EDN Columnist: July 20, 1995
But be ye doers of the word, and not hearers only.--James 1:22.
By now, regular readers of this column will recognize my conviction that most learning of any value comes from doing, rather than reading about what others have done. Nevertheless, we all need to start somewhere, and I still receive a number of requests for information sources on the application of fuzzy logic to engineering problems. Here are my current recommendations.
Conferences
There are a number of annual conferences dedicated to fuzzy logic. Most of them are purely research oriented and, therefore, are less interesting to me. For economic reasons, I can justify attending only one conference per year--and for the third year in a row it is Fuzzy Logic '95, which runs from November 7 to 9, 1995, in Burlingame, CA.
Conference sponsors tout Fuzzy Logic '95 as an "international conference on fuzzy-neural applications, systems, and tools." It focuses on applications, although some research material manages to creep in. The conference is also billed as "total immersion," with tutorial sessions, papers, luncheon talks (one led by Lotfi Zadeh, the father of fuzzy logic, and another by me), and evening rap sessions. Contact Michelle Keyworth, Conference & Exhibitions Manager, PennWell Publishing Co, 10 Tara Blvd, Fifth Fl, Nashua, NH 03062 (phone (603) 891-9265, fax (603) 891-0597).
Texts
The Fuzzy Systems Handbook by Earl Cox (AP Professional, 1994)
This is one of two texts currently available that doesn't presume knowledge of college-level set theory and its notation. It provides a good introduction to fuzzy set theory, operations, and hedges. The book addresses fuzzy reasoning, including one of the few discussions available on decomposition (which I've called "combination" in previous columns) and defuzzification. The book concludes with a thorough description of fuzzy models, a number of case studies, and a chapter on building fuzzy systems. Interspersed throughout are C++ code examples of fuzzy classes, which are also contained in a DOS-compatible disk.
An Introduction to Fuzzy Control by Dimiter Driankov, Hans Hellendoorn, and Michael Reinfrank (Springer-Verlag, 1993)
The preface to An Introduction to Fuzzy Control describes the book as "an introductory textbook for control engineers, covering just the relevant part of the theory and focusing on the principles of fuzzy control rather than particular applications or tools." The book lives up to this claim. For, despite its focus on control, it was the first text I read that aimed at the practicing engineer rather than at students or researchers. The mathematical representations are at a comfortable level for most practicing engineers.
Chapter headings include The Mathematics of Fuzzy Control, FKBC (fuzzy-knowledge-based controller) Design Parameters, Nonlinear Fuzzy Control, Adaptive Fuzzy Control, and Stability of Fuzzy Control Systems. All good stuff. The topics are well-discussed, and the text includes many references to additional resources. The English is quite readable.
Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence by Bart Kosko (Prentice-Hall, 1992)
The latter half of this book is a good choice for the engineer who wants to understand the theory behind fuzzy-rule-based systems and how such systems compare with other modern systems. The first half of the book (chapters 1 to 6) covers neural networks. Part 2, entitled Adaptive Fuzzy Systems, begins with chapter 7.
Kosko introduces his hypercube representation of fuzzy sets and explains the concept of fuzzy associative memory (FAM), a mapping between hypercubes. Most fuzzy-rule-based systems are a special case of a FAM. The next three chapters compare a fuzzy control system with a neural system, address fuzzy image-transform coding, and present a comparison of a fuzzy and Kalman-filter control system.
Fuzzy Logic: The Discovery of a Revolutionary Computer Technology--and How it is Changing Our World by Daniel McNeill and Paul Freiberger (Simon & Schuster, 1993)
This is not a technical book. It intends to teach readers about fuzzy logic, its history, the people involved, and its potential impact on technology. To this end, the authors have done a reasonably good job. The book's major strength is that it explains the basics of the technology in understandable terms. Its major weakness is that it contains significant fluff, resulting from some misrepresentation of facts (I believe it's inadvertent), and from a tendency toward sensationalism (note the subtitle). Although written with a "pro-fuzzy" spin, it also fairly represents critics' opinions of fuzzy logic. (I finally learned the basis for the "anti-fuzzy" claims that supporters of Bayesian probability make.)
Fuzzy Logic--A Practical Approach by F Martin McNeill and Ellen Thro (AP Professional, 1994)
If you are searching for an introduction to fuzzy systems with an absolute bare minimum of mathematical notation, this is your best bet. In addition to a discussion of fuzzy rulebases, the book addresses fuzzy decision making and fuzzy cognitive maps, two architectures often overshadowed by the currently more popular rulebase. A number of basic Windows-based fuzzy tools, which McNeill wrote, come with the book; the tools are thoroughly discussed in the text and serve as the basis for many of the examples.
Industrial Applications of Fuzzy Control edited by Michio Sugeno (North Holland, 1985).
This book, now a decade old, describes how fuzzy logic had been used in industrial applications prior to 1985. The book describes 10 applications, 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. Sugeno also includes an annotated bibliography of fuzzy control, which Richard Tong compiled.
This is an excellent book. It presents, at various depths, how fuzzy systems were being used world-wide in the mid-1980s. Although a bit expensive (currently more than $100), the book is worth it for those seriously involved in fuzzy control.
Fuzzy Systems Theory and Its Applications by Toshiro Terano, Kiyoji Asai, and Michio Sugeno (Academic Press, (English) 1992)
This book is an English translation of the Japanese original, which appeared in print in 1987. It contains a fair amount of mathematical representation but has well-supported explanations. Prior to the book by Yager and Filev (listed below), this book was my first recommendation for anyone interested in both theory and application.
The book has 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 discuss applying theory to diagnosis, control, human activities, robots, image recognition, databases, information re-trieval, and damage assessment. These chapters present how fuzzy approaches are currently applied, rather than discussing actual applications. Nonetheless, the book is thorough, and the English translation is quite good.
Essentials of Fuzzy Modeling and Control by Ron Yager and Dimitar Filev (John Wiley & Sons, 1994).
This text is new enough that I have not yet finished reading it. After a complete reading of the first few chapters and a skim of the rest of the book, I am impressed. The book introduces fuzzy sets and logic operators, and then it details approximate reasoning ("a powerful framework for reasoning in the face of uncertain information") and fuzzy control. Its middle chapters discuss fuzzy-system models and how to develop them; the latter chapters address theoretical aspects of fuzzy-logic control, defuzzification, and various fuzzy-reasoning paradigms. The book's mathematical notation is fairly easy to understand and work with. Overall, this is an easy book to recommend.
Journals
Price and content typically rule against a practicing engineer's subscribing to the following journals, but if you have access to one or more of these publications, review them regularly.
As additional references become available, I shall bring them to your attention in future columns. If you know of a good fuzzy-logic reference I have not discussed here, please let me know. All comments are welcome.
| Most learning comes from doing, but reading goes a long way, too |