### An interview with Lotfi Zadeh, the father of fuzzy logic

Even at 73 years of age, Lotfi Zadeh, the father of fuzzy logic, has an energetic stage presence. Nowhere is this more evident than in the rapt attention he commands when presenting his paper, "Fuzzy Logic: Issues, Contentions and Perspectives," at the 22nd Annual ACM Computer Science Conference in Phoenix, Arizona on March 8, 1994.

It is during this session that, once again, Zadeh's colleague and friendly personal gadfly, Professor William Kahan, rises to challenge, for three full minutes, Zadeh's lifework as an assault of illogic upon the scientific foundation of control engineering. "A scientific idea is one which contains within it the germ of a refutation," says Kahan. "A test can then be posited whereby the hypothetical refutation can be proven or disproven. Fuzzy logic has no scientific content because it doesn't assert anything upon which we can model such a hypothetical refutation."

Zadeh's lips tighten into a tolerant smile. He toys with the lapels of his suit coat, he lowers his eyes and rocks back and forth slightly at the podium as he again hears the familiar arguments.

Afterwards, Zadeh (referred to as "LZ" in the following interview) and I chat on subjects ranging from the theory and economics of fuzzy logic, to AI, fractals, philosophy, and Zadeh's boyhood in Stalin's Soviet Union. We are joined by William Kahan (WK) who, like Zadeh, is a professor at the University of California, Berkeley, and John Osmundsen (JO), associate director, public affairs, of the ACM.

In the first installment of this two-part article, Zadeh examines the philosophical underpinnings of fuzzy logic, how it relates to disciplines such as fractals and AI, and his youth in the USSR and Iran. Next month, we'll discuss fuzzy applications, such as Japan's Sendai train, and hear in detail what Professor Kahan thinks of fuzzy logic.

** DDJ:** What you said in your lecture today that struck me the most is that fuzzy logic is a means of presenting problems to computers in a way akin to the way humans solve them.

**LZ:** There is one way of expressing that, which I use sometimes: The role model for fuzzy logic is the human mind. If you examine the way the human mind functions, you find that the human mind has this remarkable capability to deal with information which is incomplete, imprecise, uncertain, and so forth. Computers do not have that capability to any significant extent.

Classical logic is normative. Classical logic in effect tells you, "That's the way you should be reasoning." There is a big difference in that sense between the spirit of classical logic, which is prescriptive, and the spirit of fuzzy logic, which is descriptive. That is, it merely asks the question "How *do* you reason about this or that?" It's like translation. The translator does not take responsibility for what he or she translates.

** DDJ:** And the analogy of translation to fuzzy logic is that fuzzy logic is simply a translation mechanism?

**LZ:** Well, there are many facets to fuzzy logic, so you cannot summarize the whole thing in one sentence. I'm talking here about one particular facet of fuzzy logic. That facet has to do with most practical applications today in the realm of consumer products and in many other fields, where what you do is you use the language of fuzzy rules. You start with a human solution and you translate it into that language. But it doesn't mean that that is all there is to fuzzy logic, because there are many other things that fall within the province of fuzzy logic that would not fit this description. The essence of fuzzy logic is that *everything* is a matter of degree, including the notion of subsethood.

** DDJ:** Is this a philosophical point of view that finds itself translated into computer logic--the notion that everything is a matter of shades, and varyings, and degrees? Is there a personal philosophical viewpoint that is finding its expression in computer science in your work?

**LZ:** Not yet, but consider the following: The real world that we live in is very fuzzy, very imprecise, very uncertain. The theories that we have constructed are, on the other hand, very precise. We have mathematics, we have all kinds of things which are very precise in nature.

Now, these theories have proved to be very successful in many respects, but their ability to come to grips with the analysis of complex systems--I mean complex not just in terms of number of components, for example, a chip that has two million resistors_. When I say "complex," I mean "complex economic systems" and things of that kind, systems with many components, with relationships that are not well defined. The successes of classical techniques, in connection with certain kinds of systems, have led us to believe they can be successful also in dealing with the other types of systems, such as economic systems.

There is no question about it, classical mathematics has proved to be very successful in astronomy, where you compute the orbits of stars and planets. But people then conclude from that that you can apply mathematics equally successfully to laws of economic systems. And that's where I question this thing.

I say "No, these systems don't fit. You need a concept of classes which don't have well-defined boundaries." And if you do, as fuzzy logic attempts to do, construct such a framework, then you enhance your ability to model economic systems and other systems of that kind. It doesn't mean you'll be able to solve all the problems, but at least you'll be able to do much more.

This applies, for example, to natural languages. Notice that we didn't make that much headway in machine translation, and essentially *nothing* in machine summarization. If I ask you to write a program that will look at a book and summarize it, I think you'll say that we cannot do that. Not only can't we do it today, there's no way that we can conceive of doing that in the foreseeable future.

The situation is this, that there is this tradition of believing that conventional, traditional techniques have the power within them to solve some of these problems. My position is that this is not the case.

** DDJ:** It sounds like you are making a point analogous to that of Benoit Mandelbrot in

*The Fractal Geometry of Nature,*in which he pointed out that mathematicians at the turn of the twentieth century, including his father…

**LZ:** His uncle…

** DDJ:**_his uncle, had examined fractal forms and had been roundly criticized in the math world for studying these "monstrosities," and asked why they did not go back to studying genuine geometrical forms such as the sphere. Mandelbrot points out that there are no spheres in nature, no squares, nothing which has perfect form to it. It's just a question of to what degree our measurement instruments are able to penetrate the form and discover the imperfections that nature has placed there--the "sacred error," as it were.

**LZ:** I know Mandelbrot quite well, and hold great respect and admiration for him. Mandelbrot stays within the traditional framework. He does consider objects, fractals, and he did raise questions of the kind that other people somehow did not raise, for example: What is the length of the coastline of Brittany? To me, that's a very good question, because somehow people took it for granted that there is an answer to that question. But he pointed out that there isn't an answer to that question, because it depends on the degree of resolution.

** DDJ:** It ends up being a question about your measuring instruments, and not about the problem you're trying to solve.

**LZ:** That's right. So I think it was a very incisive observation that questions like that *cannot *be answered within the traditional framework. But what Mandelbrot tried to do--and I think it's a very significant accomplishment, but different from what you do in fuzzy logic--he attempted to come up with a reasonably precise theory of this sort of thing. So he talks about fractional dimension. Basically, Mandelbrot is a mathematician by training, and he has not abandoned his home, so to speak.

So to me, the theory of fractals is an important theory, and it helped to focus attention on issues that were not really properly formulated before. But by itself, it stays within the traditional paradigm. In other words, you're still committed to the goal of mathematicians: to come up with theorems. I'm not saying that that goal is not a worthwhile goal, I'm merely saying that in many cases it is *unattainable*.

** DDJ:** When you come down to the field of practical engineering, especially in problems of embedded control, the problem of making machines that can in real time make, if not perfect decisions, then reasonable decisions…

**LZ:** Certainly.

** DDJ:** My father is 74 years old, and he doesn't know which end of the computer you hook up the airhose to, but he knows what fuzzy logic is because he has been an amateur photographer for 60 years, and his Japanese camera can determine the illumination of dim objects against bright background light--using fuzzy logic. "Fuzzy logic" is also part of the advertising.

**LZ:** Minolta uses fuzzy logic very extensively.

** DDJ:** Do you derive any royalties from this?

**LZ:** Zero. The thought of applying for a patent did not even occur to me at the time I did the work.

** DDJ:** Is this an oversight which you regret?

**LZ:** No, not at all. Perhaps I would be a rich man, but so long as I can live in reasonable comfort, that's enough.