Tutorial On Fuzzy Neural Computing Systems

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Tutorial Information


Fuzzy neural networks (FNNs), being the product of fuzzy logic and neural networks, are computational machines with unique capabilities for dealing with both numerical data and linguistic knowledge (fuzzy) information. In this tutorial, first we will provide an illustrative discussion on the biological basis of neural networks: learning from nature. Then we will continue our discussion on the basic notions, mathematical methodology and morphology, and learning and adaptation algorithms for static neural networks (SNNs). Also, some basic notions of conventional multilayered feedforward neural networks (MFNNs) with the well-known backpropagation (BP) learning algorithm will be discussed. This discussion will be illustrated by means of some examples taken from logic circuits, neuro-control systems, neuro-vision systems, pattern recognition, medical systems, and economics. Then we will discuss some advanced theory, with illustrative examples, of higher-order correlative neural networks (HOC-NNs).

Then we will provide an extensive discussion on dynamic neural networks (DNNs) with applications to dynamic memory, control systems, vision systems, and robotics. For developing FNNs, we will provide some necessary mathematical theory on fuzzy sets, fuzzy arithmetic, and fuzzy logic. Several fuzzy logic operations for various types of fuzzy neurons (FNs), which have fuzzy inputs and fuzzy weights, will be introduced. Analogous to the BP learning algorithm for MFNNs, the concepts and formulations of fuzzy backpropagation (FBP) learning algorithms for FNNs will then be developed. Moreover, the capabilities and limitations of FNNs consisting of many interconnected FNs will be discussed. The universal approximation capabilities of fuzzy basis function networks (FBFNs) that are represented as a modified version of Gaussian radial basis function networks (GRBFNs) will also be addressed. The material presented in this tutorial will not only provide an overview of the existing results, but also present some state-of-the-art achievements and open problems in the field of neural computing and fuzzy neural computing.

Tutorial Outline

  1. Introduction to Neural Networks: Biological Basis of Neural Networks
  2. Morphology of Conventional Neural Networks
  3. Learning and Adaptation for Neural Networks
  4. Multilayered Neural Networks
  5. Higher-Order Correlative Type of Neural Networks (HOC-NN)
  6. Dynamic Neural Networks (DNN)
  7. Learning and Adaptation for Fuzzy Neurons (FNs)
  8. Fuzzy Sets, Fuzzy Arithmetic, and Fuzzy Logic: An Overview
  9. Building Fuzzy Neurons (FNs) Using Fuzzy Arithmetic and Fuzzy Logic Operations
  10. Conclusions

Keywords: fuzzy logic, neural networks, fuzzy neural networks, learning, universal approximation.


  1. Gupta, Madan M., Jin, Liang, and Homma, Noriyasu [2003], Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory, Joint publishers: Wiley-Interscience and IEEE Press, John Wiley & Sons, Inc., 722 pages, ISBN: 0-471-21948-7.
  2. Kaufmann, A. and Gupta, M. M. [1985]. Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold Company Inc., New York, 350 pages, [Revised, Second Edition, 1991]. Japanese Translation by Dr. H. Matsuoka, and Dr. H. Tanaka, Ohmsha Publisher Ltd., Tokyo, December 1992, 362 pages.
  3. Gupta, M. M. and. Knopf, G. K. (Editors), 1994. Neuro-Vision Systems: Principles and Applications, A Volume of Selected Reprints, IEEE-Neural Networks Council, IEEE-Press, New York, 555 pages.
  4. Gupta, M. M. and Rao, D. H. (Editors), 1994. Neuro-Control Systems: Theory and Applications, A Volume of Selected Reprints, IEEE Neural Networks Council, IEEE-Press, New York, 607 pages.
  5. Fuzzy Neural Computing Systems: Theory and Applications, 80 pages notes (will be supplied).


Dr. Madan M. Gupta

Dr. Madan M. Gupta is a professor (Emeritus) in the College of Engineering and the Director of the Intelligent Systems Research Laboratory at University of Saskatchewan. Dr. Gupta’s current research interests are in the areas of neuro-vision systems, neuro-control systems, integration of fuzzy-neural systems, and neuronal morphology of biological vision systems, intelligent and cognitive robotic systems, cognitive information, new paradigms in information processing, and chaos in neural systems. He is also developing architectures of computational neural networks and computational fuzzy neural networks for application to advanced robotics, aerospace, and industrial systems.

Dr. Gupta has authored or coauthored over 800 published research papers. He recently Co-authored the seminal book Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. Dr. Gupta previously coauthored Introduction to Fuzzy Arithmetic: Theory and Applications, the first book on fuzzy arithmetic, and Fuzzy Mathematical Models in Engineering and Management Science. Both of these books had Japanese translations. Also, Dr. Gupta edited 19 books in the fields of adaptive control systems, fuzzy computing, neuro-computing, neuro-vision systems, and neuro-control systems.

Dr. Gupta was elected fellow of the Institute of Electrical and Electronics Engineers (IEEE) for his contributions to the theory of fuzzy sets and adaptive control systems and for the advancement of the diagnosis of cardiovascular disease. He was elected fellow of the International Society for Optical Engineering (SPIE) for his contributions to the field of neuro-control and neuro-fuzzy systems. He was elected fellow of the International Fuzzy Systems Association (IFSA) for his contributions to fuzzy-neural systems. In 1991, Dr. Gupta was co-recipient of the Institute of Electrical Engineering Kelvin Premium. In 1998, Dr. Gupta received the Kaufmann Prize Gold Medal for research in the field of fuzzy logic. He has been elected as a visiting professor and a special advisor in the area of high technology to the European Centre for Peace and Development (ECPD), University for Peace, which was established by the United Nations.

Dr. Gupta received B.E. (Hons.) and M.E. degrees in electronics-communications engineering from the Birla Engineering College (now the Birla Institute of Technology & Science), Pilani, India, in 1961 and 1962, respectively. He received his Ph.D. degree from the University of Warwick, United Kingdom, in 1967 in adaptive control systems. In 1998, for his extensive contributions in neuro-control, neuro-vision, and fuzzy-neural systems, Dr. Gupta received an earned doctor of science (D.Sc.) degree from the University of Saskatchewan.

Contact Information: Email: Madan_dot_Gupta_at_usask_dot_ca

Dr. Noriyasu Homma

Dr. Noriyasu Homma received a BA, MA, and PhD in electrical and communication engineering from Tohoku University, Japan, in 1990, 1992, and 1995, respectively.

From 1995 to 1998, he was a lecturer at the Tohoku University, Japan. He is currently an associate professor of the Faculty of Medicine at the Tohoku University. From 2000 to 2001, he was a visiting professor at the Intelligent Systems Research Laboratory, University of Saskatchewan, Canada. His current research interests include neural networks, complex and chaotic systems, soft computing, cognitive sciences, and actual brain functions. He has published over 70 papers, and co-authored 1 book and 3 chapters in 3 research books in these fields.

Contact Information: Email: homma_at_abe_dot_ecei_dot_tohoku_dot_ac_dot_jp

Dr. Zeng-Guang Hou

Dr. Zeng-Guang Hou received the B.E. and M.E. degrees in electrical engineering from Yanshan University (former North-East Heavy Machinery Institute), Qinhuangdao, China in 1991 and 1993, respectively. He received the Ph.D. degree in electrical engineering from Beijing Institute of Technology, Beijing, China in 1997.

From 1997 to 1999, he was a Postdoctoral Research Fellow at the Institute of Systems Science, Chinese Academy of Sciences, Beijing, China. From 1999 to 2004, he was an Associate Professor at the Institute of Automation, Chinese Academy of Sciences, Beijing, China, where now he serves as a Full Professor. From September 2003 to October 2004, he was with the Intelligent Systems Research Laboratory, University of Saskatchewan, Canada, as a Visiting Professor. His current research interests include neural networks, fuzzy logic, SVM, optimization algorithms, intelligent control and robotics. He has published over 50 papers in these fields.

Contact Information: Email: zengguang_dot_hou_at_mail_dot_ia_dot_ac_dot_cn

Ashu M. G. Solo

Ashu M. G. Solo is an electrical and computer engineer, mathematician, political writer, and entrepreneur. His primary research interests are in math and intelligent systems theory and applications as well as public policy. Solo has over 150 publications in these and other fields. He co-developed some of the best published methods for maintaining power flow in and multiobjective optimization of radial power distribution system operations using intelligent systems. He has served on numerous international program committees for research conferences. Solo has won a Distinguished Service Award and two Achievement Awards from research conferences. Solo is the principal of Maverick Technologies America Inc. He previously worked in nine different research and development labs in universities and industry. Solo served honorably as an infantry officer and platoon commander understudy in the Cdn. Army Reserve.

Contact Information: Email: amgsolo-at-mavericktechnologies-dot-us

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