One of my biggest gripes about fuzzy logic today- - ranking right up there with fuzzy opponents who vehemently criticize fuzzy systems they do not understand and fuzzy proponents who favorably compare fuzzy systems to traditional systems they do not understand- - is that the term "fuzzy logic" has become synonymous with "fuzzy rule base." When we hear of a "fuzzy logic system," we immediately want to know what its rules and membership functions are and what inference and defuzzification methods the designer used.

This view is too myopic. Taken by itself, fuzzy logic is not a procedure, method, structure, or technique; it is a logic, a mathematical basis. Conversely, a fuzzy rule base is a structure- - a rule base- - that uses fuzzy logic.

I point out this difference not merely for the sake of semantics, but because when we accept that "fuzzy logic" equals "fuzzy rule base," we severely limit our thinking as to what fuzzy logic is capable of. We are content standing on the first rung of the fuzzy-technology ladder and have no idea how tall the ladder is or where it leads. My original title for this column was "Fuzzy logic doesn’t need rules."

I am not opposed to fuzzy rule bases. I have designed a fair number of systems using them and, no doubt, will design many more. However, I feel we also need to be actively and anxiously engaged in finding ways to use fuzzy logic in structures that do not incorporate a rule base.

Here is one way to look at it. Consider the three-tiered pyramid in Figure 1. At the top is fuzzy logic, the mathematical basis formalized by Lotfi Zadeh 30 years ago. It is a generalization of bilevel, or Boolean, logic and allows for shades of gray in the transition from true to false. Those who feel most comfortable at this top level are mathematicians- - or at least the mathematically oriented.

The second tier of the pyramid consists of methods, procedures, structures, models, and techniques that fuzzy logic or fuzzy set theory can strengthen considerably. (Because I shall refer to them often, for the rest of the column I shall lump "methods, procedures, structures, models, and techniques" all under the single category, "methods.") This second tier is where the fuzzy rule base resides, and there are many other methods at this level, as well. Figure 1 shows those methods with which I have worked, and these are but a small number of many. If there is such an animal as a "fuzzy engineer," this second tier is where he or she belongs, developing and refining methods. This is where domain experts belong as well, at least those who feel comfortable with fuzzy logic and are able to apply it to the methods they use in their own domains.

Applications make up the third tier of the pyramid, its base. This is where the problems are solved that we as engineers face. These are the domains of domain experts, where knowledge unique to the problem is more important than knowledge of the inner workings of fuzzy structures- - although how you apply fuzzy, and other engineering methods, is critical.

The first tier, fuzzy logic, feeds the second tier, fuzzy-logic methods, which, in turn, feeds the third tier, applications. To date, fuzzy rule bases have been applied to myriad applications in myriad disciplines. To a lesser degree, so have fuzzy cognitive maps and, still less, fuzzy constraints, fuzzy evidence, and fuzzy states.

Where is all this leading? First, we must clarify in our own minds what fuzzy logic is, how to apply it, and what it can be applied to, and, second, doing so is merely the first step in a process that ultimately will lead to far greater use of fuzzy logic. And why am I interested in far greater use of fuzzy logic, other than just billing myself as a consultant in fuzzy-system design?

Earlier, I mentioned a fuzzy-technology ladder. While working a number of particularly thorny problems in which fuzzy logic has played a role, I have had the opportunity to briefly climb a step or two above the sometimes madding crowd on the first rung of that ladder and have caught glimpses farther upward. Those glimpses have considerably strengthened what I already believed- - that, when fully utilized, fuzzy logic, or, perhaps, fuzziness in general will become a significant part of all that we engineers do.

I do not intend this to be a melodramatic declaration, full of fury, but signifying nothing. With the advent, ever-increasing power, and utilization of the computer, I see time-honored, closed analytic models giving way to computer-simulated models of great sophistication. The impetus may be the computer, but the ultimate justification for moving from analytic to computer-simulated models is that mathematical models are really only convenient approximations that have been used because they give reasonable, believable, and often accurate answers. By including complex system subtleties that are typically removed from analytic models to make them malleable, a well-designed computer-based model can achieve greater accuracy in its representation of the modeled system. And, used judiciously, computer simulations can include the fuzziness that appears to be inherent in much of the real world.

Another title I considered for this column was "A call to action." That call would be neither to set aside the techniques for solving those problems that are peculiar to your specialties, replacing them with a fuzzy rule base, nor to add fuzzy logic to your individual collection of problem-solving tools, although that is counsel I strongly give.

Rather, the call is to learn- - really learn- - what fuzzy logic is (and by fuzzy logic, I mean the top tier of the pyramid). Learn it sufficiently well that you are able to enhance those methods you already know, the second tier items. I’m not haranguing you to replace your PID controller with a fuzzy-rule-based controller, or your neural-net super-widget with a fuzzy-logic super-widget. I am haranguing you to become comfortable with the concept of fuzziness and then to look at your PID structure or super-widget structure and determine if and how the use of fuzzy logic can make it stronger.

My "call to action" is actually a "call to innovation"- - a request that you step away from cookbook solutions and look for fuzzy alternatives. Base these primarily on your individual domain expertise and on your understanding of how fuzzy logic can strengthen the various available methods with which you are already familiar. Don’t get too caught up with canonical solutions, fuzzy or otherwise, until and unless you can convince yourself that a canonical solution is best for your problem. Your problem is unique; the solution to your problem may be as well.

The move toward fuzzy methods will not always be easy, and the difficulties seem more often to be political, rather than a lack of technical understanding. There are those (many of my nonfuzzy clients among them) who, based on its name, want nothing to do with fuzzy logic. For those of you who face this hurdle, I have a proposal.

Over the past 30 years, there have been many suggestions for a replacement for the term "fuzzy." "Infinite valued," "continuous," and "gray" all come to mind, and I know I have read many others. I even thought of holding a contest through this column to see who could come up with the best name. However, Professor Zadeh is quoted as having originally considered most of the suggested alternatives he had heard and others ("cloudy," for instance), when he settled on "fuzzy"; and he is still quite happy with "fuzzy," despite having taken three decades worth of flak for it.

There is one name Zadeh did not think of and would have never considered, which I believe to be a worthy substitute. I hereby formally propose, both to honor Zadeh as the father of fuzzy logic and to provide an alternative term for appropriate situations, that we accept as a synonym for the term "fuzzy," the term "Zadehan." Bilevel and Boolean are largely synonymous; I suggest that we do the same with fuzzy and Zadehan. "Zadehan" would be used in the phrases "Zadehan logic," "Zadehan sets," "Zadehan numbers," "Zadehan evidence," and so forth. It is my intent, in future EDN columns, in presentations I give, and in papers I write, to use the terms "fuzzy" and "Zadehan" interchangeably. In talking with clients who want nothing to do with anything fuzzy, I shall, of course, use "Zadehan" exclusively.

Zadeh and I have spoken, and, with characteristic humility, he will not oppose what I am proposing. I have contacted those whom I feel are the top 25 fuzzy researchers in the United States, Japan, and Europe and have received supportive responses from them. I invite your support as well.

Of the too many titles for this column, here are the final two and the best: "Zadehan logic: There’s nothing fuzzy about it" and "Zadehan logic: It’s fuzzy to the core." Take your pick.