Concluding our conversation with the father of fuzzy logic
Last month, Jack Woehr spoke with Lotfi Zadeh, the father of fuzzy logic, shortly after Zadeh presented a paper entitled "Fuzzy Logic: Issues, Contentions and Perspectives" at the 22nd Annual ACM Computer Science Conference in Phoenix, Arizona on March 8, 1994. In this installment, Woehr and Zadeh (identified as "LZ" in the following interview) are joined by Professor William Kahan (WK) and John Osmundsen (JO), associate director, public affairs, of the ACM.
DDJ: Professor Zadeh, do you travel to Japan?
LZ: Yes, I was there a week ago. There are many misconceptions. One of the misconceptions is that the Japanese just jumped on this thing. No. I wrote my paper in 1965. Starting in 1968, you'll find that there are quite a few papers in Japanese literature dealing with fairly sophisticated applications of fuzzy logic. In 1970 a study group was formed and met once a month, sometimes in Tokyo, sometimes in Kyoto.
There were some people in Japan, influential people, who saw that this was promising. The director of the National Laboratory for Fuzzy Engineering is one of them, Toshio Terano. The late Okicha Tanaka was one of them.
In 1974, there was a joint America-Japan symposium on fuzzy-set theory in Berkeley. There were about 20 people from Japan that time. Professor Terano was among them. The Japanese came in at an early stage. It was not a rash decision. They started working on it a long time ago.
They started working on the Sendai train in 1979. Sendai is a modern city, beautifully planned. The system is a real model. It runs beautifully, it's clean, it's an outstanding system. They went into operation in 1987, so they spent eight years. Hitachi did the electronics, Kawasaki Heavy Industries built the train. I must take my hat off to the Hitachi people and Kawasaki people for starting with an idea that, in 1979, was still in a somewhat embryonic stage. Subway systems are not toys! Lives are at stake.
In Japan, people are so careful, and bureaucracy is so strong. The regulatory agencies in Japan are notorious in their insistence on all kinds of tests. Three-hundred thousand simulations and two thousand actual runs before they finally certified that system. No American company would have done that. No American company would have spent eight years on that sort of thing.
Today in Japan they have a large number of engineers working for various companies who have quite a bit of experience in the use of fuzzy logic.
DDJ: Hitachi was daring in going with an embryonic technology that did not have an overwhelming body of field trials. To what extent was this confidence in your work? To what extent was it confidence in Japanese work? To what extent was it hubris, the Japanese deciding confidently they could solve any problems found along the way?
LZ: I would say it was a combination of all of these things. These people are very serious. They take an idea which perhaps did not originate in Japan, but are much more thorough, much more serious about developing [it] than we would be in this country.
All of these systems--our system, their system--have certain strengths and weaknesses. Their system is very strong when it comes to very methodical, very detailed research and development. They also have many original ideas, but the crux of their strength lies in the areas I have noted. They're tenacious, they're persistent, so they can take an idea and do wonders with it, because of the way in which they function.
JO: What applications would one definitely prefer to do using fuzzy logic?
LZ: There are many. When you talk about applications, you can divide them into a couple of groups.
In one group are those applications in which there is no competition for fuzzy logic. Then in the second group are applications in which you can use fuzzy logic, or you can use something else. Then it becomes a question of what is better.
Now, the first group I refer to as the issue of tractability. Forget the economics: Can you solve the problem? Let me give you some examples of this sort of thing. Let me start with a very practical sort of thing: the Isuzu hand-braking system.
In Japan, automotive applications are becoming very widespread. This is a very simple idea. If you are in a car, and you are going uphill, and you want to park your car, it becomes a problem. You have to play with the hand brake, and if you have one of those hand brakes which you have to release with your foot, you are in real trouble.
This simple idea occurred to the Isuzu people. Assume you know what you want to do. Express that in fuzzy rules. IF you are on a hill AND you want to back into a parking space AND IF you want so much pressure to be applied, and so forth, THEN do this and so forth. Just take these rules and implement them. The Isuzu system makes it possible for you to slide into a parking space.
DDJ: So you are saying that the various degrees of release of the brake, the gradations of speed of forward and backward motion, all combine to render this a fuzzy problem for fuzzy logic.
LZ: Yes. Bill, come and join us! We're talking about fuzzy logic.
WK: As in, "What's the difference between fuzzy logic and fuzzy thinking?"
LZ: We were talking about problems in which there is competition for fuzzy logic and problems in which there is no competition, problems where if you want to solve them, you must use fuzzy logic, problems intractable by conventional solutions.
How do you cross a traffic intersection in a vehicle? In our head, we have a bunch of rules. For example, if there is a light, a stop sign, two-way street, one-way street…various dynamics which describe the situation. But given those parameters, then you can formulate the rules.… IF there is a car that is approaching, if there's a red light, a green light, a yellow light. IF you are going so fast, THEN do something, press on the brake, et cetera. You can formulate a bunch of rules. Now, my point is that there is no way in which such rules could be formulated using some other methodology; there is no way you can do it.
DDJ: Do you mean there is no practical way, or there is, in an ideal sense, no mathematical way?
LZ: Humans can't do it. First of all, operations research or something like that can't provide any answers, and secondly, humans can't formulate these rules crisply. If this car's speed is greater than or equal to 25 mph and you are within a distance of 20 feet, then apply so much pressure to the brake. People just cannot do it.
DDJ: There is a nonfinite number of rules without fuzzy logic.
LZ: People can't be this precise. They have this fuzzy perception of what to do.
WK: That's an interesting claim. It's always very hard to prove a negative. I don't know of any evidence, or for that matter, of any body of opinion that would say that no such set of rules could be formulated.
I suppose we could put it to a test by creating a robot-controlled vehicle and seeing whether it succeeded in crossing a traffic intersection at least about as often as human-controlled vehicles do. I feel more optimistic than Lotfi. I feel I could design such a thing myself. I don't think it would be hard. All I have to do is get it to know when to stop and when to proceed through the intersection. There's one difficulty, perhaps what Lotfi is thinking about. It's called the "Paradox of Buridan's Ass," the hungry donkey so neatly situated between two equally attractive piles of straw….
DDJ: …that he starves to death.
WK: It turns out that in every decision situation, every go/no-go situation, there is always a finite risk….
DDJ: …of stasis.
WK: …of being hung up. In fact, switching circuits offer a similar finite risk, although they are designed to make that risk so tiny that you don't normally notice it. If that is the difficulty Lotfi means, then there's an intrinsic impossibility. But if that's not the difficulty he means, if we're willing to take the chance that every now and then, maybe once in every millennium, the device may be paralyzed by indecision, then I rather dispute that it can't be done (by conventional control theory).
DDJ: I have two thoughts simultaneously. One is that I'm not sure that you and Professor Zadeh have the same meaning for the word "can't."
WK: Perhaps not.
DDJ: The second is that, [speaking] as a former taxi driver, the problem in a San Francisco intersection is that you are never sure that the oncoming cross-traffic is actually going to stop for the red light. Thus you are constantly adjusting your speed planning for a fail-safe abort pending the diminishing speed of the car coming down the hill towards the red light on the cross street.
WK: I don't believe that those calculations are of the kind that can only be characterized in the language of fuzzy sets. The perceptions that you have as a driver can be quantified. With patience, one can enumerate these perceptions, and with sensors create a robot that can approximate a human being's actions without resorting to concepts like "very," "somewhat," et cetera.
DDJ: Let's look at another domain. The game of chess has an absolute mathematical solution for every sequence of moves. Knowing that there exists, in theory…an absolute solution, the field of computer chess does not seek any such solution except in the endgames, wherein brute force can solve the problem exhaustively in real time.
Is it possible that there is a "Platonic Ideal" solution to all these engineering problems that Professor Zadeh brings up, but one that can't be reached in real time in the late twentieth century by American engineers, only approximated by fuzzy logic?
WK: No, I think that's a different problem. In chess you have combinatorial explosion which makes it impossible to implement. The mathematical solution's existence you can prove, but a generalized algorithm is intractable because it would simply take too much computing. And so instead, we devise a variety of strategies. We have extremely good chess-playing programs. These have not been devised using the fuzzy calculus.
DDJ: But the heuristics of the chess-playing programs resemble fuzzy logic in many respects.
LZ: Take backgammon. [Chess grand master emeritus] Hans Berliner wrote a program that was very good at playing backgammon. He used crisp rules. Then he introduced fuzzy rules, and the performance of the program improved to the point where the program played championship-quality backgammon. If you look at commentaries on chess, you'll find that all of the comments are fuzzy. They say, "the center was strengthened," et cetera. The reason fuzziness comes into chess is that you have an ultimate goal--checkmate--which is crisp, but that ultimate goal is too far away, in some sense, at the intermediate stages of the game. So you have to replace it with local goals. The local goals are fuzzy goals.
WK: Lotfi's error here is a failing of pride. He has a fuzzy calculus, infers that this is the way the mind works, and imputes to the commentators on chess a similar strategy.
Another game in which the combinatorial explosion caused even more despair than chess is the Japanese game of Go. A book has come out recently by Burlekamp and Wolf which analyzes a large class of endgames in Go--endgames which used to use the same vocabulary as Lotfi is using for chess. What they've shown is that you can actually analyze these quite exactly, and consequently discover that positions which experts in Go would have given up as a draw or loss, are actually wins.
DDJ: When you gentlemen get into mathematical theory, you fly way over my head. But when you talk about chess, Go, and backgammon, I'm a United States Chess Federation expert-class player. I understand your references to Go research, and there is a similar problem in chess. That is, if you start backwards from the end of the game, you can analyze many, many positions. Nowadays, with the aid of computers, many endings which were unclear have been solved definitively by brute-force calculation.
I know several grand masters of chess. The chess world hasn't had any doubt since the 1950s that computers would eventually revolutionize the endgame. They didn't use to believe they would be beaten by computers over the board, however, because by the standard of computers of the 1950s and 1960s, it didn't appear that computers would ever get good enough at working through approximate situations which have no potential for being solved deterministically in real time.
WK: In other words, that they would never be able to formulate a strategy.
DDJ: Yes. But now people like grand master Julio Kaplan in Berkeley and Kaufmann and others have been instrumental in aiding the computer programmers to understand what strategy in chess consists of. It's a very fuzzy set! If the center is flexible (which covers a wide variety of possible pawn positions), then don't attack on the wing….
WK: The question about the use of fuzzy calculus in the context of computing is a question about whether that design paradigm is preferable in circumstances where you can see the possibility of using the standard design paradigms, albeit laboriously, to accomplish the desired technological goals.
When it comes to playing various games, since it may very well be that there is no design paradigm that can be guaranteed to be better than another, it may not hurt very much to say, "Let's try fuzzy logic, what have we got to lose?"
LZ: There is one transparency which I sometimes show in my lectures which I call the "effectiveness chart." I have a triangle there, the vertices of which are labeled "fuzzy logic," "neural net," and "probabilistic reasoning." Particular problems are represented as points. I put a problem close to the vertex labeled "fuzzy logic." It means that that problem can be solved effectively using fuzzy logic. It may be far away from "neural network," or it might be perhaps somewhere in between, meaning it can be solved using fuzzy logic or neural networks.
The purpose of this sort of thing is to say, "Look, you cannot take the position that any one of these methodologies in itself is superior to the other ones." It depends really on the problems you are examining.
Returning to backgammon, there has recently been what I consider to be a highly significant development. Gerald Tesauro [at IBM Hawthorne] came out with a paper in which he described using reinforcement learning. You start with a description of the legal moves, the board, the rules. That's all. The system then begins to play, and eventually it learns to play quite well, until finally it plays championship-quality backgammon!
JO: The interesting thing for me is not only the fact that the program eventually plays world-class backgammon, but that for the first few hundred thousand games it is a mess. Its weighting is graphed, and the weights appear randomly distributed. All of a sudden it kicks in, and there is order in the distribution of the weighted guesses. It reaches a point where it self-organizes its neural net and can repeat its high-quality plays from then on.
LZ: If you look then at what Hans Berliner did, he himself supplied the rules. What can fuzzy logic do? Nothing. In that kind of a thing, fuzzy logic can do nothing, because fuzzy logic does not have the capability to start from scratch and learn. In combination with neural networks, it can, but not by itself. There is learning and training in fuzzy logic, but it is nowhere nearly as advanced as Tesauro's work and neural networking in general.
Here is an example of a problem which can be solved in an impressive way by one methodology and not at all by other techniques!
