1、北京师范大学模糊系统与人工智能方向简介（讨论稿）北京师范大学模糊数学与人工智能方向是国内最早从事模糊数学及其应用研究的单位之一，可以说是国内模糊数学研究的重要基地。早在1979年北师大数学科学学院开始就开始招收模糊数学研究方向的硕士研究生，是我国最早从事模糊数学研究的硕士学科点。1986年，汪培庄先生牵头，以模糊数学为主申请下来应用数学博士点，这也是我国最早从事模糊数学研究的博士学科点。迄今为止，北师大数学科学学院已培养几十名硕士和博士研究生，并且在各种工作岗位已成为骨干力量。北京师范大学模糊系统与模糊信息研究中心暨复杂系统实时智能控制实验室创建于2000年。现任中心主任为国家级有突出贡献中青
2、年专家李洪兴教授。目前，实验室拥有博导教授2人，副教授3人，博士后2人，在读博士生15人（其中具有教授职称者2人，副教授4人），硕士研究生19人。该研究中心现有一个应用数学的博士学位授权点，应用数学和控制理论与控制工程两个硕士学位授权点。1982年至今，北京师范大学模糊数学与人工智能研究群体先后提出并研究了因素空间、真值流推理、随机集落影、模糊计算机、模糊摄动理论、幂结构提升理论、基于变权综合的智能信息处理、模糊系统的插值表示、变论域智能计算、复杂系统建模以及知识表示的数学理论模糊计算机等一些先进的理论方法。近期的主要研究成果包括：1）给出因素空间理论，建立知识表示的数学框架，并系统研究概念的
3、内涵与外延表示问题，为专家经验、领域知识在软件系统中的表示与计算提供了理论基础；2）揭示了模糊逻辑系统的数学本质，给出常用模糊逻辑系统地插值表示，并系统研究了模糊逻辑系统的构造、分析以及泛逼近性等理论问题；3）提出变论域自适应智能信息处理理论，设计了基于变论域思想的一类高精度模糊控制器，在世界上第一个实现了四级倒立摆控制实物系统，经教育部组织专家鉴定，确认这是一项原创性的具有国际领先水平的重大科研成果；4）引入变权的概念，并给出基于自适应变权理论的智能信息处理方法；5）提出模糊计算机的概念，并研究了模糊计算机设计的若干理论问题；6）给出数学神经网络理论，从数学上揭示了模糊逻辑系统与人工神经网络
4、之间的关系，首次定义了“输出返回”的模糊逻辑系统并证明了它与反馈式神经网络等价；7）提出一种基于数据集成、规则提取和模糊推理的复杂系统的建模方法，即基于模糊推理的建模方法，由此可突破障碍模糊控制理论发展的一些瓶颈问题，诸如稳定性、能控性、能观测性等的判据问题。8）揭示了Fuzzy系统的概率论意义，指出Fuzzy系统中常用的清晰化方法，即重心法是合理的且在平均平方意义下是最优的方法. 基于不同的Fuzzy蕴涵算子，给出几种典型的概率分布，如Zadeh分布、Mamdani分布、Lukasiewicz分布等，它们充当Fuzzy系统的“系统内核”作用.9）利用随机过程理论刻画了变论域自适应模糊控制的自
5、适应机理，并且为经典自适应控制的自适应机理的源头给出了数学描述。模糊信息处理与人工智能目前已是计算机科学的重要分支之一，在国际范围里已有相当的影响。据了解，在北美、欧洲和日本的许多大学的计算机系，都有专家在从事模糊信息处理与人工智能研究与教学；他们所取得的成果已显示出模糊信息处理与人工智能在计算机科学研究与发展中的巨大作用。北京师范大学是国内模糊系统及其应用研究的发源地之一，李洪兴及其带领的学术团队在这一领域做出了一系列原创性、具有世界领先或先进水平的研究成果，在国内外具有重要的影响。由于模糊信息处理是新兴学科，我国在这一领域的研究水平与国外差距不大，因此，发展模糊信息处理与智能计算等相关领域
6、的研究对于我国计算机科学研究赶超世界先进水平是很有意义的。附录 该方向近期主要研究成果一. 获奖情况1 1987年获国家自然科学四等奖。2 2003年获教育部自然科学一等奖。3 2005年获国家科技进步二等奖。二. 已获得的专利1 发明专利：预焙电解铝生产的变论域自适应模糊控制方法及装置 发 明 人：李洪兴；王加银；谷云东；冯艳宾专 利 号：ZL 02 1 58123.1 授权公告日：2004年12月1日2 实用新型专利：四级倒立摆实验仪 设 计 人：李洪兴专 利 号：ZL 02 2 57287.2 授权公告日：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 汪培庄，李洪兴, 知识表示的数学理论，天津科技出版社，1994.6 汪培庄，李洪兴, 模糊系统理论与模糊计算机，科学出版社，1996.7 李洪兴等, 工程模糊数学方法及应用，天津科技出版社，1993.8 李洪兴，汪培庄, 模糊数学，国防工业出版社，1994.四. 已发表的主要论文（按时间顺序）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 (中国科学, 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 (中国科学, Series E), 42(2), 1999, 215-224. (SCI)11 Hong-Xing Li, Adaptive fuzzy controllers based on variable universe, Science in China (中国科学, 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（科学通报）, 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 (中国科学, 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 (中国科学, 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 (中国科学, 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 (中国科学, 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 (中国科学, 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 controller
27、s, 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). (SCI)37 Sh
28、ang-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, Computers & Math
29、ematics 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 controllers based o
30、n 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, 131-149.42 Song-Chol H
31、an 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, 15(3), 2004, 545-
32、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 Applications, 389(
33、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, 390(2004), 183-19
34、6. (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 pe
35、rformance. 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, Fuzzy Sets and Systems, 150, 2005, 373-396. (SCI)51 Pu-Yin Liu and Hong-Xing Li, Hierarchical TS fu
36、zzy system and its universal approximation, Information Sciences, 169(3-4), 2005, 279-303. (SCI)52 Song-Chol Han, Hong-Xing Li, Notes on “Pseudo-t-norms and implication operators on a complete Brouwerian lattice” and “Pseudo-t-norms and implication operators: direct products and direct product decom
37、positions”, Fuzzy Sets and Systems, 153(2005), 289-294. (SCI)五. 承担科研基金情况（只列主持的项目，参加的项目略去不列）项目名称（下达编号）项目来源起讫时间科研经费计算智能理论基础及其应用国家教育部高等学校骨干教师资助计划（振兴计划）2000.6-2002.636万变论域自适应模糊控制与平面运动多级倒立摆实现 (批准号：60474023)国家自然科学基金2005.1-2007.1228万模糊控制的数学本质与高精度模糊控制理论 (批准号：69674014)国家自然科学基金1997.1-1999.129.5万基于论域的自适应模糊控制器(
38、批准号：69974006)国家自然科学基金2000.1-2002.1210万模糊控制系统的建模 (批准号：60174013)国家自然科学基金2002.1-2004.1217万复杂生产制造过程实时、智能控制与优化理论和方法研究(项目编号：2002CB312200)973国家重大基础研究项目2003.1-2007.1270万变论域自适应模糊控制理论及其在倒立摆控制中的应用国家教育部跨世纪优秀人才培养计划基金资助项目1998.1-2000.1210万复杂系统的变论域自适应模糊控制理论与建模 (批准号：20020027013)高等学校博士学科点专项科研基金2003.1-2005.127万复杂系统的变论域自适应模糊控制理论与模型逼近 (批准号：03184)教育部科学技术重点项目2003.1-2005.1220万211工程，项目名称: 数学与信息科学教育部2003.1-2005.1276万注：国家自然科学基金项目“基于论域的自适应模糊控制器(批准号：69974006)”结题后被国家自然科学基金委评为特优项目。8
