Columnist February 3, 1997

I'll be back

David Brubaker, contributing editor

  I'm taking a sabbatical from this column to work on a book. As currently conceived, it will describe the application of Zadehan (fuzzy) logic to a number of engineering procedures, methods, structures, models, and techniques other than the now very familiar rule base. EDN has given me its blessing; I plan to return as a full-time columnist when the book is finished.

  To provide some closure to the set of nearly 30 columns I have written, I'll summarize three important points. Based on a number of conversations I have had over the past several months, there are still a lot of engineers who do not understand fuzzy systems even at a general level.

  First point: There is no magic in a fuzzy-rule-based system. Whether used in control, prediction, estimation, detection, decision- making, or whatever, a fuzzy rule base is a function approximator that contains

• membership functions that divide the input space into unique regions
• rules that assign an output value (or function) to each of those regions.

Fuzzy logic provides a more or less smooth transition between adjacent output values.

  That's it—no glitz, no glamour. There are no special training algorithms, no hidden layers of complexity. Even the fuzzy community's only attempt to add mystery to its specialty, the defuzzification algorithm, is unnecessary in the vast majority of applications. (That is, although input membership functions are good and valuable, in all but a very few applications, output membership functions should be replaced either with singletons or with linear functions that are dependent on input, not output, parameters. "Defuzzification" should be nothing more than a weighted average. And no, this is not my second point.)

  So, how has fuzzy logic attained what seems to be an almost- mystical reputation for both good and evil? Here is my guess.

  The use of fuzzy logic considerably strengthens the traditional rule base in many applications. It accomplishes this goal by providing interpolation among output values, thereby allowing the number of input regions (and, therefore, the number of rules) to be reduced. Although use of look-up tables has traditionally been pooh-poohed as a viable engineering approach, the look-up table in the form of a fuzzy rule base was suddenly able to provide a practical solution to significant problems.

  The union of rule-base and Zadehan logic is highly complementary. A rule base can generate logically expressed solutions, with rules most often of the form, "If the input is this value, then set the output to that value." Fuzzy logic additionally allows expressing input values using words, with the translation into manipulatable numbers occurring in membership function definitions. Using a fuzzy-logic-en-hanced rule base, system designers, therefore, found themselves solving complex problems using nothing more than a model of their own, intuitive thought pro-cess. A verbally expressed, logically processed set of rules linking system inputs to system outputs re-placed highly specialized, often-esoteric techniques and methods, where the understanding of the method often seemed (and still seems) more difficult than understanding the problem being solved.

  This shift in how complex solutions could be obtained resulted in

• the apparently magical manner in which a fuzzy rule base could be used to generate solid, workable solutions (with solutions now capable of being cast largely in problem-domain terms)
• the "any-idiot-can-design-a-fuzzy-system" attitude both hailed and derided in the industry. This leads nicely into my…

  Second point: Any idiot cannot design a fuzzy-rule-based system. It takes an intelligent and experienced idiot. Despite not having to learn the complex methods often associated with other approaches, the system designer must still thoroughly understand the system being designed, the problem being solved. I repeat what I wrote in an earlier column: That a system is fuzzy does not guarantee that it is good or even adequate. The garbage-in, gar-bage-out law still applies. Enough said.

  Third (and final) point: Despite the tendency by most to do so, the terms "fuzzy logic" and "fuzzy rule base" are not synonymous. Fuzzy logic is the mathematics—a type of logic. A fuzzy rule base is the result of applying fuzzy logic to a crisp rule base. I have strong feelings on this point, and it is not merely a study in semantics. To allow the term "fuzzy logic" to be overloaded in this manner clouds our vision of fuzzy logic's application to other, logic-based techniques and methods, which, as I mentioned in the beginning, the topic of my book. Wish me luck. Or, better yet, wish me success. And if you have any thoughts or ideas, please let me know via e-mail: dbbaker@ix.netcom.com.

David Brubaker is a consultant in fuzzy-system design. You can reach him at Huntington Advanced Technology, 883 Santa Cruz Ave, Suite 31, Menlo Park, CA 94025-4608 or on the Internet at: dbbaker@ix.netcom.com.

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