From: erik@til.til.com (Erik Horstkotte)
Subject: Re: fuzzy logic, lisp, AI
Keywords: fuzzy logic lisp AI
Organization: Togai InfraLogic, Inc.
Date: Wed, 22 Jul 1992 16:59:05 GMT

In article <35902@sdcc12.ucsd.edu>, arao@sdcc13.ucsd.edu (Andy Rao)
writes:
|> [...]
|> one more thing, could somone give me a good definition of fuzzy
|> logic? my concept of it is...fuzzy at best. :)

Fuzzy logic, first discussed by Dr. Lotfi Zadeh of U.C. Berkeley around
1960,  is a superset of conventional Boolean logic that allows
truth values in the interval [0, 1], instead of just the set { 0, 1 }.
There is a rigorous set of mathematical operations that define how
the logic system works.  The most common definitions for the basic
operations are:

truth(x AND y) = min (truth(x), truth(y))
truth(x OR y) = max (truth(x), truth(y))
truth(NOT x) = 1 - truth(x)

where x and y are truth (degree of belief, degree of membership) values.
Note that these are *not* cast in concrete.  Several researchers in
the field believe that some other ways of defining the operations
yield more meaningful results.  Personally, I'll stick with the
traditional definitions above until someone *proves* there's a reason
to change (other than to get him a Ph.D. :-).

Fuzzy logic on its own isn't used terribly often.  It appears most
commonly as the underlying logic for an extension of the idea of an
expert system, called (well what do you know, Vern) a fuzzy expert
system.

A fuzzy expert system is basically an expert system which uses fuzzy
logic for all of the logic operations instead of Boolean logic.  The
mathematical details are slightly messy (especially trying to draw
pictures in ASCII!), and are well described in several books (A
short bibliography follows).

If you want, I can send you a short printed introduction to fuzzy
logic that we distribute to our potentional customers - Togai
InfraLogic is an Irvine, CA based company that develops and sells
fuzzy logic and fuzzy expert system software development systems,
hardware development systems, chip- and board-level products, and
engineering services.

The following bibliography is
1. Very incomplete.
2. Slanted toward stuff we have found useful.

Books

Kaufmann, Arnold and Gupta, Madan M., Introduction to Fuzzy Arithmetic:
Theory and Applications, New York: Van Nostrand Reinhold Company Ltd.,
1985. 350 pp.

Klir, George J. and Folger, Tina A., Fuzzy Sets, Uncertainty, and
Information, Englewood Cliffs,  NJ: Prentice Hall, 1988. 355 pp.

Kosko, Bart A., Neural Networks and Fuzzy Systems, Prentice-Hall, 1990.

Mamdani, E.H. and Gaines, B.R., Fuzzy Reasoning and its Applications,
New York: Academic Press, 1981. 380 pp.

Negoita, Constantin Virgil, Fuzzy Systems, Cybernetics and Systems
Series, Abacus Press, 1981. 120 pp.

Sugeno, Michio, Industrial Applications of Fuzzy Control, New York: 
North-Holland, 1985. 270 pp.

Togai, M., Reasoning with Uncertainty for Rule-based Expert Systems, 
John Wiley & Sons, in progress.

Zimmermann, Hans J., Fuzzy Set Theory and its Applications, Boston MA: 
Kluwer-Nijhoff Publishing, 1985. 360 pp.

Papers

Asai, K. and Tanaka, H., "Applications of Fuzzy Sets Theory to 
Decision-Making and Control," J. JAACE, 19, 235-242, 1975.

Bezdek, J.C., "Fuzzy Mathematics in Pattern Classification," Ph.D. 
Dissertation, Center for Applied Mathematics, Cornell University, 1973.

Blin, J.M., "Fuzzy Relations in Group Decision Theory," Journal of
Cybernetics, 4, 17-22, 1974.

Kosko, Bart A., "Foundations of Fuzzy Estimation Theory," Ph.D. 
Dissertation, University of California, Irvine, 1987.

Larkin, Lawrence I., "A Fuzzy Controller for Aircraft Flight Control," 
Proceedings of the 23rd Conference on Decision and Control, Las Vegas, 
NV, December 1984.

Togai, M., "Principles and Applications of Fuzzy Inference: A New 
Approach for Decision-making in an Ill-defined System," Ph.D. 
Dissertation, Duke University, 1982.

Togai, M. and Watanabe, H., "An Inference Engine for Real-Time 
Approximate Reasoning: Toward an Expert System on a Chip," IEEE Expert,
August 1986.

Yasunobu S., Miyamoto S., and Ihara H., "Fuzzy Control for Automatic 
Train Operation System," IFAC-CISSS, 4th IFAC/IFIP/IFORS Conference on 
Control in Transportation Systems, Baden-Baden, F.R.G., April 1983.

Zadeh, L.A., "Fuzzy Sets," Information and Control, 8, 338-353, 1965.

Zadeh, L.A., "A Rationale for Fuzzy Control," Journal of Dynamic
Systems, Measurement and Control, G94, 3-4, 1972.

Zadeh, L.A., "Fuzzy Logic and Approximate Reasoning," Synthese, 30, 
407-428, 1975.

PS: C'mon, guy, get a shift key! :-)

PPS: My apologies for the length of this response, but I think a lot of
other people out there are looking for a starting place in fuzzy
logic also.

PPPS: If you want a starting place for investigating fuzzy logic and
fuzzy expert systems, my opinion is to start with either George Klir
or Hans Zimmermann's book.  I'm not really fond of Bart Kosko's book
(but it's hard to tell how much of that is just my reaction to Bart!).
Don't overlook the conference proceedings of NAFIPS (the North
American Fuzzy Information Processing Society) and IFSA (the
International Fuzzy Systems Association).  They are full of
interesting ideas about the use and theory of fuzzy logic.
-- 
Erik Horstkotte, Manager, Software Development, Togai InfraLogic, Inc.
erik@til.til.com, uunet!til!erik - (714) 975-8522
Standard disclaimer: the preceding are my opinions, not TIL's.
Newsgroups: comp.ai