                              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 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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