模糊神经网络的性能及其学习算法研究
|
摘要
软计算技术是包含模糊逻辑(fuzzy logic)、神经计算(neuro-computing)、进化计算(Evolutionary computing)和概率计算(Probabilistic computing)等基本成员的计算方法论的集合,它是求解高度非线性复杂系统的有效工具。模糊神经网络(Fuzzy Neural Network, FNN)是软计算技术的主要研究内容之一,是智能控制理论中的一个十分活跃的分支,是由人工神经网络与模糊逻辑系统的有机结合而产生的一种混合智能系统。模糊神经网络是一种能处理抽象信息的网络结构,它具有强大的自学习和自调整功能。因此,模糊神经网络的相关研究对软计算技术和智能控制发展具有非常重要的意义。
本文在分析模糊神经网络理论和应用现状的基础上,系统研究了单体FNN和折线FNN这两类FNN模型的性能和学习算法,并将所得成果应用于模糊控制领域,其中主要包括单体FNN训练模式对的摄动问题和折线FNN的逼近性能,并为折线FNN设计了两种模糊学习算法,这些工作为FNN乃至软计算技术的实际应用奠定必要的理论基础。
本文所做的主要工作和研究成果如下：
(1)对模糊神经网络的训练模式对的摄动问题进行了研究。首先给出了一般模糊神经网络的训练模式对摄动的鲁棒性定义,然后具体以单体模糊神经网络为例,进行了系统分析,理论研究表明当训练模式对发生最大γ保序摄动时,在h=5的条件下,单体模糊神经网络对训练模式对的摄动全局拥有好的鲁棒性。
(2)对折线模糊神经网络的泛逼近性进行了深入研究。首先限制折线FNN输入或权值的范围,对两种特殊的折线FNNs的泛逼近性进行了系统分析,然后进一步分析了一般意义上的折线FNN的泛逼近性,此处的一般折线FNN是指对网络输入和权阈值没有其他限制。理论研究表明,上述三种折线FNNs均能作为模糊连续函数的通用逼近器,并且证明了：递增性是折线模糊函数保证折线FNN泛逼近性成立的等价条件,从而解决了折线FNN的泛逼近性问题。
(3)为折线模糊神经网络提出了两种模糊梯度学习算法。首先系统研究了Λ—(?)函数导数的基本性质,然后针对折线FNN设计了基于遗传算法或量子遗传算法的两种模糊共扼梯度(CG)算法,在算法迭代的每一步,利用遗传算法或量子遗传算法(GA)来确定最优学习常数,从理论上证明了该模糊共扼梯度算法的收敛性,用于实际模糊控制领域中的实例验证了上述学习过程。
Soft computation technology, whose primary members are fuzzy logic (FL), neuro-computing (NC), evolutionary computing (EC), and probabilistic computing (PC) and so on, is an association of computing methodologies and an effective tool to deal with nonlinear complicated systems. Fuzzy neural network (FNN), which is the organic integration of neural network and fuzzy system, is an important hybrid intelligent system of soft computing technique and an active branch of intelligent control theory. FNN can deal with the abstract information, such as the language information and has good self-learning and self-tuning capabilities. Therefore, the research of FNN is significant in soft computation technology and intelligent control.
This thesis systematically studies the performances and learning algorithms of two FNN models, monolithic FNN and polygonal FNN, based on the past progress of FNN theory and application. The major issues in the thesis are the perturbation of monolithic FNN, the learning algorithms and universal approximation of polygonal FNN and the achievements obtained here are applied to fuzzy control area. The research in the thesis provides the applications of FNN and soft computing technique with the necessary theoretic basis.
The main contributions of the thesis can be enumerated as follows:
1. The perturbation of training pattern pairs on a fuzzy neural network is researched. The definition is established for the robustness of a general FNN to perturbation of training pattern pairs. As a typical instance, this kind of robustness of monolithic fuzzy neural network (MFNN) is analyzed, and the theoretical studies in this paper show that the MFNN has good robustness when training pattern pairs come into the y maximum keep-order perturbations with the coefficient h= 5.
2. The universal approximation capability of polygonal FNN is deeply studied. Firstly, the universal approximation of two special polygonal FNNs is analyzed, where inputs or weights of the polygonal FNNs are limited to a small class of fuzzy number. Secondly, universal approximation of the general polygonal FNN are deeply analyzed where there is no limit to inputs or weights of the polygonal FNN. The theory research show that the polygonal FNN can be as a universal approximator to the fuzzy continuous function and the equivalent conditions is the fuzzy functions'increase.
3. Two fuzzy learning algorithms are proposed for polygonal FNN. Two fuzzy conjugate gradient algorithms based on genetic algorithm (GA) or quantum genetic algorithm (QGA) are designed for the polygonal FNN. In every step of the algorithms, the learning constant is optimized by GA or QGA and the theory study shows the astringency of the algorithms. The simulate experiments in fuzzy control are employed to illustrate the realization of the corresponding learning algorithms.
本文在分析模糊神经网络理论和应用现状的基础上,系统研究了单体FNN和折线FNN这两类FNN模型的性能和学习算法,并将所得成果应用于模糊控制领域,其中主要包括单体FNN训练模式对的摄动问题和折线FNN的逼近性能,并为折线FNN设计了两种模糊学习算法,这些工作为FNN乃至软计算技术的实际应用奠定必要的理论基础。
本文所做的主要工作和研究成果如下：
(1)对模糊神经网络的训练模式对的摄动问题进行了研究。首先给出了一般模糊神经网络的训练模式对摄动的鲁棒性定义,然后具体以单体模糊神经网络为例,进行了系统分析,理论研究表明当训练模式对发生最大γ保序摄动时,在h=5的条件下,单体模糊神经网络对训练模式对的摄动全局拥有好的鲁棒性。
(2)对折线模糊神经网络的泛逼近性进行了深入研究。首先限制折线FNN输入或权值的范围,对两种特殊的折线FNNs的泛逼近性进行了系统分析,然后进一步分析了一般意义上的折线FNN的泛逼近性,此处的一般折线FNN是指对网络输入和权阈值没有其他限制。理论研究表明,上述三种折线FNNs均能作为模糊连续函数的通用逼近器,并且证明了：递增性是折线模糊函数保证折线FNN泛逼近性成立的等价条件,从而解决了折线FNN的泛逼近性问题。
(3)为折线模糊神经网络提出了两种模糊梯度学习算法。首先系统研究了Λ—(?)函数导数的基本性质,然后针对折线FNN设计了基于遗传算法或量子遗传算法的两种模糊共扼梯度(CG)算法,在算法迭代的每一步,利用遗传算法或量子遗传算法(GA)来确定最优学习常数,从理论上证明了该模糊共扼梯度算法的收敛性,用于实际模糊控制领域中的实例验证了上述学习过程。
Soft computation technology, whose primary members are fuzzy logic (FL), neuro-computing (NC), evolutionary computing (EC), and probabilistic computing (PC) and so on, is an association of computing methodologies and an effective tool to deal with nonlinear complicated systems. Fuzzy neural network (FNN), which is the organic integration of neural network and fuzzy system, is an important hybrid intelligent system of soft computing technique and an active branch of intelligent control theory. FNN can deal with the abstract information, such as the language information and has good self-learning and self-tuning capabilities. Therefore, the research of FNN is significant in soft computation technology and intelligent control.
This thesis systematically studies the performances and learning algorithms of two FNN models, monolithic FNN and polygonal FNN, based on the past progress of FNN theory and application. The major issues in the thesis are the perturbation of monolithic FNN, the learning algorithms and universal approximation of polygonal FNN and the achievements obtained here are applied to fuzzy control area. The research in the thesis provides the applications of FNN and soft computing technique with the necessary theoretic basis.
The main contributions of the thesis can be enumerated as follows:
1. The perturbation of training pattern pairs on a fuzzy neural network is researched. The definition is established for the robustness of a general FNN to perturbation of training pattern pairs. As a typical instance, this kind of robustness of monolithic fuzzy neural network (MFNN) is analyzed, and the theoretical studies in this paper show that the MFNN has good robustness when training pattern pairs come into the y maximum keep-order perturbations with the coefficient h= 5.
2. The universal approximation capability of polygonal FNN is deeply studied. Firstly, the universal approximation of two special polygonal FNNs is analyzed, where inputs or weights of the polygonal FNNs are limited to a small class of fuzzy number. Secondly, universal approximation of the general polygonal FNN are deeply analyzed where there is no limit to inputs or weights of the polygonal FNN. The theory research show that the polygonal FNN can be as a universal approximator to the fuzzy continuous function and the equivalent conditions is the fuzzy functions'increase.
3. Two fuzzy learning algorithms are proposed for polygonal FNN. Two fuzzy conjugate gradient algorithms based on genetic algorithm (GA) or quantum genetic algorithm (QGA) are designed for the polygonal FNN. In every step of the algorithms, the learning constant is optimized by GA or QGA and the theory study shows the astringency of the algorithms. The simulate experiments in fuzzy control are employed to illustrate the realization of the corresponding learning algorithms.
引文
[1]刘普寅,李洪兴.软计算及其哲学内涵.自然辩证法研究,2000,16(5)：29～34
[2]斯洛廷,李卫平.应用非线性系统.北京：国防工业出版社,1989
[3]卢强,孙元章.电力系统非线性控制.北京：科学出版社,1993
[4]陈予恕,唐云.非线性动力学中的现代分析方法.北京：科学出版社,1992
[5]Zadeh L A. Fuzzy logic,neural networks and soft computing. One-page Course Announcement of CS-the University of Califonria at Berkeley,1993,294
[6]王立新.自适应模糊系统与控制——设计与稳定性分析.北京：国防工业出版社,1995
[7]Horikawa S, Furuhashi T, Uchikawa Y. On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm. IEEE Trans.on Neural Networks,1992, 3(5):801～806.
[8]刘普寅,张维民.通信网络可靠性研究中的数学问题.通信学报,2000,21(10)：50～57
[9]Deng XS, Wang XZ. Incremental learning of dynamic fuzzy neural networks for accurate system modeling. Fuzzy Sets and Systems,2009,160(7):972～987
[10]Gobi AF, Pedrycz W. The potential of fuzzy neural networks in the realization of approximate reasoning engines. Fuzzy Sets and Systems,2006,157(22):2954～2973
[11]Juang CF, Chen TM. Birdsong recognition using prediction-based recurrent neural fuzzy networks. Neurocomputing,2007,71(1-3):121～130
[12]Brouwer R K. A fuzzy recurrent artificial neural network(FRANN) for pattern classification. International Journal of Uncertain,Fuzziness and Knowledge-Based Systems, 2000,8(5):525～538
[13]Juang CF, Chen LT. Moving object recognition by a shape-based neural fuzzy network. Neurocomputing,2008,71(13-15):2937～2949
[14]SimpsonP K. FuzzyMin-Max neural networks.2.clustering. IEEE Trans.Fuzzy Systems,1993,1:32～45
[15]Singh M, Srivastava S, Hanmandlu M, et al. Type-2 fuzzy wavelet networks (T2FWN) for system identification using fuzzy differential and Lyapunov stability algorithm. Applied Soft Computing,2009,9(3):977～989
[16]Zadeh LA. Fuzzy Set. Information and Control,1965,8(3):338～358
[17]Mamanadi E H. Application of fuzzy algorithms of simple dynamic plant. In Proc. IEEE,1974,121(12):1585～1588
[18]McCulloch W S, Pitts W. A logic calculus of the ideas imminent in neurons activity. Bulletin of Mathematics Biology,1943,5:115～133
[19]Hebb D 0. The organization of behavior. Wiley, New York,1949
[20]Rosenblatt F. Principles of neuro dynamics. New York, Spartan Book,1962
[21]Hopfield J J. Neural networks and Physical system with emergent collective computational abilities. Proc. Acad. Sci., USA,1982,79:2554～2558
[22]Hinton G E, Sejnowski T J, Ackley D H. Boltzmann machine:constraint satisfaction networks that learn. CM-VCS-84-119, Carneie-Mellon University,1984
[23]Ackley D H, Hinton G E, Sejnowski T J. A Learning algorithm for Boltzmann machines. Cognitive Science,1985,9(1):147～169
[24]Rumelhart D E, McClelland J L. Parallel Distributed Processing. USA:MIT Press, 1986
[25]王振雷.模糊神经网络理论及其在复杂系统中的应用研究.沈阳：东北大学,2002
[26]Gupta M M, Rao D H. On the principle of fuzzy neural networks. Fuzzy Sets and Systems,1994,61(1):1～18
[27]Hornik K, Stinchcombe M, White H. Multiplayer feedforward networks are universal approximator. Neural Computing,1990,2:210～215
[28]Kosko B. Fuzzy systems as universal approximators. IEEE Transactions on Computers.1994,43 (11):1329～1333
[29]Wang L, Mendel J. Fuzzy basis functions, approximation,and orthogonal least square learning. IEEE Trans. on Neural Network,1992,3 (5):807～814
[30]沈建强,李平.模糊神经技术的研究现状和展望.控制与决策,1996,11(5)：527～532
[31]张凯,钱锋,刘漫丹.模糊神经网络技术综述.信息与控制,2003,32(5)：431～435
[32]刘普寅,张汉江,吴孟达等.模糊神经网络理论研究综述.模糊系统与数学,1998,10(1)：77～87
[33]周春光,梁艳春.计算智能：人工神经网络、模糊系统、进化计算.吉林：吉林大学出版社,2001
[34]Wang L X. Adaptive fuzzy systems and control:design stability analysis. PTR Prentice-Hall, Englewood Cliffs, NJ,1994
[35]Nguyen H T. A note on the extension principle for fuzzy sets. Journal of Math Analysis Application,1976,64:369～380
[36]Nauck D. Neuro-fuzzy systems:review and prospects. Proc. of the 5th Europe Congress on Intelligent Techniques and Soft Computing,1997:1044～1053
[37]Lee S C, Lee E T. Fuzzy neural networks. Math.Biosci.,1975,23:151～177
[38]Lee S C, Lee E T. Fuzzy sets and neural networks. Cybenretics,1974,4:83～103
[39]Kosko B. Bidirectional associative memory. IEEE Transactions on System, Man and Cybernetics,1988,18(1):49～60
[40]Kosko B. Bidirectional associative memory in fuzzy expert systems. Kandel A.Ed. USA:Addison Wesley,1987
[41]Kosko B. Fuzzy associative memories. In:Kandel A(ed):Fuzzy Expert Systems Reading. MA, USA:Addison Wesley,1987
[42]Jang S R. ANFIS:Adaptive-network-based fuzzy inference systems. IEEE Trans, on Systems, Man & Cybernetics,1993,23(3):665～685
[43]Pedrycz W. Genetic tolerance fuzzy neural networks:From data to fuzzy hyperboxes. Neurocomputing,2007,70(7-9):1403～1413
[44]Konar A, Chakraborty U K, Wang P P. Supervised learning on a fuzzy Petri net. Information Sciences,2005,172(3-4):397～416
[45]Mastorocostas P A, Theocharis J B. An orthogonal least-squares method for recurrent fuzzy-neural modeling. Fuzzy Sets and Systems,2003,140(2):285～300
[46]Juang CF, Chung IF. Recurrent fuzzy network design using hybrid evolutionary learning algorithms. Neurocomputing,2007,70(16-18):3001～3010
[47]Leng G, Prasad G, McGinnity TM. An on-line algorithm for creating self-organizing fuzzy neural networks. Neural Networks,2004,17(14):1477～1493
[48]Carpenter G A, et al. Fuzzy ART:fast stable learning and categorization of analog pattern by an adaptive resonance system. Neural Networks,1991,4(5):759～771
[49]Pal S K, Mitra S. Multilayer perceptron, fuzzy sets and classification. IEEE Trans. Neural Networks,1992,3(5):698～713
[50]Jou C C.A fuzzy cerebella model articulation controller. Proc. IEEE Int. Conf. Fuzzy Sets.1992:1171～1178
[51]Kosko B. Neural Networks and Fuzzy Systems:A Dyhamical Systems Approach to Machine Intelligence. NJ:Prentice Hall Inc,1992
[52]Pedrcy W, Roeha A F. Fuzzy-Set based models of neurons and knowledge-based networks. IEEE Trans. on Fuzzy System,1993,1(4):254～266
[53]Simpson P K. Fuzzy min-max neural networks-Part 1:Classification. IEEE Trans. Neural Networks,1992,3(5):776～786
[54]Wang L X, Mendel J M. Fuzzy basis functions, universal approximation and orthogonal least squares learning. IEEE Trans. on Neural Networks,1992,3(5):807～814
[55]Wang XS, Cheng YH, Yi JQ. A fuzzy Actor-Critic reinforcement learning network. Information science,2007,177(18):3764～3781
[56]Pedrcyz W, Rocha A F. Fuzzy-set based models of neurons and knowledge-based networks. IEEE Trans. on Fuzzy System,1993,1(4):254～266
[57]Hirota K, Pedrycz W. Knowledge-based networks in classification problems. Fuzzy Sets and Systems,1993,59 (3):271～279
[58]孙增沂,张再兴,邓志东.智能控制理论与技术.北京：清华大学出版社,1997
[59]Chao C T, Chen Y J, Teng C C. Simplification of Fuzzy-Neural System Using Similarity Analysis. IEEE Trans. on Systems, Man and Cybernetics-Part B:Cybernetics, 1996,26(3):344～354
[60]周志坚,毛宗源.一种最优模糊神经网络控制器.控制与决策,2000,15(3)：358～361
[61]王振雷,顾树生.基于实值遗传算法的模糊神经网络辨识器.东北大学学报(自然科学版),2000,21(4)：354～356
[62]Cao S G, Rees N W. Analysis and design for a class of complex control systems, Part I:Fuzzy modeling and identification. Automatica,1997,33(11):1017～1028
[63]Takagi T, Sugeno M. A robust stabilization Problem of fuzzy control systems and its application to backing up control of truck-trailer. IEEE Trans. on Fuzzy sets,1994, 2(2):119～133
[64]Alexandra P J, Asaad Y S. Development of rainfall-runoff models using Takagi-Sugeno fuzzy inference systems. Journal of Hydrology,2006,329(1-2):154～173
[65]Dash P K, Mishra S. Damping of multimodal power system oscillations by FACTS devices using non-linear Takagi-Sugeno fuzzy controller. International Journal of Electrical Power & Energy Systems,2003,25(6):481～490
[66]Bugarin A J, Barro S. Fuzzy reasoning supported by Petri nets. IEEE Trans. Fuzzy Systems,1994,2(2):135～150
[67]王岭,焦李成.区间估计的FWNN及其区间学习算法.电子学报,1998,26(4)：41-45
[68]张志华,史罡,郑南宁等.模糊对向传播神经网络及其应用.自动化学报,2000,26(1)：56～60
[69]王益群,唐勇,姜万录等.神经网络软测量模型中全共轭梯度算法.机械工程学报,2005,41(6)：97～101
[70]Lee CW, Shin YC. Construction of fuzzy systems using least-squares method and genetic algorithm. Fuzzy Sets and Systems,2003,137(3):297～323
[71]Arnold F S. The merging of neural networks, fuzzy logic and genetic algorithms. Insurance Mathematics & Economics,2002,31(1):115～131
[72]邹恩,李祥飞,刘耦耕等.最优模糊神经网络参数的设计——混沌模拟退火学习法.中南大学学报(自然科学版),2004,35(3)：443～447
[73]史东生,弟宇鸣,周春林.粒子群优化算法在神经网络识别γ能谱中的应用.核技术,2007,30(7)：615～618
[74]王文娟,曹俊兴,张元标等.基于微粒群算法的神经网络储层物性参数预测.西南石油大学学报,2007,29(6)：31～33
[75]Zou En, Li Xiangfei, Zhang Taishan. Chaos optimization algorithm design for fuzzy neural network. Control Theory & Applications,2005,22(4):578～582
[76]Yuan K, Cao JD, Deng JM. Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing,2006, 69(13-15):1619～1627
[77]Lou XY, Cui BT. Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays. Fuzzy Sets and Systems,2007,158(24):2746～2756
[78]Niu SY, Jiang HJ, Teng ZD. Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays. Neurocomputing,2008, 71(13-15):2929～2936
[79]Ali M S, Balasubramaniam P. Exponential stability of uncertain stochastic fuzzy BAM neural networks with time-varying delays. Neurocomputing,2009,72(4-6): 1347～1354
[80]Li HY, Chen B, Lin C, et al. Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays. Neurocomputing,2009,72(7-9):2017～2023
[81]Chen B, Liu XP, Lin C, et al. Robust H-infinity control of Takagi-Sugeno fuzzy systems with state and input time delays. Fuzzy Sets and Systems,2009,160(4):403～422
[82]Feng S, Li HX, Hu D. A new training algorithm for HHFNN based on Gaussian membership function for approximation. Neurocomputing,2009,72(7-9):1631～1638
[83]Mashinchi MR, Selamat A. An improvement on genetic-based learning method for fuzzy artificial neural networks. Applied Soft Computing,2009,9(4):1208～1216
[84]Castro JR, 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
[85]Aliev RA, Guirimov BG, Fazlollahi B, et al. Evolutionary algorithm-based learning of fuzzy neural networks. Part 2:Recurrent fuzzy neural networks. Fuzzy Sets and Systems, 2009,160(17):2553～2566
[86]Zekri M, Sadri S, Sheikholeslam F. Adaptive fuzzy wavelet network control design for nonlinear systems. Fuzzy Sets and Systems,2008,159(20):2668～2695
[87]Mahmoodabadi SZ, Alirezaie J, Babyn P, et al. Wavelets and fuzzy relational classifiers:A novel spectroscopy analysis system for pediatric metabolic brain diseases. Fuzzy Sets and Systems,2010,161(1):75～95
[88]Lin CJ, Chung IF, Chen CH. An entropy-based quantum neuro-fuzzy inference system for classification applications. Neurocomputing,2007,70(13-15):2502～2516
[89]Hu YC. Fuzzy integral-based perceptron for two-class pattern classification problems. Information Sciences,2007,177(7):1673～1686
[90]Kaburlasos V G, Moussiades L, Vakali A. Fuzzy lattice reasoning (FLR) type neural computation for weighted graph partitioning; Neurocomputing,2009,72 (10-12):2121～2133
[91]Juang CF, Huang ST, Duh FB. Mold temperature control of a rubber injection-molding machine by TSK-type recurrent neural fuzzy network. Neurocomputing, 2006,70(1-3):559～567
[92]Leu YG, Wang WY, Li IH. RGA-based on-line tuning of BMF fuzzy-neural networks for adaptive control of uncertain nonlinear systems. Neurocomputing,2009, 72(10-12):2636～2642
[93]Khashei M, Hejazi SR, Bijari M. A new hybrid artificial neural networks and fuzzy regression model for time series forecasting. Fuzzy Sets and Systems,2008,159(7):769 ～786
[94]Baruch IS, Lopez RB, Guzman JLO, et al. A fuzzy-neural multi-model for nonlinear systems identification and control. Fuzzy Sets and Systems,2008,159(20):2650～2667
[95]Abdukhalikov K S, Kim C. Fuzzy neurons and fuzzy multi-linear mappings. Proc. IEEE Internat. Conf. on Neural Networks,1997:543～547
[96]梁怡,张文修.模糊规则的谐调度与矛盾规则的排除算法.计算机学报,1997,20(10)：949-952
[97]Ying MingSheng. Perturbation of fuzzy reasoning. IEEE Transactions on Fuzzy Systems,1999,7(5):625～629
[98]袁和军,李骏.模糊推理的摄动性.模糊系统与数学,2001,15(4)：8～13
[99]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)：1700～1707
[100]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和控制.计算机学报,2006,29(2)：337～344
[101]Chunmei He, Youpei Ye, Weihong Xu. Research on Perturbation of Training Pattern Pairs on Monolithic Fuzzy Neural Networks. Journal of Information Computational Science,2007,4(3):905～911
[102]何春梅,叶有培,徐蔚鸿.训练模式对的摄动对单体模糊神经网络的影响.南京理工大学学报(自科版),2009,33(1)：12～15
[103]Burton R M, Dehling H G. Universal approximation in p-mean by neural networks. Neural Networks,1998,11(4):661～667
[104]Carozza M, Rampone S. Function approximation from noise data by an incremental RBF network. Patten Recognition,1999,32:2081～2087
[105]Chen T P, Chen H, Liu R W. Approximation capability in C((?)) by multilayer feedforward networks and related problems. IEEE Trans. on Neural Networks,1995,6(1): 25～30
[106]陈天平,梁源.神经网络计算输入定义在全空间上的动力系统输出能力.中国科学(E辑),1998,28(4)：338～349
[107]Gelenbe E, Mao ZH, Li YD. Function approximation with spiked random networks. IEEE Transaction on Neural Networks,1999,10(1):3～9
[108]Haykin S. Neural Networks, A comprehensive foundation. New York:IEEE Press, 1993
[109]Scarselli F, Tsoi A C. Universal approximation using feedforward neural networks: a survey of some existing methods, and some new results. Neural Networks,1998, 11(1):15～37
[110]Tsoi A C, Tan S. Recurrent neural networks:A constructive algorithm, and its-properties. Neurocomputing,1997,15(3-4):309～326
[111]Castleman K R. Digital image processing. Beijing:Tsinghua University Press, Prentice Hall, Inc..1998
[112]陈天平.神经网络系统辨识中的近似问题.中国科学(A辑),1994,37(4)：414～422
[113]Tomandl D, Schober A. A modified general regression neural network (MGRNN) with new, efficient training algorithms as a robust'black box'-tool for data analysis. Neural Networks,2001,14(8):1023～1034
[114]陆金桂,余俊,王浩.基于人工神经网络的结构近似分析研究.中国科学(A辑), 1994,24(6):653～658
[115]Buckley J J, Hayashi Y. Can fuzzy neural nets approximate continuous fuzzy functions? Fuzzy Sets and Systems,1994,61(1):43～52
[116]Buckley J J, Hayashi Y. Can neural nets be universal approximators for fuzzy functions? Fuzzy Sets and Systems,1999,101(3):323～330
[117]Dai Y, Han J, Liu G, et al. Convergence properties of nonlinear conjugate gradient algorithms. SIAM Journal on Optimization,1999,10:345～358
[118]Liu Puyin. Fuzzy valued functions approximated arbitrarily close by a class of regular fuzzy neural networks. Journal of Fuzzy Mathematics,1999,7(4):826～837
[119]刘普寅,王华兴.正则模糊神经网络对一类连续模糊值函数的普遍近似性.电子学报,1997,25(11)：48～52
[120]Puyin Liu. Analyses of regular fuzzy neural networks for approximation capabilities. Fuzzy Sets and Systems,2000,114(2):329～338
[121]Liu Puyin. Feedforward fuzzy neural networks can be the universal approximators for fuzzy valued functions. Proc.7th European Congress on Intelligent Techniques and Soft Computing,1999:13～16
[122]Liu Puyin. Universal approximations of continuous fuzzy valued functions by multi-layer regular fuzzy neural networks. Fuzzy Sets and Systems,2001,119(2):313～320
[123]Liu Puyin. On the approximation realization of fuzzy closure mapping by multilayer regular fuzzy neural network. Multiple Valued Logic,2000,5:463～480
[124]Feuring T, Lippe W M. The fuzzy neural network approximation lemma. Fuzzy Sets and Systems,1999,102(2):227～237
[125]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
[126]Puyin Liu. Universal approximation of continuous fuzzy-valued functions by multi-layer regular fuzzy neural networks. Fuzzy Sets and Systems,2001,119(2):313～320
[127]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
[128]Puyin Liu, Hongxing Li. Approximation analysis of feedforward regular fuzzy neural networks with two hidden layers. Fuzzy Sets and Systems,2005,150(2):373～396
[129]Puyin Liu. Approximation capabilities of Multilayer feedforward regular fuzzy neural networks. Appl.Math. J. Chinese Univ. Ser. B,2001,16 (1):45～57
[130]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
[131]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
[132]何春梅,叶有培,李健,徐蔚鸿.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
[133]Buckley J J, Hayashi Y. Fuzzy neural networks:a survey. Fuzzy Sets and Systems, 1994,66(1):1～13
[134]Ishibuchi H, Fujioka R, Tanaka H. Neural networks that learn from fuzzy if-then rules. IEEE Transaction on Fuzzy Systems,1993,1:85～97
[135]Dunyak J, Wunsch D. A training technique for fuzzy number neural networks. Proc.IEEE Intenrat.Conf.on Neural Network,1997:533～536
[136]Dunyak J, Wunsch D. Training fuzzy number neural networks with alpha-cut refinements. Proc.IEEE Intenrat.Conf.on systems, Man, cybernet,1997:189～194
[137]Feuring T. Learning in fuzzy neural networks. Proc.IEEE Intenrat.Conf.on Neural Networks,1996:1061～1066
[138]Feuring T, Lippe W M. A goodness-function for trained fuzzy neural networks. Proc.IEEE Intenrat.Conf.on Neural Networks,1995:2264～2269
[139]Hayashi Y, Buckley J J, Czogala E. Fuzzy neural network with fuzzy signals and weights. Intenrat Journal of Intelligent Systems,1993,8(4):527～537
[140]Ishibuchi H, Kwon K, Tanaka H A. Learning algorithm of fuzzy neural networks with triangular fuzzy weights. Fuzzy sets and Systems,1995,71(3):277～293
[141]Ishibuchi H, Morioka K, Turksen I B. Learning by fuzzified neural networks. Internat. Journal of Approximation Reasoning,1995,13(4):327～358
[142]Ishibuchi H, Nii M. Numerical analysis of the learning of fuzzified neural networks from fuzzy if-then rules. Fuzzy Sets and Systems,2001,120(2):281～307
[143]Park S, Han T. Iterative inversion of fuzzified neural networks. IEEE Transaction on Fuzzy Systems,2000,8(3):266～280
[144]Aliev R A. Genetic algorithm-based learning of fuzzy neural network. Part 1: feed-forward fuzzy neural networks. Fuzzy Sets and Systems,2001,118(2):351～358
[145]Krishnamraju P V, Buckley J J, Reilly K D, et al. Genetic learning algorithms for fuzzy neural nets. Proc.IEEE Intenrat.Conf.on Fuzzy Systems,1994:1969～1974
[146]Maniezzo V. Genetic evolution of the topology and weight distribution of neural networks. IEEE Transaction on Neural Networks,1994,5(1):39～53
[147]Rudolph G. Convergence analysis of canonical genetic algorithms. IEEE Transaction on Neural Networks,1994,5(1):96～101
[148]Wang C C, Chen C C.A GA-based method for constructing fuzzy systems directly from numerical data. IEEE Transaction on Systems, Man and Cybenret, Part B,2000, 30(6):904～911
[149]李祥飞,邹恩,张泰山.一种新型的混沌BP混合学习算法.中南工业大学学报(自然科学版),2003,34(5)：540～542
[150]Ishibuchi H, Nii M, Oh C H. Approximate realization of fuzzy mapping by regression models, neural networks and rule-based systems. Proc.IEEE Intenrat.Conf.on Fuzzy Systems,1999:939～944
[151]Linden A, Kindermann J. Inversion of multilayer nets. Porc.Intenrat.Joint Conf.on Neural Networks,1989:425～430
[152]Puyin Liu, Hongxing Li. Efficient learning algorithms for three-layer regular feedforward fuzzy neural networks. IEEE Transaction on Neural Networks,2004, 15(3):545～558
[153]刘普寅.模糊神经网络理论及应用研究.北京师范大学数学研究所,2002
[154]Hey T. Quantum computing:An introduction. Computing & Control Engineering Journal,1996,10(3):105～112
[155]Narayanan A. An introductory tutorial to quantum computing. Proc. of IEEE Colloquium on Quantum Computing:Theory, Applications and Implications. London: IEEE Press,1997:1～3
[156]杨俊安,庄镇泉,史亮.多宇宙并行量子遗传算法.电子学报,2004,32(6)：923～928
[157]Narayanan A, Moore M. Quantum inspired genetic algorithm. Proc. of IEEE International Conference on Evolutionary Computation. Piscataway:IEEE Press,1996: 61～66
[158]Han K H, Kim J H. Genetic quantum algorithm and its application to combinatorial optimization problems. Proc. of IEEE Conference on Evolutionary Computation. Piscataway:IEEE Press,2000:1354～1360
[159]Han K H, Park K H, et al. Parallel quantum-inspired genetic algorithm for combinatorial optimization problems. Proc. of the IEEE Conference on Evolutionary Computation. Piscataway:IEEE Press,2001:1442～1429
[160]张葛祥,李娜,金炜东等.一种新量子遗传算法及其应用.电子学报,2004,32(3)：476～479
[161]李士勇,李盼池.基于实数编码和目标函数梯度的量子遗传算法.哈尔滨工业大学学报,2006,38(8)：1216～1218
[162]李士勇,李盼池,袁丽英.量子遗传算法及在模糊控制器参数优化中的应用.系统工程与电子技术,2007,29(7)：1134～1138
[163]李士勇,李盼池.基于量子遗传算法的正规模糊神经网络控制器设计.系统仿真学报,2007,19(16)：3710～3714
[164]王振峰,靳东明,李志坚.模糊逻辑神经网络及其智能学习研究.神经网络及应用——94'最新进展,武汉：华中理工大学出版社,1994
[165]Wang Z F, Jin D M, Li Z J. The intelligent controller based on fuzzy logic neural networks(FLNNs). Int.Conf.in Neural Information,1994:1163～1169
[166]王振峰,靳东明,李志坚.单体模糊神经网络：在智能控制中的应用及VLSI实现.电子学报,1997,25(5)：79～85
[167]王振峰.单体模糊神经网络自学习问题研究.北京：清华大学出版社,1995
[168]王振峰,靳东明,李志坚.单体模糊神经网络智能控制系统及其VLSI研究.电子学报,1997,25(2)：33～38
[169]朱晓铭,王士同.单体模糊神经网络的学习规则及其收敛性研究.计算机研究与发展,2001,38(9)：1057～1060
[170]梁久祯,何新贵,黄德双.关于单体模糊神经网络感知机收敛定理的讨论.电子学报,2002,30(3):407～409
[171]梁久祯,何新贵.单体模糊神经网络的函数逼近能力.计算机研究与发展,2000,37(9)：1045～1049
[172]Diamond P, Kloeden P. Metric Spaces of Fuzzy Sets. Singapore:World Scientific Press,1994
[173]Dick S, Kandel A. Comment on Combinatorial rule explosion eliminated by a fuzzy rule configuration. IEEE Transaction on Fuzzy Systems,1999,7(4):475～477
[174]Chen S H. Operations of fuzzy numbers with step form membership function using function principle. Information Sciences,1998,108(1-4):140～155
[175]Diamond P, Kloeden P. Characterization of compact subsets of fuzzy sets. Fuzzy Sets and Systems,1989,29(3):341～348
[176]Giachetti R E,Young R E. Analysis of the error in the standard approximation used for multiplication of triangular and trapezoidal fuzzy numbers and the development of a new approximation. Fuzzy Sets and Systems,1997,91 (1):1～13
[177]Aytar S, Pehlivan S, Mammadov MA. The core of a sequence of fuzzy numbers. Fuzzy Sets and Systems,2008,159(24):3369～3379
[178]刘普寅,吴孟达.模糊理论及其应用.长沙：国防科技大学出版社,1998
[179]Saeidifar A, Pasha E. The possibilistic moments of fuzzy numbers and their applications. Journal of Computational and Applied Mathematics,2009,223(2):1028～1042
[180]Chi-Chi Chen, Hui-Chin Tang. Ranking non-normal p-norm trapezoidal fuzzy numbers with integral value. Computers and Mathematics with Applications,2008,56: 2340～2346
[181]Chen SM, Chen JH. Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number arithmetic operators. Expert Systems with Applications,2009,36(3):6309～6317
[182]Gokhan A, Et M, Mursaleen M. Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers. Mathematical and Computer Modelling,2009,49(3-4):548～555
[183]Abbasbandy S, Hajjari T. A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications,2009,57(3):413～419
[184]Rong M, Mahapatra NK, Maiti M. A multi-objective wholesaler-retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number. Applied Mathematical Modelling,2008,32(12):2670～2685
[185]Mesiar R, Fuller R. Special issue-Fuzzy arithmetic-Foreword. Fuzzy Sets and Systems,1997,91(2):135～136
[186]Buckley J J, Hayashi Y. Fuzzy input-output controllers are universal approximators. Fuzzy Sets and Systems,1993,58(3):273～278
[187]Feuring T, Buckley J J, Hayashi Y. Fuzzy neural nets can solve the over fitting problem. Proc. Internat. Joint Conf. Neural Networks,1999:4197～4201
[188]Arakawa K. Median filter based on fuzzy rules and its application to image processing. Fuzzy Sets and Systems,1996,77(1):3～13
[189]Cai K Y. Introduction to Fuzzy Reliability. London:Kluwer Academic Publishers, 1996
[190]Gerla G, Scarpati L. Extension principles for fuzzy set theory. Information Sciences,1998,106(1-2):49～69
[191]毛志宏,张雪枫,张衍达.模糊系统作为通用函数逼近器的研究.中国科学,E辑,1997,27(4)：362～371
[192]Alefeld G, Herzberger J. Introduction to Interval Computations. New York: Academic Press,1983
[193]Bagley J D. The Behavior of Adaptive system which Employ Genetic and Correlation Algorithm. Dissertation Abstracts Inrernational,1967
[194]Holland J H. Adaptation in Nature and Artificial Systems. USA:MIT Press,1992
[195]Holland J H, Reitman J S. Cognitive Systems Based on Adaptive Algorithms. In: Waterman D A, Hays-Roth F Eds, Pattern Directed Inference Systems, New York: Academics Press,1978:313～329
[196]De Jong. Analysis of the Behavior of a class of genetic adaptive systems. Department of Computer and Communication Science, University of Michigan, Ann Arbor, 1975
[197]Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley Publishing Company,1989
[198]Davis L D, Handbook of Genetic Algorithms. Van Nostrand Reinhold,1991
[199]Koza J R. Genetic Programming, on the Programming of Computers by Means of Natural Selection, USA:MIT Press,1992
[200]Koza J R. Genetic Programming Ⅱ. Automatic Discovery of Reusable Programs, USA:MIT Press,1994
[201]Cordon O, Gomide F, Herrera F, et al. Ten years of genetic fuzzy systems:current framework and new trends. Fuzzy Sets and Systems,2004,141(1):5～31
[202]Wenhua Tao. Fuzzy neural network control of truck backer-upper using hybrid genetic algorithms.Proceedings of the International Conference on Information Acquisition, 2004:9～12
[203]ChengJian Lin. A GA-based neural fuzzy system for temperature control. Fuzzy Sets and System,2004,143(2):311～333
[204]Stoico CO, Renzi DG, Vericat F. A genetic algorithm for the 1D electron gas. Physica A-Statistical Mechanics And Its Applications,2008,387(1):159～166
[205]Dae-Jin Kim, Sang-Wan Lee, Zeungnam Bien. Facial Emotional Expression Recognition with Soft Computing Techniques. IEEE International Workshop on Robots and Human Interactive Communication,2005:661～666
[206]Hefny HA, Bahnasawi AA, Wahab AHA, et al. Logical radial basis function networks a hybrid intelligent model for function approximation. Advances in Engineering Software,1999,30(6):407～417
[207]Neggaz N, Benyettou A. Hybrid models based on biological approaches for speech recognition. Artificial Intelligence Review,2009,34(1-4):45～57
[208]Perrot N, Me L, Trystram G, et al. Optimal control of the microfiltration of sugar product using a controller combining fuzzy and genetic approaches. Fuzzy Sets and Systems,1998,94(3):309～322
[209]Chen LH, Chiang CH. New Approach to Intelligent Control Systems With Self-Exploring Process. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics,2003,33(1):56～66
[210]彭金柱,胡耀南,孙炜.基于混合学习算法的模糊小波神经网络控制.湖南大学学报(自然科学版),2006,33(2)：51～54
[211]Yu LX, Zhang YQ. Evolutionary Fuzzy Neural Networks for Hybrid Financial Prediction. IEEE Transactions on Systems, Man, and Cybernetics-Part C:Applications and Reviews,2005,35(2):244～249
[212]Turkmen I, Guney K. Genetic tracker with adaptive neuro-fuzzy inference system for multiple target tracking. Expert Systems with Applications,2008,35(4):1657～1667
[213]周明,孙树栋.遗传算法原理及其应用.第一版.北京：国防工业出版社,1999
[214]Narayanan A. Quantum computing for beginners. Proc of the 1999 Congress on Evolutionary Computation. Piscataway:IEEE Press,1999:2231～2238
[215]Yang Junan, Li Bin, Zhuang Zhenquan. Research of quantum genetic algorithm and its application in blind source separation. Journal of Electronics(China),2003, 20(1):62～68
[216]Panchi Li, Shiyong Li. Quantum-inspired evolutionary algorithms for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing,2008, 1(4):1～11
[217]Vlachogiannis JG, Ostergaard J. Reactive power and voltage control based on general quantum genetic algorithms. Expert Systems with Applications,2009,36(3): 6118-6126
[218]张葛祥,金炜东,胡来招.基于量子遗传算法的特征选择算法.控制理论与应用,2005,22(5)：810～819
[219]Jang J S R, Sun C T, Mizutani E. Neuro-fuzzy and soft computing. Prentice Hall, 1997
[220]Chen Hui, Zhang Jiashu, Zhang Chao, et al. Chaos updating rotated gates quantum-inspired genetic algorithm. International Conference on Communications Circuits and Systems. Chengdu:IEEE Press,2004:108～112
[221]周殊,潘炜,罗斌.一种基于粒子群优化方法的改进量子遗传算法及应用.电子学报,2006,34(5)：897～901
[222]Grover L. Quantum computing. Proc of the 12 th Int Conf on VLSI Design. Piscataway:IEEE Press,1999:548～553
[223]Simon Haykin著,叶世伟,史忠植译.神经网络原理(Neural Networks).第二版.北京：机械工业出版社,2004
[224]Saarinen S, Bramley R B, Cybenko G. Neural networks, back-propagation, and automatic differentiation, automatic Differentiation of Algorithms:Theory, Implementation, and Application, A. Grienwank and G.F. Corliss, eds, Philadelphial:SIAM,31～42
[225]Fletcher R. Practical Methods of Optimization.2nd edition, New York:Wiley,1987
[226]Luenberger D G. Linear and nonlinear programming.2nd edition, Reading, MA: Addison-Wesley,1984
[227]Bertsekas D P. Dynamic Programming and Optimal Control. Belmont, MA:Athenas Sicentific,1995,
[228]Bertsekas D P. Nonlinear Programming. Belmont, MA:Athenas Scientific,1995
[229]Dubios D, Prade H, Testemale C. Weighted fuzzy pattern matching. Fuzzy Sets and Systems,1988,28(3):313～331
[230]Shewchuk J R. An introduction to the conjugate gradient method without the agonizing pain. School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1994
[231]Moller M F. A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks,1993,6(4):525～534
[2]斯洛廷,李卫平.应用非线性系统.北京：国防工业出版社,1989
[3]卢强,孙元章.电力系统非线性控制.北京：科学出版社,1993
[4]陈予恕,唐云.非线性动力学中的现代分析方法.北京：科学出版社,1992
[5]Zadeh L A. Fuzzy logic,neural networks and soft computing. One-page Course Announcement of CS-the University of Califonria at Berkeley,1993,294
[6]王立新.自适应模糊系统与控制——设计与稳定性分析.北京：国防工业出版社,1995
[7]Horikawa S, Furuhashi T, Uchikawa Y. On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm. IEEE Trans.on Neural Networks,1992, 3(5):801～806.
[8]刘普寅,张维民.通信网络可靠性研究中的数学问题.通信学报,2000,21(10)：50～57
[9]Deng XS, Wang XZ. Incremental learning of dynamic fuzzy neural networks for accurate system modeling. Fuzzy Sets and Systems,2009,160(7):972～987
[10]Gobi AF, Pedrycz W. The potential of fuzzy neural networks in the realization of approximate reasoning engines. Fuzzy Sets and Systems,2006,157(22):2954～2973
[11]Juang CF, Chen TM. Birdsong recognition using prediction-based recurrent neural fuzzy networks. Neurocomputing,2007,71(1-3):121～130
[12]Brouwer R K. A fuzzy recurrent artificial neural network(FRANN) for pattern classification. International Journal of Uncertain,Fuzziness and Knowledge-Based Systems, 2000,8(5):525～538
[13]Juang CF, Chen LT. Moving object recognition by a shape-based neural fuzzy network. Neurocomputing,2008,71(13-15):2937～2949
[14]SimpsonP K. FuzzyMin-Max neural networks.2.clustering. IEEE Trans.Fuzzy Systems,1993,1:32～45
[15]Singh M, Srivastava S, Hanmandlu M, et al. Type-2 fuzzy wavelet networks (T2FWN) for system identification using fuzzy differential and Lyapunov stability algorithm. Applied Soft Computing,2009,9(3):977～989
[16]Zadeh LA. Fuzzy Set. Information and Control,1965,8(3):338～358
[17]Mamanadi E H. Application of fuzzy algorithms of simple dynamic plant. In Proc. IEEE,1974,121(12):1585～1588
[18]McCulloch W S, Pitts W. A logic calculus of the ideas imminent in neurons activity. Bulletin of Mathematics Biology,1943,5:115～133
[19]Hebb D 0. The organization of behavior. Wiley, New York,1949
[20]Rosenblatt F. Principles of neuro dynamics. New York, Spartan Book,1962
[21]Hopfield J J. Neural networks and Physical system with emergent collective computational abilities. Proc. Acad. Sci., USA,1982,79:2554～2558
[22]Hinton G E, Sejnowski T J, Ackley D H. Boltzmann machine:constraint satisfaction networks that learn. CM-VCS-84-119, Carneie-Mellon University,1984
[23]Ackley D H, Hinton G E, Sejnowski T J. A Learning algorithm for Boltzmann machines. Cognitive Science,1985,9(1):147～169
[24]Rumelhart D E, McClelland J L. Parallel Distributed Processing. USA:MIT Press, 1986
[25]王振雷.模糊神经网络理论及其在复杂系统中的应用研究.沈阳：东北大学,2002
[26]Gupta M M, Rao D H. On the principle of fuzzy neural networks. Fuzzy Sets and Systems,1994,61(1):1～18
[27]Hornik K, Stinchcombe M, White H. Multiplayer feedforward networks are universal approximator. Neural Computing,1990,2:210～215
[28]Kosko B. Fuzzy systems as universal approximators. IEEE Transactions on Computers.1994,43 (11):1329～1333
[29]Wang L, Mendel J. Fuzzy basis functions, approximation,and orthogonal least square learning. IEEE Trans. on Neural Network,1992,3 (5):807～814
[30]沈建强,李平.模糊神经技术的研究现状和展望.控制与决策,1996,11(5)：527～532
[31]张凯,钱锋,刘漫丹.模糊神经网络技术综述.信息与控制,2003,32(5)：431～435
[32]刘普寅,张汉江,吴孟达等.模糊神经网络理论研究综述.模糊系统与数学,1998,10(1)：77～87
[33]周春光,梁艳春.计算智能：人工神经网络、模糊系统、进化计算.吉林：吉林大学出版社,2001
[34]Wang L X. Adaptive fuzzy systems and control:design stability analysis. PTR Prentice-Hall, Englewood Cliffs, NJ,1994
[35]Nguyen H T. A note on the extension principle for fuzzy sets. Journal of Math Analysis Application,1976,64:369～380
[36]Nauck D. Neuro-fuzzy systems:review and prospects. Proc. of the 5th Europe Congress on Intelligent Techniques and Soft Computing,1997:1044～1053
[37]Lee S C, Lee E T. Fuzzy neural networks. Math.Biosci.,1975,23:151～177
[38]Lee S C, Lee E T. Fuzzy sets and neural networks. Cybenretics,1974,4:83～103
[39]Kosko B. Bidirectional associative memory. IEEE Transactions on System, Man and Cybernetics,1988,18(1):49～60
[40]Kosko B. Bidirectional associative memory in fuzzy expert systems. Kandel A.Ed. USA:Addison Wesley,1987
[41]Kosko B. Fuzzy associative memories. In:Kandel A(ed):Fuzzy Expert Systems Reading. MA, USA:Addison Wesley,1987
[42]Jang S R. ANFIS:Adaptive-network-based fuzzy inference systems. IEEE Trans, on Systems, Man & Cybernetics,1993,23(3):665～685
[43]Pedrycz W. Genetic tolerance fuzzy neural networks:From data to fuzzy hyperboxes. Neurocomputing,2007,70(7-9):1403～1413
[44]Konar A, Chakraborty U K, Wang P P. Supervised learning on a fuzzy Petri net. Information Sciences,2005,172(3-4):397～416
[45]Mastorocostas P A, Theocharis J B. An orthogonal least-squares method for recurrent fuzzy-neural modeling. Fuzzy Sets and Systems,2003,140(2):285～300
[46]Juang CF, Chung IF. Recurrent fuzzy network design using hybrid evolutionary learning algorithms. Neurocomputing,2007,70(16-18):3001～3010
[47]Leng G, Prasad G, McGinnity TM. An on-line algorithm for creating self-organizing fuzzy neural networks. Neural Networks,2004,17(14):1477～1493
[48]Carpenter G A, et al. Fuzzy ART:fast stable learning and categorization of analog pattern by an adaptive resonance system. Neural Networks,1991,4(5):759～771
[49]Pal S K, Mitra S. Multilayer perceptron, fuzzy sets and classification. IEEE Trans. Neural Networks,1992,3(5):698～713
[50]Jou C C.A fuzzy cerebella model articulation controller. Proc. IEEE Int. Conf. Fuzzy Sets.1992:1171～1178
[51]Kosko B. Neural Networks and Fuzzy Systems:A Dyhamical Systems Approach to Machine Intelligence. NJ:Prentice Hall Inc,1992
[52]Pedrcy W, Roeha A F. Fuzzy-Set based models of neurons and knowledge-based networks. IEEE Trans. on Fuzzy System,1993,1(4):254～266
[53]Simpson P K. Fuzzy min-max neural networks-Part 1:Classification. IEEE Trans. Neural Networks,1992,3(5):776～786
[54]Wang L X, Mendel J M. Fuzzy basis functions, universal approximation and orthogonal least squares learning. IEEE Trans. on Neural Networks,1992,3(5):807～814
[55]Wang XS, Cheng YH, Yi JQ. A fuzzy Actor-Critic reinforcement learning network. Information science,2007,177(18):3764～3781
[56]Pedrcyz W, Rocha A F. Fuzzy-set based models of neurons and knowledge-based networks. IEEE Trans. on Fuzzy System,1993,1(4):254～266
[57]Hirota K, Pedrycz W. Knowledge-based networks in classification problems. Fuzzy Sets and Systems,1993,59 (3):271～279
[58]孙增沂,张再兴,邓志东.智能控制理论与技术.北京：清华大学出版社,1997
[59]Chao C T, Chen Y J, Teng C C. Simplification of Fuzzy-Neural System Using Similarity Analysis. IEEE Trans. on Systems, Man and Cybernetics-Part B:Cybernetics, 1996,26(3):344～354
[60]周志坚,毛宗源.一种最优模糊神经网络控制器.控制与决策,2000,15(3)：358～361
[61]王振雷,顾树生.基于实值遗传算法的模糊神经网络辨识器.东北大学学报(自然科学版),2000,21(4)：354～356
[62]Cao S G, Rees N W. Analysis and design for a class of complex control systems, Part I:Fuzzy modeling and identification. Automatica,1997,33(11):1017～1028
[63]Takagi T, Sugeno M. A robust stabilization Problem of fuzzy control systems and its application to backing up control of truck-trailer. IEEE Trans. on Fuzzy sets,1994, 2(2):119～133
[64]Alexandra P J, Asaad Y S. Development of rainfall-runoff models using Takagi-Sugeno fuzzy inference systems. Journal of Hydrology,2006,329(1-2):154～173
[65]Dash P K, Mishra S. Damping of multimodal power system oscillations by FACTS devices using non-linear Takagi-Sugeno fuzzy controller. International Journal of Electrical Power & Energy Systems,2003,25(6):481～490
[66]Bugarin A J, Barro S. Fuzzy reasoning supported by Petri nets. IEEE Trans. Fuzzy Systems,1994,2(2):135～150
[67]王岭,焦李成.区间估计的FWNN及其区间学习算法.电子学报,1998,26(4)：41-45
[68]张志华,史罡,郑南宁等.模糊对向传播神经网络及其应用.自动化学报,2000,26(1)：56～60
[69]王益群,唐勇,姜万录等.神经网络软测量模型中全共轭梯度算法.机械工程学报,2005,41(6)：97～101
[70]Lee CW, Shin YC. Construction of fuzzy systems using least-squares method and genetic algorithm. Fuzzy Sets and Systems,2003,137(3):297～323
[71]Arnold F S. The merging of neural networks, fuzzy logic and genetic algorithms. Insurance Mathematics & Economics,2002,31(1):115～131
[72]邹恩,李祥飞,刘耦耕等.最优模糊神经网络参数的设计——混沌模拟退火学习法.中南大学学报(自然科学版),2004,35(3)：443～447
[73]史东生,弟宇鸣,周春林.粒子群优化算法在神经网络识别γ能谱中的应用.核技术,2007,30(7)：615～618
[74]王文娟,曹俊兴,张元标等.基于微粒群算法的神经网络储层物性参数预测.西南石油大学学报,2007,29(6)：31～33
[75]Zou En, Li Xiangfei, Zhang Taishan. Chaos optimization algorithm design for fuzzy neural network. Control Theory & Applications,2005,22(4):578～582
[76]Yuan K, Cao JD, Deng JM. Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing,2006, 69(13-15):1619～1627
[77]Lou XY, Cui BT. Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays. Fuzzy Sets and Systems,2007,158(24):2746～2756
[78]Niu SY, Jiang HJ, Teng ZD. Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays. Neurocomputing,2008, 71(13-15):2929～2936
[79]Ali M S, Balasubramaniam P. Exponential stability of uncertain stochastic fuzzy BAM neural networks with time-varying delays. Neurocomputing,2009,72(4-6): 1347～1354
[80]Li HY, Chen B, Lin C, et al. Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays. Neurocomputing,2009,72(7-9):2017～2023
[81]Chen B, Liu XP, Lin C, et al. Robust H-infinity control of Takagi-Sugeno fuzzy systems with state and input time delays. Fuzzy Sets and Systems,2009,160(4):403～422
[82]Feng S, Li HX, Hu D. A new training algorithm for HHFNN based on Gaussian membership function for approximation. Neurocomputing,2009,72(7-9):1631～1638
[83]Mashinchi MR, Selamat A. An improvement on genetic-based learning method for fuzzy artificial neural networks. Applied Soft Computing,2009,9(4):1208～1216
[84]Castro JR, 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
[85]Aliev RA, Guirimov BG, Fazlollahi B, et al. Evolutionary algorithm-based learning of fuzzy neural networks. Part 2:Recurrent fuzzy neural networks. Fuzzy Sets and Systems, 2009,160(17):2553～2566
[86]Zekri M, Sadri S, Sheikholeslam F. Adaptive fuzzy wavelet network control design for nonlinear systems. Fuzzy Sets and Systems,2008,159(20):2668～2695
[87]Mahmoodabadi SZ, Alirezaie J, Babyn P, et al. Wavelets and fuzzy relational classifiers:A novel spectroscopy analysis system for pediatric metabolic brain diseases. Fuzzy Sets and Systems,2010,161(1):75～95
[88]Lin CJ, Chung IF, Chen CH. An entropy-based quantum neuro-fuzzy inference system for classification applications. Neurocomputing,2007,70(13-15):2502～2516
[89]Hu YC. Fuzzy integral-based perceptron for two-class pattern classification problems. Information Sciences,2007,177(7):1673～1686
[90]Kaburlasos V G, Moussiades L, Vakali A. Fuzzy lattice reasoning (FLR) type neural computation for weighted graph partitioning; Neurocomputing,2009,72 (10-12):2121～2133
[91]Juang CF, Huang ST, Duh FB. Mold temperature control of a rubber injection-molding machine by TSK-type recurrent neural fuzzy network. Neurocomputing, 2006,70(1-3):559～567
[92]Leu YG, Wang WY, Li IH. RGA-based on-line tuning of BMF fuzzy-neural networks for adaptive control of uncertain nonlinear systems. Neurocomputing,2009, 72(10-12):2636～2642
[93]Khashei M, Hejazi SR, Bijari M. A new hybrid artificial neural networks and fuzzy regression model for time series forecasting. Fuzzy Sets and Systems,2008,159(7):769 ～786
[94]Baruch IS, Lopez RB, Guzman JLO, et al. A fuzzy-neural multi-model for nonlinear systems identification and control. Fuzzy Sets and Systems,2008,159(20):2650～2667
[95]Abdukhalikov K S, Kim C. Fuzzy neurons and fuzzy multi-linear mappings. Proc. IEEE Internat. Conf. on Neural Networks,1997:543～547
[96]梁怡,张文修.模糊规则的谐调度与矛盾规则的排除算法.计算机学报,1997,20(10)：949-952
[97]Ying MingSheng. Perturbation of fuzzy reasoning. IEEE Transactions on Fuzzy Systems,1999,7(5):625～629
[98]袁和军,李骏.模糊推理的摄动性.模糊系统与数学,2001,15(4)：8～13
[99]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)：1700～1707
[100]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和控制.计算机学报,2006,29(2)：337～344
[101]Chunmei He, Youpei Ye, Weihong Xu. Research on Perturbation of Training Pattern Pairs on Monolithic Fuzzy Neural Networks. Journal of Information Computational Science,2007,4(3):905～911
[102]何春梅,叶有培,徐蔚鸿.训练模式对的摄动对单体模糊神经网络的影响.南京理工大学学报(自科版),2009,33(1)：12～15
[103]Burton R M, Dehling H G. Universal approximation in p-mean by neural networks. Neural Networks,1998,11(4):661～667
[104]Carozza M, Rampone S. Function approximation from noise data by an incremental RBF network. Patten Recognition,1999,32:2081～2087
[105]Chen T P, Chen H, Liu R W. Approximation capability in C((?)) by multilayer feedforward networks and related problems. IEEE Trans. on Neural Networks,1995,6(1): 25～30
[106]陈天平,梁源.神经网络计算输入定义在全空间上的动力系统输出能力.中国科学(E辑),1998,28(4)：338～349
[107]Gelenbe E, Mao ZH, Li YD. Function approximation with spiked random networks. IEEE Transaction on Neural Networks,1999,10(1):3～9
[108]Haykin S. Neural Networks, A comprehensive foundation. New York:IEEE Press, 1993
[109]Scarselli F, Tsoi A C. Universal approximation using feedforward neural networks: a survey of some existing methods, and some new results. Neural Networks,1998, 11(1):15～37
[110]Tsoi A C, Tan S. Recurrent neural networks:A constructive algorithm, and its-properties. Neurocomputing,1997,15(3-4):309～326
[111]Castleman K R. Digital image processing. Beijing:Tsinghua University Press, Prentice Hall, Inc..1998
[112]陈天平.神经网络系统辨识中的近似问题.中国科学(A辑),1994,37(4)：414～422
[113]Tomandl D, Schober A. A modified general regression neural network (MGRNN) with new, efficient training algorithms as a robust'black box'-tool for data analysis. Neural Networks,2001,14(8):1023～1034
[114]陆金桂,余俊,王浩.基于人工神经网络的结构近似分析研究.中国科学(A辑), 1994,24(6):653～658
[115]Buckley J J, Hayashi Y. Can fuzzy neural nets approximate continuous fuzzy functions? Fuzzy Sets and Systems,1994,61(1):43～52
[116]Buckley J J, Hayashi Y. Can neural nets be universal approximators for fuzzy functions? Fuzzy Sets and Systems,1999,101(3):323～330
[117]Dai Y, Han J, Liu G, et al. Convergence properties of nonlinear conjugate gradient algorithms. SIAM Journal on Optimization,1999,10:345～358
[118]Liu Puyin. Fuzzy valued functions approximated arbitrarily close by a class of regular fuzzy neural networks. Journal of Fuzzy Mathematics,1999,7(4):826～837
[119]刘普寅,王华兴.正则模糊神经网络对一类连续模糊值函数的普遍近似性.电子学报,1997,25(11)：48～52
[120]Puyin Liu. Analyses of regular fuzzy neural networks for approximation capabilities. Fuzzy Sets and Systems,2000,114(2):329～338
[121]Liu Puyin. Feedforward fuzzy neural networks can be the universal approximators for fuzzy valued functions. Proc.7th European Congress on Intelligent Techniques and Soft Computing,1999:13～16
[122]Liu Puyin. Universal approximations of continuous fuzzy valued functions by multi-layer regular fuzzy neural networks. Fuzzy Sets and Systems,2001,119(2):313～320
[123]Liu Puyin. On the approximation realization of fuzzy closure mapping by multilayer regular fuzzy neural network. Multiple Valued Logic,2000,5:463～480
[124]Feuring T, Lippe W M. The fuzzy neural network approximation lemma. Fuzzy Sets and Systems,1999,102(2):227～237
[125]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
[126]Puyin Liu. Universal approximation of continuous fuzzy-valued functions by multi-layer regular fuzzy neural networks. Fuzzy Sets and Systems,2001,119(2):313～320
[127]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
[128]Puyin Liu, Hongxing Li. Approximation analysis of feedforward regular fuzzy neural networks with two hidden layers. Fuzzy Sets and Systems,2005,150(2):373～396
[129]Puyin Liu. Approximation capabilities of Multilayer feedforward regular fuzzy neural networks. Appl.Math. J. Chinese Univ. Ser. B,2001,16 (1):45～57
[130]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
[131]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
[132]何春梅,叶有培,李健,徐蔚鸿.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
[133]Buckley J J, Hayashi Y. Fuzzy neural networks:a survey. Fuzzy Sets and Systems, 1994,66(1):1～13
[134]Ishibuchi H, Fujioka R, Tanaka H. Neural networks that learn from fuzzy if-then rules. IEEE Transaction on Fuzzy Systems,1993,1:85～97
[135]Dunyak J, Wunsch D. A training technique for fuzzy number neural networks. Proc.IEEE Intenrat.Conf.on Neural Network,1997:533～536
[136]Dunyak J, Wunsch D. Training fuzzy number neural networks with alpha-cut refinements. Proc.IEEE Intenrat.Conf.on systems, Man, cybernet,1997:189～194
[137]Feuring T. Learning in fuzzy neural networks. Proc.IEEE Intenrat.Conf.on Neural Networks,1996:1061～1066
[138]Feuring T, Lippe W M. A goodness-function for trained fuzzy neural networks. Proc.IEEE Intenrat.Conf.on Neural Networks,1995:2264～2269
[139]Hayashi Y, Buckley J J, Czogala E. Fuzzy neural network with fuzzy signals and weights. Intenrat Journal of Intelligent Systems,1993,8(4):527～537
[140]Ishibuchi H, Kwon K, Tanaka H A. Learning algorithm of fuzzy neural networks with triangular fuzzy weights. Fuzzy sets and Systems,1995,71(3):277～293
[141]Ishibuchi H, Morioka K, Turksen I B. Learning by fuzzified neural networks. Internat. Journal of Approximation Reasoning,1995,13(4):327～358
[142]Ishibuchi H, Nii M. Numerical analysis of the learning of fuzzified neural networks from fuzzy if-then rules. Fuzzy Sets and Systems,2001,120(2):281～307
[143]Park S, Han T. Iterative inversion of fuzzified neural networks. IEEE Transaction on Fuzzy Systems,2000,8(3):266～280
[144]Aliev R A. Genetic algorithm-based learning of fuzzy neural network. Part 1: feed-forward fuzzy neural networks. Fuzzy Sets and Systems,2001,118(2):351～358
[145]Krishnamraju P V, Buckley J J, Reilly K D, et al. Genetic learning algorithms for fuzzy neural nets. Proc.IEEE Intenrat.Conf.on Fuzzy Systems,1994:1969～1974
[146]Maniezzo V. Genetic evolution of the topology and weight distribution of neural networks. IEEE Transaction on Neural Networks,1994,5(1):39～53
[147]Rudolph G. Convergence analysis of canonical genetic algorithms. IEEE Transaction on Neural Networks,1994,5(1):96～101
[148]Wang C C, Chen C C.A GA-based method for constructing fuzzy systems directly from numerical data. IEEE Transaction on Systems, Man and Cybenret, Part B,2000, 30(6):904～911
[149]李祥飞,邹恩,张泰山.一种新型的混沌BP混合学习算法.中南工业大学学报(自然科学版),2003,34(5)：540～542
[150]Ishibuchi H, Nii M, Oh C H. Approximate realization of fuzzy mapping by regression models, neural networks and rule-based systems. Proc.IEEE Intenrat.Conf.on Fuzzy Systems,1999:939～944
[151]Linden A, Kindermann J. Inversion of multilayer nets. Porc.Intenrat.Joint Conf.on Neural Networks,1989:425～430
[152]Puyin Liu, Hongxing Li. Efficient learning algorithms for three-layer regular feedforward fuzzy neural networks. IEEE Transaction on Neural Networks,2004, 15(3):545～558
[153]刘普寅.模糊神经网络理论及应用研究.北京师范大学数学研究所,2002
[154]Hey T. Quantum computing:An introduction. Computing & Control Engineering Journal,1996,10(3):105～112
[155]Narayanan A. An introductory tutorial to quantum computing. Proc. of IEEE Colloquium on Quantum Computing:Theory, Applications and Implications. London: IEEE Press,1997:1～3
[156]杨俊安,庄镇泉,史亮.多宇宙并行量子遗传算法.电子学报,2004,32(6)：923～928
[157]Narayanan A, Moore M. Quantum inspired genetic algorithm. Proc. of IEEE International Conference on Evolutionary Computation. Piscataway:IEEE Press,1996: 61～66
[158]Han K H, Kim J H. Genetic quantum algorithm and its application to combinatorial optimization problems. Proc. of IEEE Conference on Evolutionary Computation. Piscataway:IEEE Press,2000:1354～1360
[159]Han K H, Park K H, et al. Parallel quantum-inspired genetic algorithm for combinatorial optimization problems. Proc. of the IEEE Conference on Evolutionary Computation. Piscataway:IEEE Press,2001:1442～1429
[160]张葛祥,李娜,金炜东等.一种新量子遗传算法及其应用.电子学报,2004,32(3)：476～479
[161]李士勇,李盼池.基于实数编码和目标函数梯度的量子遗传算法.哈尔滨工业大学学报,2006,38(8)：1216～1218
[162]李士勇,李盼池,袁丽英.量子遗传算法及在模糊控制器参数优化中的应用.系统工程与电子技术,2007,29(7)：1134～1138
[163]李士勇,李盼池.基于量子遗传算法的正规模糊神经网络控制器设计.系统仿真学报,2007,19(16)：3710～3714
[164]王振峰,靳东明,李志坚.模糊逻辑神经网络及其智能学习研究.神经网络及应用——94'最新进展,武汉：华中理工大学出版社,1994
[165]Wang Z F, Jin D M, Li Z J. The intelligent controller based on fuzzy logic neural networks(FLNNs). Int.Conf.in Neural Information,1994:1163～1169
[166]王振峰,靳东明,李志坚.单体模糊神经网络：在智能控制中的应用及VLSI实现.电子学报,1997,25(5)：79～85
[167]王振峰.单体模糊神经网络自学习问题研究.北京：清华大学出版社,1995
[168]王振峰,靳东明,李志坚.单体模糊神经网络智能控制系统及其VLSI研究.电子学报,1997,25(2)：33～38
[169]朱晓铭,王士同.单体模糊神经网络的学习规则及其收敛性研究.计算机研究与发展,2001,38(9)：1057～1060
[170]梁久祯,何新贵,黄德双.关于单体模糊神经网络感知机收敛定理的讨论.电子学报,2002,30(3):407～409
[171]梁久祯,何新贵.单体模糊神经网络的函数逼近能力.计算机研究与发展,2000,37(9)：1045～1049
[172]Diamond P, Kloeden P. Metric Spaces of Fuzzy Sets. Singapore:World Scientific Press,1994
[173]Dick S, Kandel A. Comment on Combinatorial rule explosion eliminated by a fuzzy rule configuration. IEEE Transaction on Fuzzy Systems,1999,7(4):475～477
[174]Chen S H. Operations of fuzzy numbers with step form membership function using function principle. Information Sciences,1998,108(1-4):140～155
[175]Diamond P, Kloeden P. Characterization of compact subsets of fuzzy sets. Fuzzy Sets and Systems,1989,29(3):341～348
[176]Giachetti R E,Young R E. Analysis of the error in the standard approximation used for multiplication of triangular and trapezoidal fuzzy numbers and the development of a new approximation. Fuzzy Sets and Systems,1997,91 (1):1～13
[177]Aytar S, Pehlivan S, Mammadov MA. The core of a sequence of fuzzy numbers. Fuzzy Sets and Systems,2008,159(24):3369～3379
[178]刘普寅,吴孟达.模糊理论及其应用.长沙：国防科技大学出版社,1998
[179]Saeidifar A, Pasha E. The possibilistic moments of fuzzy numbers and their applications. Journal of Computational and Applied Mathematics,2009,223(2):1028～1042
[180]Chi-Chi Chen, Hui-Chin Tang. Ranking non-normal p-norm trapezoidal fuzzy numbers with integral value. Computers and Mathematics with Applications,2008,56: 2340～2346
[181]Chen SM, Chen JH. Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number arithmetic operators. Expert Systems with Applications,2009,36(3):6309～6317
[182]Gokhan A, Et M, Mursaleen M. Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers. Mathematical and Computer Modelling,2009,49(3-4):548～555
[183]Abbasbandy S, Hajjari T. A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications,2009,57(3):413～419
[184]Rong M, Mahapatra NK, Maiti M. A multi-objective wholesaler-retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number. Applied Mathematical Modelling,2008,32(12):2670～2685
[185]Mesiar R, Fuller R. Special issue-Fuzzy arithmetic-Foreword. Fuzzy Sets and Systems,1997,91(2):135～136
[186]Buckley J J, Hayashi Y. Fuzzy input-output controllers are universal approximators. Fuzzy Sets and Systems,1993,58(3):273～278
[187]Feuring T, Buckley J J, Hayashi Y. Fuzzy neural nets can solve the over fitting problem. Proc. Internat. Joint Conf. Neural Networks,1999:4197～4201
[188]Arakawa K. Median filter based on fuzzy rules and its application to image processing. Fuzzy Sets and Systems,1996,77(1):3～13
[189]Cai K Y. Introduction to Fuzzy Reliability. London:Kluwer Academic Publishers, 1996
[190]Gerla G, Scarpati L. Extension principles for fuzzy set theory. Information Sciences,1998,106(1-2):49～69
[191]毛志宏,张雪枫,张衍达.模糊系统作为通用函数逼近器的研究.中国科学,E辑,1997,27(4)：362～371
[192]Alefeld G, Herzberger J. Introduction to Interval Computations. New York: Academic Press,1983
[193]Bagley J D. The Behavior of Adaptive system which Employ Genetic and Correlation Algorithm. Dissertation Abstracts Inrernational,1967
[194]Holland J H. Adaptation in Nature and Artificial Systems. USA:MIT Press,1992
[195]Holland J H, Reitman J S. Cognitive Systems Based on Adaptive Algorithms. In: Waterman D A, Hays-Roth F Eds, Pattern Directed Inference Systems, New York: Academics Press,1978:313～329
[196]De Jong. Analysis of the Behavior of a class of genetic adaptive systems. Department of Computer and Communication Science, University of Michigan, Ann Arbor, 1975
[197]Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley Publishing Company,1989
[198]Davis L D, Handbook of Genetic Algorithms. Van Nostrand Reinhold,1991
[199]Koza J R. Genetic Programming, on the Programming of Computers by Means of Natural Selection, USA:MIT Press,1992
[200]Koza J R. Genetic Programming Ⅱ. Automatic Discovery of Reusable Programs, USA:MIT Press,1994
[201]Cordon O, Gomide F, Herrera F, et al. Ten years of genetic fuzzy systems:current framework and new trends. Fuzzy Sets and Systems,2004,141(1):5～31
[202]Wenhua Tao. Fuzzy neural network control of truck backer-upper using hybrid genetic algorithms.Proceedings of the International Conference on Information Acquisition, 2004:9～12
[203]ChengJian Lin. A GA-based neural fuzzy system for temperature control. Fuzzy Sets and System,2004,143(2):311～333
[204]Stoico CO, Renzi DG, Vericat F. A genetic algorithm for the 1D electron gas. Physica A-Statistical Mechanics And Its Applications,2008,387(1):159～166
[205]Dae-Jin Kim, Sang-Wan Lee, Zeungnam Bien. Facial Emotional Expression Recognition with Soft Computing Techniques. IEEE International Workshop on Robots and Human Interactive Communication,2005:661～666
[206]Hefny HA, Bahnasawi AA, Wahab AHA, et al. Logical radial basis function networks a hybrid intelligent model for function approximation. Advances in Engineering Software,1999,30(6):407～417
[207]Neggaz N, Benyettou A. Hybrid models based on biological approaches for speech recognition. Artificial Intelligence Review,2009,34(1-4):45～57
[208]Perrot N, Me L, Trystram G, et al. Optimal control of the microfiltration of sugar product using a controller combining fuzzy and genetic approaches. Fuzzy Sets and Systems,1998,94(3):309～322
[209]Chen LH, Chiang CH. New Approach to Intelligent Control Systems With Self-Exploring Process. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics,2003,33(1):56～66
[210]彭金柱,胡耀南,孙炜.基于混合学习算法的模糊小波神经网络控制.湖南大学学报(自然科学版),2006,33(2)：51～54
[211]Yu LX, Zhang YQ. Evolutionary Fuzzy Neural Networks for Hybrid Financial Prediction. IEEE Transactions on Systems, Man, and Cybernetics-Part C:Applications and Reviews,2005,35(2):244～249
[212]Turkmen I, Guney K. Genetic tracker with adaptive neuro-fuzzy inference system for multiple target tracking. Expert Systems with Applications,2008,35(4):1657～1667
[213]周明,孙树栋.遗传算法原理及其应用.第一版.北京：国防工业出版社,1999
[214]Narayanan A. Quantum computing for beginners. Proc of the 1999 Congress on Evolutionary Computation. Piscataway:IEEE Press,1999:2231～2238
[215]Yang Junan, Li Bin, Zhuang Zhenquan. Research of quantum genetic algorithm and its application in blind source separation. Journal of Electronics(China),2003, 20(1):62～68
[216]Panchi Li, Shiyong Li. Quantum-inspired evolutionary algorithms for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing,2008, 1(4):1～11
[217]Vlachogiannis JG, Ostergaard J. Reactive power and voltage control based on general quantum genetic algorithms. Expert Systems with Applications,2009,36(3): 6118-6126
[218]张葛祥,金炜东,胡来招.基于量子遗传算法的特征选择算法.控制理论与应用,2005,22(5)：810～819
[219]Jang J S R, Sun C T, Mizutani E. Neuro-fuzzy and soft computing. Prentice Hall, 1997
[220]Chen Hui, Zhang Jiashu, Zhang Chao, et al. Chaos updating rotated gates quantum-inspired genetic algorithm. International Conference on Communications Circuits and Systems. Chengdu:IEEE Press,2004:108～112
[221]周殊,潘炜,罗斌.一种基于粒子群优化方法的改进量子遗传算法及应用.电子学报,2006,34(5)：897～901
[222]Grover L. Quantum computing. Proc of the 12 th Int Conf on VLSI Design. Piscataway:IEEE Press,1999:548～553
[223]Simon Haykin著,叶世伟,史忠植译.神经网络原理(Neural Networks).第二版.北京：机械工业出版社,2004
[224]Saarinen S, Bramley R B, Cybenko G. Neural networks, back-propagation, and automatic differentiation, automatic Differentiation of Algorithms:Theory, Implementation, and Application, A. Grienwank and G.F. Corliss, eds, Philadelphial:SIAM,31～42
[225]Fletcher R. Practical Methods of Optimization.2nd edition, New York:Wiley,1987
[226]Luenberger D G. Linear and nonlinear programming.2nd edition, Reading, MA: Addison-Wesley,1984
[227]Bertsekas D P. Dynamic Programming and Optimal Control. Belmont, MA:Athenas Sicentific,1995,
[228]Bertsekas D P. Nonlinear Programming. Belmont, MA:Athenas Scientific,1995
[229]Dubios D, Prade H, Testemale C. Weighted fuzzy pattern matching. Fuzzy Sets and Systems,1988,28(3):313～331
[230]Shewchuk J R. An introduction to the conjugate gradient method without the agonizing pain. School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1994
[231]Moller M F. A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks,1993,6(4):525～534