1、北京師范大學模糊系統與人工智能方向簡介（討論稿）北京師范大學模糊數學與人工智能方向是國內最早從事模糊數學及其應用研究的單位之一，可以說是國內模糊數學研究的重要基地。早在1979年北師大數學科學學院開始就開始招收模糊數學研究方向的碩士研究生，是我國最早從事模糊數學研究的碩士學科點。1986年，汪培莊先生牽頭，以模糊數學為主申請下來應用數學博士點，這也是我國最早從事模糊數學研究的博士學科點。迄今為止，北師大數學科學學院已培養幾十名碩士和博士研究生，并且在各種工作崗位已成為骨干力量。北京師范大學模糊系統與模糊信息研究中心暨復雜系統實時智能控制實驗室創建于2000年?，F任中心主任為國家級有突出貢獻中青

2、年專家李洪興教授。目前，實驗室擁有博導教授2人，副教授3人，博士后2人，在讀博士生15人（其中具有教授職稱者2人，副教授4人），碩士研究生19人。該研究中心現有一個應用數學的博士學位授權點，應用數學和控制理論與控制工程兩個碩士學位授權點。1982年至今，北京師范大學模糊數學與人工智能研究群體先后提出并研究了因素空間、真值流推理、隨機集落影、模糊計算機、模糊攝動理論、冪結構提升理論、基于變權綜合的智能信息處理、模糊系統的插值表示、變論域智能計算、復雜系統建模以及知識表示的數學理論模糊計算機等一些先進的理論方法。近期的主要研究成果包括：1）給出因素空間理論，建立知識表示的數學框架，并系統研究概念的

3、內涵與外延表示問題，為專家經驗、領域知識在軟件系統中的表示與計算提供了理論基礎；2）揭示了模糊邏輯系統的數學本質，給出常用模糊邏輯系統地插值表示，并系統研究了模糊邏輯系統的構造、分析以及泛逼近性等理論問題；3）提出變論域自適應智能信息處理理論，設計了基于變論域思想的一類高精度模糊控制器，在世界上第一個實現了四級倒立擺控制實物系統，經教育部組織專家鑒定，確認這是一項原創性的具有國際領先水平的重大科研成果；4）引入變權的概念，并給出基于自適應變權理論的智能信息處理方法；5）提出模糊計算機的概念，并研究了模糊計算機設計的若干理論問題；6）給出數學神經網絡理論，從數學上揭示了模糊邏輯系統與人工神經網絡

4、之間的關系，首次定義了“輸出返回”的模糊邏輯系統并證明了它與反饋式神經網絡等價；7）提出一種基于數據集成、規則提取和模糊推理的復雜系統的建模方法，即基于模糊推理的建模方法，由此可突破障礙模糊控制理論發展的一些瓶頸問題，諸如穩定性、能控性、能觀測性等的判據問題。8）揭示了Fuzzy系統的概率論意義，指出Fuzzy系統中常用的清晰化方法，即重心法是合理的且在平均平方意義下是最優的方法. 基于不同的Fuzzy蘊涵算子，給出幾種典型的概率分布，如Zadeh分布、Mamdani分布、Lukasiewicz分布等，它們充當Fuzzy系統的“系統內核”作用.9）利用隨機過程理論刻畫了變論域自適應模糊控制的自

5、適應機理，并且為經典自適應控制的自適應機理的源頭給出了數學描述。模糊信息處理與人工智能目前已是計算機科學的重要分支之一，在國際范圍里已有相當的影響。據了解，在北美、歐洲和日本的許多大學的計算機系，都有專家在從事模糊信息處理與人工智能研究與教學；他們所取得的成果已顯示出模糊信息處理與人工智能在計算機科學研究與發展中的巨大作用。北京師范大學是國內模糊系統及其應用研究的發源地之一，李洪興及其帶領的學術團隊在這一領域做出了一系列原創性、具有世界領先或先進水平的研究成果，在國內外具有重要的影響。由于模糊信息處理是新興學科，我國在這一領域的研究水平與國外差距不大，因此，發展模糊信息處理與智能計算等相關領域

6、的研究對于我國計算機科學研究趕超世界先進水平是很有意義的。附錄 該方向近期主要研究成果一. 獲獎情況1 1987年獲國家自然科學四等獎。2 2003年獲教育部自然科學一等獎。3 2005年獲國家科技進步二等獎。二. 已獲得的專利1 發明專利：預焙電解鋁生產的變論域自適應模糊控制方法及裝置 發 明 人：李洪興；王加銀；谷云東；馮艷賓專 利 號：ZL 02 1 58123.1 授權公告日：2004年12月1日2 實用新型專利：四級倒立擺實驗儀 設 計 人：李洪興專 利 號：ZL 02 2 57287.2 授權公告日：2003年9月17日三已出版的主要著作1 Hong-Xing Li, P.C. P

7、hilip Chen and Han-Pang Huang, Fuzzy Neural Intelligent Systems, CRC Press, FL, USA, 2001. 2 Hong-Xing Li and Vincent C.Yen, Fuzzy Sets and Fuzzy Decision-Making, CRC Press, FL, USA, 1995. 3 Peizhuang Wang and Hong-Xing Li, Fuzzy Information Processing and Fuzzy Computers, Science Press New York/Bei

8、jing, 1997.4 Puyin Liu and Hong-Xing Li, Fuzzy Nerual Network Theory and Application, World Scientific Press, Singapore, 2004. 5 汪培莊，李洪興, 知識表示的數學理論，天津科技出版社，1994.6 汪培莊，李洪興, 模糊系統理論與模糊計算機，科學出版社，1996.7 李洪興等, 工程模糊數學方法及應用，天津科技出版社，1993.8 李洪興，汪培莊, 模糊數學，國防工業出版社，1994.四. 已發表的主要論文（按時間順序）1 Hong-Xing Li, Fuzzy pe

9、rturbation analysis, part 1, Fuzzy Sets and Systems, 17(2), 1985, 189-197. (SCI)2 Hong-Xing Li, Fuzzy perturbation analysis, part 2, Fuzzy Sets and Systems, 19(2), 1986, 165-175. (SCI) 3 Hong-Xing Li, Multifactorial fuzzy sets and multifactorial degree of nearness, Fuzzy Sets and Systems, 19(3), 198

10、6, 291-297. (SCI)4 Hong-Xing Li, Fuzzy clustering methods based on perturbation, Fuzzy Sets and Systems, 32(3), 1989, 291-302. (SCI) 5 Hong-Xing Li, Multifactorial functions in fuzzy sets theory, Fuzzy Sets and Systems, 33(1), 1990, 69-84. (SCI) 6 Hong-Xing Li, Chengzhong Luo and Peizhuang Wang, The

11、 cardinality of fuzzy sets and the continuum hypothesis, Fuzzy Sets and Systems, 55(1993), 61-77. (SCI) 7 Hong-Xing Li etc, The operations of fuzzy cardinalities, Journal of Mathematical Analysis and Applications, 182(1994),768-778. (SCI)8 Hong-Xing Li, Interpolation mechanism of fuzzy control, Scie

12、nce in China (中國科學, Series E), 41(3), 1998, 312-320. (SCI) 9 Hong-Xing Li, Factor spaces theory and its applications to fuzzy information processing (I), Fuzzy Sets and Systems, 95(2), 1998, 147-160. (SCI) 10 Hong-Xing Li, The relationship between fuzzy controllers and PID controllers, Science in Ch

13、ina (中國科學, Series E), 42(2), 1999, 215-224. (SCI)11 Hong-Xing Li, Adaptive fuzzy controllers based on variable universe, Science in China (中國科學, Series E), 42(1), 1999, 10-20. (SCI)12 Hong-Xing Li and L.X. Li, Representing diverse mathematical problems using neural networks in hybrid intelligent sys

14、tems, Expert Systems, 16(4), 1999, 262-272. (SCI)13 Hong-Xing Li and C.L. Philip Chen, The equivalence between fuzzy logic systems and feedforward neural networks, IEEE Transactions on Neural Networks, 11(2), 2000, 356-365. (SCI)14 Hong-Xing Li, Output-back fuzzy logic systems and equivalence with f

15、eedback neural networks, Chinese Science Bulletin（科學通報）, 45(7), 2000, 592-596. (SCI) 15 Hong-Xing Li and Li-Da Xu, A neural network representation of linear programming, European Journal of Operational Research, 124(2), 2000, 224-234. (SCI)16 Hong-Xing Li, V.C. Yen and E.S. Lee, Model of neurons bas

16、ed on factor space, Computers and Mathematics with Applications, 39(2000), 91-100. (SCI) 17 Hong-Xing Li etc, Factor spaces theory and its applications to fuzzy information processing: Two kinds of factor space canes, Computers and Mathematics with Applications, 40(2000), 835-843. (SCI) 18 Hong-Xing

17、 Li etc, Factor space theory and fuzzy information processing: Fuzzy decision making based on the concepts of feedback extension, Computers and Mathematics with Applications, 40(2000), 845-864. (SCI) 19 Hong-Xing Li, V.C. Yen and E.S. Lee, Factor space theory in fuzzy information processing: Composi

18、tion of states of factors and multifactorial decision making, Computers and Mathematics with Applications, 39(2000), 245-265. (SCI) 20 Pu-Yin Liu and Hong-Xing Li, Approximation of generalized fuzzy systems to integrable functions, Science in China (中國科學, Series E), 43(6), 2000, 613-624. (SCI)21 Qin

19、g He and Hong-Xing Li, Extension principles and fuzzy set categories, Computers and Mathematics with Applications, 39(2000), 45-53. (SCI)22 V.C. Yen and Hong-Xing Li, Concept representation, factor space theory and information systems research, Systems Research and Behavioral Science, 17(2000), 163-

20、172. (SCI)23 Hong-Xing Li and Li D Xu, Feature space theorya mathematical foundation for data mining, Knowledge-Based Systems, 14(5-6), 2001, 253-257. (SCI)24 Pu-Yin Liu and Hong-Xing Li, Analyses for Lp()-norm approximation capability of generalized Mamdani fuzzy systems, Information Sciences, 138

21、(2001), 195-210. (SCI)25 Bing-Xue Yao and Hong-Xing Li, Weak HX-ring on a ring, Italian Journal of Pure and Applied Mathematics, No.10, 2001, 125-131.26 Hong-Xing Li, Zhi-Hong Miao, Jia-Yin Wang, Variable universe adaptive fuzzy control on the quadruple inverted pendulum, Science in China (中國科學, Ser

22、ies E), 2002, 45(2), 213-224. (SCI)27 Hong-Xing Li, Zhi-Hong Miao, Jia-Yin Wang, Variable universe stable adaptive fuzzy control of nonlinear system, Science in China (中國科學, Series E), 2002, 45(3), 225-240. (SCI)28 Hong-Xing Li, Jia-Yin Wang, Zhi-Hong Miao, Modeling on fuzzy control systems, Science

23、 in China (中國科學, Series A), 2002, 45(12), 1506-1517. (SCI)29 Xue-Hai Yuan, Hong-Xing Li and E. Stanley Lee, Categories of fuzzy sets and weak topos, Fuzzy Sets and Systems, 127(2002), 291-297. (SCI)30 Pu-Yin Liu and Hong-Xing Li, Image restoration techniques based on fuzzy neural networks, Science i

24、n China (中國科學, Series F), 2002, 45(4), 274-285. (SCI)31 Hong-Xing Li, Li D Xu, Jia-Yin Wang and Zhi-Wen Mo, Feature space theory in data mining: transformations between extensions and intensions in knowledge representation, Expert Systems, 20(2), 2003, 60-71. (SCI)32 Hong-Xing Li, Jia-Yin Wang and Z

25、hi-Hong Miao, Marginal linearization method in modeling on fuzzy control systems, Progress in Nature Science, 2003, 13(7), 489-496. (SCI)33 Hong-Xing Li, Ling-Xia Li and Jia-Yin Wang, Interpolation representation of feedforward neural networks, Mathematical and Computer Modeling, 37, 7-8, (2003), 82

26、9-847. (SCI)34 Hong-Xing Li and E. S. Lee, Interpolation representations of fuzzy logic systems, Computers & Mathematics with Applications, Volume 45, Issues 10-11, Pages 1683-1693 (May - June 2003). (SCI)35 Hong-Xing Li , Yan-Da Li, Zhi-Hong Miao and E. S. Lee, Control functions of fuzzy contro

27、llers, Computers & Mathematics with Applications, Volume 46, Issues 5-6, Pages 875-890 (September 2003). (SCI)36 Hong-Xing Li and E. S. Lee, Interpolation functions of feedforward neural networks, Computers & Mathematics with Applications, Volume 46, Issue 12, Pages 1861-1874 (December 2003)

28、. (SCI)37 Shang-Ming Zhou, Hong-Xing Li and Li-Da Xu, A variational approach to intensity approximation for remote sensing images using dynamic neural, Expert Systems, 20(4), 2003, 163-170. (SCI)38 Qing He, Hong-Xing Li, Zhong-Zhi Shi and E.S. Lee, Fuzzy clustering method based on perturbation, Comp

29、uters & Mathematics with Applications, Volume 46, Pages 929-946 ( 2003). (SCI)39 Hong-Xing Li, Li LX, Wang Jiayin, Mo Zhiwen, Li Yanda, Fuzzy decision making based on variable weights, Mathematical and Computer Modeling, 39(2004), 163-179. (SCI)40 Hong-Xing Li, You Fei and Peng Jiayin, Fuzzy con

30、trollers based on some fuzzy implication operators and their response functions, Progress in Nature Science, 2004, 14(1), 15-20. (SCI)41 Pu-Yin Liu and Hong-Xing Li, Fuzzy techniques in restoration researchA survey (invited paper), International Journal of Computational Cognition, 2(2), 2004, 131-14

31、9.42 Song-Chol Han and Hong-Xing Li, Indices and periods of incline matrices, Linear Algebra and Its Applications, 387(2004), 143-165. (SCI)43 Pu-Yin Liu and Hong-Xing Li, Efficient learning algorithms for three-layer regular feedforward fuzzy neural networks, IEEE Transactions on Neural Networks, 1

32、5(3), 2004, 545-558. (SCI)44 Xiao-Jun Tong, Mianyun Chen, Hong-Xing Li, Pan-operators, strunture with non-idempotent pan-addition, Fuzzy Sets and Systems, 145, 2004, 463-470. (SCI)45 Song-Chol Han and Hong-Xing Li, Invertible incline matrices and Cramers rule over inclines, Linear Algebra and Its Ap

33、plications, 389(2004), 121-138. (SCI)46 Song-Chol Han, Hong-Xing Li and Yun-Dong Gu, Standard eigenvectors of incline matrices, Linear Algebra and Its Applications, 389(2004), 235-248. (SCI)47 Song-Chol Han, Hong-Xing Li, The semigroup of incline Hall matrices, Linear Algebra and Its Applications, 3

34、90(2004), 183-196. (SCI)48 Hong-Xing Li, Jia-Yin Wang, Yan-Bin Feng and Yun-Dong Gu, Hardware implementation of the quadruple inverted pendulum with single motor, Progress in Nature Science, 2004, 14(9), 822-827. (SCI)49 Zhihong Miao, Hongxing Li, Jiayin Wang. Optimal adaptive fuzzy control systems with tracking performance. Advances in Systems Science and Applications, 2004, 4(3): 367-374.50 Pu-Yin Liu and Hong-Xing Li, Approximation analysis of feedforward regular fuzzy netural network with two hidden layers