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Computer Design April 1992 FUZZY LOGIC IS ANYTHING BUT FUZZY --------------------------------- INTERVIEW WITH PROFESSOR LOTFI ZADEH CD: Today fuzzy logic appears to be most widely used in control applications, but still seems to be having trouble gaining acceptance. How do you view the situation? Zadeh: We have to realize that it's very natural for people, including myself, to be skeptical when they're presented with something that claims to provide a different way of looking at things. In 1965 my expectation was that most applications would be in the realm of ``humanistic systems,'' such as linguistics, social sciences and biological sciences where hard mathematics doesn't seem very effective. But then we began to see that fuzzy logic could be used in control. In control it is said that people want rigor and respectability. But then there are many realistic problems that cannot be rigorously defined. Fuzzy algorithms for control policy will gain increasing though perhaps grudging acceptance because conventional nonfuzzy algorithms cannot in general cope with the complexity and illdefined nature of large scale systems. Control theory must become less preoccupied with mathematical rigor and precision and more concerned with the development of qualitative or approximate solutions to pressing real world problems. CD: What do you tell people who express doubts about the reliability and stability of fuzzy systems? Zadeh: In the case of control systems, we do have a theory of stability. And presumably that theory can tell you that a certain kind of system will be stable. But actually that is much less significant from a practical point of view than one might think. Once you read the fine print, you find that what the theory can tell you is much more limited. It can tell you that if you linearize and if you do all sorts of things under certain assumptions. The trouble is it's very difficult to say whether those assumptions hold or not. So you're left with something that is not really comforting. You can't really sleep safely if someone using classical theory tells you that some control system is stable. Fuzzy systems are course systems. Fuzzy control is course control that exploits the tolerance for imprecision. So if there is some imprecision and if the imprecision can be tolerated, you try to take advantage of it by making the system more robust and less susceptible to deviation. But still it is correct to say that at this point we don't have a theory for stability of fuzzy logic control that is nearly as well developed as for classical systems. Stability theory is really effective when it comes to linear systems and fuzzy systems deal with nonlinearity. In the case of fuzzy control, the systems are very complex. In many cases you cannot describe really what they do so it is difficult to prove or disprove stability. It's not that people are stupid, it's that the problems are more complex and it's

more difficult to come out with some kind of unqualified statement. So people compensate for that with simulation. They perform many, many trial runs. In the case of the subway in the city of Sendai, Japan, I think there were some 300,000 simulations and 2,000 actual runs to prove the system because you do not play with a subway system. So I think the fact that the Sendai subway system has functioned perfectly since July 15, 1987 is a stronger testimony than theory. So here is a system where the issues of stability and reliability are of paramount importance and it has proved to be successful. CD: Is the choice then between devoting a lot of time to establishing a mathematical model for classical control in advance, or, in fuzzy logic, designing the system and then proving and refining it in simulation? Zadeh: I think you put it well. The test of any theory is the ability to predict. So if you cannot predict what will happen, you don't have much of a theory. Many so-called theories flunk this test, particularly in economics. In fuzzy systems, instead of performing some sort of analysis on paper or on computer that will predict how the system will behave, you simulate. So simulation is an alternative to prediction. It is not as desirable, but in the final analysis it may be more reliable. There's always a possibility that your theoretical analysis didn't take into consideration certain things. Software is a good example. In the final analysis you have to run the program. Only actual use will tell you if there are bugs in the program or not. -----------------------------------------------------------This is article is provided with permission from Computer Design. For subscription information to Computer Design, call Paul Westervelt at (913) 835-3161. Do not redistribute in any form (written or electronic) without permission from Computer Design. This information is provided by Aptronix FuzzyNet 408-428-1883 Data USR V.32bis