Number 32 November 92 The Huntington Technical Brief By David Brubaker Ph.D. FUZZY REFERENCES ---------------- INTRODUCTION A request I receive regularly is for a good reference book on fuzzy logic and fuzzy logic systems. This is a difficult request, as much of what is currently available is written by academic-oriented authors and contains a heavy emphasis on mathematical representation at a level foreign to most practicing engineers. However, some of these texts are more readable than others, and by searching individual topics and only wading into the more esoteric math when absolutely necessary, much can be gained. Journal articles are also available, although again the articles have an academic bent. Two journals that cover fuzzy topics are Fuzzy Sets and Systems, from North-Holland, with Constantin Negoita, Lotfi Zadeh, and Hans Zimmermann (principle) as editors, and the International Journal of Approximate Reasoning, also from North Holland, with James Bezdek as editor-in-chief. Although price and content would typically rule against a practicing engineer subscribing, access to these journals and ongoing review is advisable - the basis for future fuzzy techniques is being investigated by researchers today. What follows is a list of texts from my library that are dedicated to fuzzy topics. The list should be considered representative of what is available, although not complete. My acquisition technique has been to stop by the Stanford Bookstore approximately once a month and purchase any book with the term "fuzzy" either explicitly contained or implied by its title. The first section contains the books I most often recommend to others, and includes the comments I typically offer with my recommendation. The second section contains those books that are difficult to read, or for one reason or another, do not directly apply to applied fuzzy engineering. Sadly, space prohibits comments on these. Both sections are ordered alphabetically by author. Recommended Books Klir and Folger: Fuzzy Sets, Uncertainty, and Information - Prentice- Hall, 1988. This is a good, solid book, and the one I most easily recommend to the serious newcomer. Although the discussion is strongly based on mathematical principles, the concepts and notation are easily understood and are explained in the text. During an initial reading, sections may need to be studied several times, but the content is worth the effort. Chapter titles are: Crisp Sets and Fuzzy Sets; Operations on Fuzzy Sets; Fuzzy Relations; Fuzzy Measures; Uncertainty and Information; and Applications. Applications are discussed less deeply than the theory of the previous chapters, with general, rather than detailed, examples. The book is a by-product of a graduate level class taught by the authors, and has exercises to be worked at the end of each chapter. That it is intended as a teaching tool definitely enhances its readability. Kosko: Neural Networks and Fuzzy Systems - A Dynamical Systems Approach to Machine Intelligence - Prentice-Hall, 1992. Although less general than Klir and Folger, the last half of this book is an excellent choice for the engineer who wants to understand the theory behind fuzzy rule-based systems, and how such systems compare to other modern systems. The first half, chapters 1 through 6, is on neural networks. Part 2, titled Adaptive Fuzzy Systems, starts with chapter 7. To set the stage, the author introduces his hypercube representation of fuzzy sets (which terminology is used, incidentally, in both the company name HyperLogic, and its fuzzy product, CubiCalc), and then the concept of a fuzzy associative memory, or FAM, a mapping between hypercubes. He shows how most current fuzzy rule-based systems are a special case of a FAM. Turning now to applications, the next three chapters present a comparison of a fuzzy control system and a neural system, address fuzzy image transform coding, and present another comparison, this time of a fuzzy and Kalman-filter control system. Often we learn and discover by looking at something we already know from a new angle and recognize nuances and the potential for growth we could not previously see. To me, this is the value of this book, to view something we thought was familiar, fuzzy rule-based systems, in an entirely different way, and by doing so to expand our own awareness of what is possible using a fuzzy approach. Sugeno, editor: Industrial Applications of Fuzzy Control - North Holland, 1985. This is a meat-and-potatoes description of how fuzzy logic has been used in industry. Ten applications are described, including automatic train control, water purification, and control of a diesel engine. In addition, three articles discuss the development and application of fuzzy models, one article describes a microprocessor based fuzzy controller, and finally, there is an annotated bibliography of fuzzy control compiled by Richard Tong. This book is excellent, presenting at various levels of depth how fuzzy systems were being used world-wide in the 1985 time frame. It is a bit pricey, presently selling for over $100, but worth it for those serious in fuzzy control. Yager, Ovchinnikov, Tong, and Nguyen, editors: Fuzzy Sets and Applications: Selected Papers by L. A. Zadeh - John Wiley & Sons, 1987. This is a wonderful collection of eighteen papers written by Lotfi Zadeh, the father of fuzzy logic. It starts with the seminal 1965 paper, and concludes with a 1986 paper on a computational approach to the representation of meaning. Between are such titles as: "Decision- Making in a Fuzzy Environment", "A Theory of Approximate Reasoning", and "A Theory of Commonsense Knowledge". That it is a collection of Zadeh's papers alone gives this book great value. To read the lucid, (for the most part) easy-to-understand renderings on the application of fuzzy set theory to widely disparate topics further enhances the value. But to me, the joy comes from seeing, in these papers, a great mind at work. Terano, Asai and Sugeno: Fuzzy Systems Theory and Its Applications - Academic Press, (English) 1992. This is a new book, recently translated from Japanese, and one I have only skimmed. It looks good. There is a fair amount of mathematical representation, but well supported by explanations in the text. The book contains sixteen chapters. The first eight chapters address basic fuzzy theory, fuzzy relations, fuzzy regression models, statistical decision making, fuzzy quantification theory, fuzzy mathematical programming, and evaluation. The last eight chapters address applying theory, and deal with diagnosis, control, human activities, robots, image recognition, databases, information retrieval, and damage assessment. The English translation is very good - from those parts I have read, it is impossible to tell that English is not the original language. A preliminary thumbs up. Support and Specialized Books Bezdek and Pal, editors: Fuzzy Models For Pattern Recognition - Methods That Search for Structures in Data - IEEE Press, 1992. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms - Plenum Press, 1981. Dubois and Prade: Fuzzy Sets and Systems: Theory and Applications - Plenum Press, 1980. Dubois and Prade: Possibility Theory - An Approach to Computerized Processing of Uncertainty - Plenum Press, (English) 1988. Kandel: Fuzzy Techniques in Pattern Recognition - John Wiley & Sons, 1982. Kandel: Fuzzy Mathematical Techniques with Applications - Addison- Wesley, 1986. Kandel: Fuzzy Expert Systems - CRC Press, 1992. Kaufman and Gupta: Introduction to Fuzzy Arithmetic - Theory and Applications - Van Nostrand Reinhold, 1985. Negoita: Expert Systems and Fuzzy Systems - Benjamin/Cummings, 1985. Negoita and Ralescu: Simulation, Knowledge-Based Computing, and Fuzzy Statistics - Van Nostrand Reinhold, 1987. Novak: Fuzzy Sets and Their Applications - Adam Hilger, (English) 1989. Pedrycz: Fuzzy Control and Fuzzy Systems - Research Studies Press / John Wiley & Sons, 1989. Schmucker: Fuzzy Sets, Natural Language Computations, and Risk Analysis - Computer Science Press, 1984. Smithson: Fuzzy Set Analysis for Behavioral and Social Sciences - Springer-Verlag, 1987. Smithson: Ignorance and Uncertainty - Emerging Paradigms - Springer-Verlag, 1989. Yager and Zadeh, editors: An Introduction to Fuzzy Logic Applications in Intelligent Systems - Kluwer Academic, 1992. Zadeh and Kacprzyk, editors: Fuzzy Logic for the Management of Uncertainty - John Wiley & Sons, 1992. Zimmermann: Fuzzy Set Theory - and Its Applications - Kluwer- Nijhoff, 1985. Zimmermann: Fuzzy Sets, Decision Making, and Expert Systems - Kluwer Academic Publishers, 1987. Happy reading. ---------------------------------------------------------------- The Huntington Technical Brief is published monthly as part of the marketing effort of Dr. David Brubaker of The Huntington Group. The unedited version complete with all figures is available at a subscription price of $24.00 per year. Past issues are available for $1.00 and samples of the Huntington Report are available at no charge. Please call Dr. David Brubaker at the number below for complete details. The 42-page report "Introduction to Fuzzy Logic Systems" is available for $35.00. For the past sixteen years Dr. Brubaker has provided technical consulting services in the design of complex systems, real-time, embedded processor systems, and for the past five years, fuzzy logic systems. If you need out-of-house expertise in any of these, please call 415-325-7554. ---------------------------------------------------------------- Copyright 1992 by The Huntington Group 883 Santa Cruz Avenue, Suite 31 Menlo Park, CA 94025-4608 This information is provided by Aptronix FuzzyNet 408-428-1883 Data USR V.32bis