Fuzzy Logic: What is it ?
To understand this statement by Jesse
"Crude mathematical models do not have real predictive power ......................"
Excerpts of an interview with Prof Lotfi A Zedda (a Berkley prof. still practising)
Q. In other words, some of the more difficult problems
in AI won't be solved by innovations in supercomputer
architecture--innovations like parallel
processing?
ZADEH. That's right, such innovations aren't going to
help much.
But there is more to this fuzzy logic than simply the
enhancement of the ability of computers to solve various
problems--to perform nontrivial cognitive tasks.
Accepting fuzzy logic will also call for a certain fundamental
shift in attitudes, particularly in theoretical
computer science. At this point theoretical computer
science is mathematical in spirit, in the sense that it is
oriented toward the discovery and proof of results that
can be stated as theorems.
Unfortunately, there is an incompatibility between
precision and complexity. As the complexity of a system
increases, our ability to make precise and yet nontrivial
assertions about its behavior diminishes. For example,
it is very difficult to prove a theorem about the
behavior of an economic system that is of relevance to
real-world economics.What I anticipate in the future is a growing recognition
of the necessity to find an accommodation with the
pervasive imprecision of the real world. This change is
needed to be able to make assertions that are not just
nontrivial theorems, but something of relevance to
practice. In computer science today, people use twovalued
logic to establish certain results. But such resuits
are often limited in their relevance to the real
world--because they are excessively precise. In other
words, we have to accord acceptance to assertions that
do not adhere to high standards of precision.
This accommodation with imprecision will require
the use of fuzzy logic. Gradually and perhaps rather
slowly, there will be a growing acceptance of fuzzy
logic as a conceptual framework for computer science.
Now, it is a little bit more difficult to articulate this
particular position than some of the earlier things that I
said. For this gets into issues that relate not just to
computer science but, more generally, to science itself.
Science at this point is based on two-valued logic. So
what I'm talking about is a significant shift in attitude,
not just in computer science, but more generally in
scientific thinking.
At this point there is a long-standing and deep-seated
tradition of according respectability to what is mathematical
and precise. We may have to retreat from this
tradition in order to be able to say something useful
about complex systems and in particular about systems
in which human reasoning plays an important role.
Q. Okay, then, there have been instances in the past
where scientists have been too preoccupied with
mathematics and precision and, as a result, have
failed to come up with useful results. Does an example
come to mind?
ZADEH. Yes. Take economics. Time and again, it has
been demonstrated that what actually happens in the
realm of economics is very different from what the
experts predicted. These experts might be using largescale
econometric models, sophisticated mathematics,
large-scale computers, and the like. Despite all that, the
forecasts turn out to be wrong--very wrong.
Why? Two reasons. One is that economic systems are
very complex. Second, and more important, human
psychology plays an essential role in the behavior of
such systems. And this complexity, together with human
reasoning, makes the classical mathematical approaches,
based on two-valued logic, ineffective.
So, again, to approximate the way humans can sort
through large masses of data and arrive at some sort of
a qualitative conclusion, it might be necessary to use
fuzzy logic.
Q. Has fuzzy logic been able to solve some of the
difficult problems in AI you mentioned earlier? Or is
it still just a promise?
ZADEH. These problems are intrinsically complex,
and fuzzy logic by itself does not provide a solution to
them. Rather, it merely enhances our ability to do so
without guaranteeing success. It's a little like finding a
cure for cancer. You may develop a technique that may
help in finding a cure but it doesn't guarantee a cure
will be found.
Fuzzy logic, then, is a necessary but not sufficient
condition to finding solutions to these problems. It is a
tool that enhances our ability to deal with problems
that are too complex and too ill-defined to be susceptible
to solution by conventional means. It will be an
ingredient of the tools that will eventually be used to
solve these problems.
Q. Have you made any headway in persuading people
that they needn't always be superprecise, that in
fact such an approach may be an inappropriate approach
for attacking certain types of problems?
ZADEH. It will be a slow process. It's not very easy to
change some of the basic attitudes people have been
educated with, like the attitude that we must be very
precise and that we have to try to come up with results
that can be stated as theorems. It's difficult to change
these attitudes.
Let me draw an analogy with the way people dress.
Classical logic is like a person who comes to a party
dressed in a black suit, a white, starched shirt, a black
tie, shiny shoes, and so forth. And fuzzy logic is a little
bit like a person dressed informally, in jeans, tee shirt,
and sneakers. In the past, this informal dress wouldn't
have been acceptable. Today, it's the other way around.
Somebody who comes dressed to a party in the way I
described earlier would be considered funny.
Changes in attitude may take place not only in dress
but also in science, music, art, and many other fields.
And, in science, there may be an increasing willingness
to realize that excessively high degree of formalism,
rigor, and precision is counterproductive.
Freedom of expression in science could exhibit itself
as a movement away from two-valued logic and toward
fuzzy logic. Fuzzy logic is much more general and it
gives you much more flexibility.
Q. How long will it take for traditional scientific attitudes
about precision to change and fuzzy logic to
take hold?
ZADEH. Well, I think it will take something on the
order of perhaps a couple of decades. Fuzzy logic is
making inroads, but it is not something that has coalesced
into a broad movement. In other words, there
are pockets. These pockets exist in various fields, and
of course, there are some people who view these pockets
with suspicion and hostility--just as some people
who are conservative look with suspicion on those who
dress informally.
The difficulty of persuading people has to do also
with the question of where does respectability lie. Traditionally,
respectability went along with being more
mathematical, more precise and more quantitative.
And these attitudes go back to Lord Kelvin who said
that it's not really a science if it's not quantitative.
But fuzzy logic now challenges that. There are many
things that cannot be expressed in numbers, for exam-
ple, probabilities that have to be expressed as "very
likely," or "unlikely." Such linguistic probabilities may
be viewed as fuzzy characterizations of conventional
numeric probabilities.
And so in that sense fuzzy logic represents a retreat.
It represents a retreat from standards of precision that
are unrealistic.
There are many parallels to that sort of thing in the
history of human thought, where people didn't realize
that the objectives they set were unrealizable.
Q. Does an example or two come to mind of a situation
where scientists had to retreat from standards of
precision that were not attainable?
ZADEH. Well, a good example of that sort of thing is
statistical mechanics. People in the beginning of the
nineteenth century were firm believers in the possibility
of using the mechanics that were developed at that
time by people like Lagrange and applying those mechanics
to the solution of all sorts of problems involving
the motion of bodies. But then they encountered the
"two-body," "three-body," and "n-body" problems, and
it became clear that they could not push this too far.
That's where the groundwork was laid for statistical
mechanics.
So statistical mechanics represented a retreat, a retreat
in the sense that you say, "Well, I cannot say
something precisely, but I'll say it statistically."
Now, the same thing happened in the case of the
solution of differential equations. Today we freely accept
numerical solutions. It is hard to realize that the
idea of a numerical solution was not acceptable even as
recently as perhaps 30-40 years ago.
Q. The rise of numerical analysis, then, constituted a
retreat. Was it more of a brute force approach rather
than an elegant, logical approach to the solution of
differential equations?
ZADEH. Effectively, yes. People were simply not willing
to say that, if you use the computer to come up
with a numerical solution, you have really done something
worthwhile. Somehow we tend to forget that
things that are acceptable today were not acceptable 20
to 30 years ago.
Q. I can remember reading books on science of a few
decades ago that always spelled science with a capital
S.
ZADEH. Yes. It's that kind of veneration or worship
I'm talking about. I sometimes use a word that offends
people who take the more traditional view, and that
word is f e t i s h i s m - - f e t i s h i s m of precision and rigor in
the context of classical logic.
There is also what might be referred to as "the curse
of respectability in science." In trying to be respectable,
scientists deny themselves the use of more flexible logical
systems in which truth is a matter of degree.
Q. Is there anything that could be done to get certain
people to stop worshiping precision?
ZADEH, I think it has to be a natural process. But
because of the current emphasis on AI, and in particular
on expert systems, there is a rapidly growing interest
in inexact reasoning and processing of knowledge
that is imprecise, incomplete, or not totally reliable.
And it is in this connection that it will become more
and more widely recognized that classical logical systems
are inadequate for dealing with uncertainty and
that something like fuzzy logic is needed for that purpose.
Q. Since you first developed the concept of fuzzy
logic in the 1960s, Professor Zadeh, has there been
much of a growth in interest? Have others picked up
the banner?
ZADEH. Between then and now, somewhere between
3,000 and 4,000 papers have been written worldwide on
fuzzy sets and their applications. And there are two
regular journals: Fuzzy Sets and Systems, in English, and
Fuzzy Mathematics, in Chinese. In addition, a quarterly
entitled Bulletin on Fuzzy Sets and their Applications is
published in France. The countries where most activity
is taking place at this point are the Soviet Union,
China, Japan, France, Great Britain, West Germany,
East Germany, Poland, Italy, Spain and India. There has
been less activity in the United States.
There is growing acceptance, but there is also considerable
skepticism and in some instances hostility. At
this point the largest number of researchers working on
fuzzy sets is in China.
There appears to be more sympathy for other than
two-valued systems in oriental countries, perhaps because
their logic is not like Western, Cartesian logic.
There is a greater acceptance of truth that is neither
perfect truth nor perfect falsehood. This is particularly
characteristic of Hindu, Chinese, and Japanese cultures.
Q. Professor Zadeh, that's the end of our questions.
We on the editorial staff of Communications thank you
warmly for giving our readers some of your views.
ZADEH. It was my pleasure.
I am proud to find India being mentioned here in this interview (all over my head)
) there used to be HEARD mentality. If the small traders see a huge volume increase they do something
