式识别与人工智能,2009,22(3): 481-487) [10] Liu Puyin.Fuzzy Neural Network Theory and Application.Ph.D Dissertation.Beijing,China: Beijing Normal University,2002 (in Chinese) (刘普寅.模糊神经网络理论及其应用研究.博士学位论文.北京:北京师范大学,2002) [11] Castro J R,Castillo O,Melin P,et al.A Hybrid Learning Algorithm for a Class of Interval Type-2 Fuzzy Neural Networks.Information Sciences,2009,179(13): 2175-2193 [12] Deng Xingsheng,Wang Xinzhou.Incremental Learning of Dynamic Fuzzy Neural Networks for Accurate System Modeling.Fuzzy Sets and Systems,2009,160(7): 972-987 [13] Syedali M,Balasubramaniam P.Exponential Stability of Uncertain Stochastic Fuzzy BAM Neural Networks with Time-Varying Delays.Neurocomputing,2009,72(4): 1347-1354 [14] Wu Wei,Li Long,Yang Jie,et al.A Modified Gradient-Based Neuro-Fuzzy Learning Algorithm and Its Convergence.Information Sciences,2010,180(9): 1630-1642 [15] Wang Guijun,Li Xiaoping.Universal Approximation of Polygonal Fuzzy Neural Networks in Sense of K-Integral Norms.Science China: Information Sciences,2011,54(11): 2307-2323 [16] Huang Huan,Wu Congxin.Approximation of Fuzzy Functions by Regular Fuzzy Neural Networks.Fuzzy Sets and Systems,2011,177 (1): 60-79
2012, Vol. 25 
