Fuzzy Logic Basics

Allen Bonde
GTE Government Systems Corp.
Needham, MA 02194
abonde@gte.com

Fuzzy Logic is a departure from classical two-valued sets and logic, that uses "soft" linguistic (e.g. large, hot, tall) system variables and a continuous range of truth values in the interval [0,1], rather than strict binary (True or False) decisions and assignments.

Formally, fuzzy logic is a structured, model-free estimator that approximates a function through linguistic input/output associations.

Fuzzy rule-based systems apply these methods to solve many types of "real-world" problems, especially where a system is difficult to model, is controlled by a human operator or expert, or where ambiguity or vagueness is common. A typical fuzzy system consists of a rule base, membership functions, and an inference procedure (see Figure).

Some Fuzzy Logic APPLICATIONS include:

Control (Robotics, Automation, Tracking, Consumer Electronics)
Information Systems (DBMS, Info. Retrieval)
Pattern Recognition (Image Processing, Machine Vision)
Decision Support (Adaptive HMI, Sensor Fusion)

The key BENEFITS of fuzzy design are:

Simplified & reduced development cycle
Ease of implementation
Can provide more "user-friendly" and efficient performance

For More Information:

Good overview articles:

Brubaker, D.I., "Fuzzy-logic Basics: Intuitive Rules Replace Complex Math," EDN, June 18, 1992.
Schwartz, D.G. and Klir, G.J., "Fuzzy Logic Flowers in Japan," IEEE Spectrum, July 1992.

Classic Papers:

Zadeh, L.A., "Fuzzy Sets," Information and Control, Vol. 8, pp. 338-353, 1965.
Zadeh, L.A., "Outline of a New Approach to the Analysis of Complex Systems and Decision Processes," IEEE Transactions on Systems, Man, and Cybernetics, SMC-3, pp. 28-44, 1973.

Excellent Books:

by George J. Klir, Bo Yuan Fuzzy Sets and Fuzzy Logic: Theory and Applications
by George J. Klir, et al . Fuzzy Set Theory: Foundations and Applications
by George J. Klir Facets of Systems Science (IFSR International Series on Systems Science and Engineering)
by N. M. Martin (Editor), L. C. Jain (Editor) Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Guido J. Deboeck (Editor) Trading on the Edge : Neural, Genetic, and Fuzzy Systems for Chaotic Financial Markets (Wiley Finance)

Journals that cover fuzzy logic:

IEEE Transactions On Neural Networks
IEEE Transactions on Systems, Man, and Cybernetics
IEEE Transactions on Fuzzy Systems (begins in February, 1993)
International Journal of Approximate Reasoning (North-Holland)
International Journal of Fuzzy Sets and Systems

   ________________     _______________     ________________
I  |               |    |              |    |               | O
N  |Crisp-to-Fuzzy |    |  Inference   |    |Fuzzy-to-Crisp | U
P  |               |--->|              |--->|               | T
U  |    FUZZIFY    |    | max-min, etc |    |   DEFUZZIFY   | P
T  |_______________|    |______________|    |_______________| U
                                                              T
  membership functions     rule base          max, average,
                                              centroid,
                                              singleton, etc