Computer Design
April 1992
FUZZY LOGIC IS ANYTHING BUT FUZZY
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- 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 ill-
defined 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.
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