Errata for T. Munakata and Yashvant Jani. "Fuzzy Systems: An Overview," Communications of the ACM, 37, 3, March, 1994, pp. 69-76. p. 72 Right column, Line 5: b(u) --> b(v) p. 73 Right column, Line 21: m(W) and W0 --> m(W) as W0

Fuzzy An

Syst em s: Overview

TOSHINORI MUNAKATA n YASHVANT JANI

B otn in the United States around 1965, fuzzy set theory has grown to become a major scien-

tific domain collectively referred to in this article as “fixzy systems,” which include fuzzy sets,

logic, algorithms, and control. For the past few years, particularly in Japan, approximately

1,000 commercial and industrial fuzzy systems have been successfiAly developed. The number

of industrial and commercial applications worldwide appears likely to increase significantly in

the near future (see Table 1) [6, 181. Interest in the U.S. and other countries has also been

growing recently, as indicated by both the first IEEE conference on h~zzy systems held in

March 1992 and the first IEEE Transacti~~~s on &zzy Systpms, which premiered in February

1993 (see Table 2). This article presents an overview of fuzzy systems, covering issues such as

basic concepts, currently successfid areas and examples, and some fundamentals. Also included

is a brief tutorial on fuzzy sets, logic, and control.

The most successful domain has been in fuzzy control of various phys- ical or chemical characteristics such as temperature, electric current, flow of

liquid/gas, motion of machines, etc. Also, fuzzy systems can be obtained by applying the principles of fuzzy sets and logic to other areas, for example, fuzzy knowledge-based systems such as fuzzy expert systems which may use fuzzy if-then rules; “fuzzy soft- ware engineering” which may incor- porate fuzziness in programs and data; fuzzy databases which store and retrieve fuzzy information; fuzzy pat- tern recognition which deals with

fuzzy visual or audio signals; applica- tions to medicine, economics, and management problems which involve fuzzy information processing (see Ta- bles 3 and 4).

Although there are numerovs fuzzy systems in many application

types and domains, most of them are based on a relatively simple idea. A fuzzy system allows a gradual and continuous transition, say, from 0 to 1, rather than a crisp and abrupt change between binary values of 0 and 1. (For more on the basics, see the sidebar “ATutorial on Fuzzy Sets,

Logic, and Control.“) There are certain particular char-

acteristics of fuzzy systems that give them better performance for specific applications. In general, fuzzy sys- tems are suitable for uncertain or approximate reasoning, especially for the system with a mathematical model that is difEcult to derive. For

example, the input and parameter values of a system may involve fuzzi- ness, be inaccurate, or incomplete. Similarly, the formulas or inference rules to derive conclusions may be incomplete or inaccurate. Fuzzy logic

allows decision making with esti-

mated values under incomplete in- formation. Note that the decision may not be correct and can be changed at a later time when addi- tional information is available. Com- plete lack of information will not sup- port any decision making using any form of logic. For difficult problems, conventional nonfuzzy methods are usually expensive and depend on mathematical approximations (e.g., linearization of nonlinear problems), which may lead to poor performance. Under such circumstances, fuzzy sys- tems often outperform conventional methods such as a proportional, inte- gral, and differential (PID) control.

Fuzzy system approaches also allow us to represent descriptive or qualitative expressions such as “slow” or “moderately fast,” and these are easily incorporated with symbolic