# Examining Fuzzy Logic's Widespread Success

By Peterson, Ivars | Science News, July 24, 1993 | Go to article overview

# Examining Fuzzy Logic's Widespread Success

Peterson, Ivars, Science News

Fuzzy logic attempts to capture within a mathematical framework the vagueness of such qualitative terms as "warm" or "fast." In essence, it allows engineers to specify the degree to which something occurs--how hot it may be outside or how rapidly a motor should turn -- without setting a particular threshold value for crisply separating "warm" from "hot" or "moderate" from "fast." The boundaries between categories become, well fuzzy.

Over the last few years, fuzzy logic has permitted engineers to design control systems for air conditioners, washing machines, rice cookers, and dozens of other devices, enabling the machines to respond smoothly and appropriately to changs in operating conditions. These successes have led to increased interest in applying fuzzy logic to more complicated "expert systems" that involve, for example, making a diagnosis or suggesting a course of action.

Whether it will really work in such situations has proved controversial. "Fuzzy logic is not adequate for reasoning about uncertain evidence in expert systems," argues computer scientist Charles P. Elkan of the University of California, San Diego. Proponents contend that no fundamental barrier stands in the way of deploying large systems based on fuzzy logic.

Elkan described his viewpoint in a paper presented at the Eleventh National Conference on Artificial Intelligence, held last week in Washington, D.C.

Fuzzy logic originated in the work of computer scientist Lotfi A. Zadeh, now retired from the University of California, Berkeley. In the 1960s, Zadeh introduced the notion of fuzzy sets as a way of circumventing the rigidity of traditional set theory, which asserts that a given object or item either does or does not belong to a particular set. For example, the number 3 belongs to the set of odd numbers but not the set of even numbers.

In contrast, in Zadeh's scheme, a given item may belong only partially to a particular fuzzy set. It may also belong simultaneously to several other fuzzy sets. Thus, in a given situation, a certain temperature may be 20 percent "cool" (and 80 percent "not cool") and 70 percent "just right."

Similarly, whereas conventional logic is based on the idea that a statement or proposition is either true or false, fuzzy logic deals with the degree of truth, expressed as an assigned value between zero and one. The choice is no longer just zero or one.

To build a fuzzy system, an engineer typically begins with a set of rules, often obtained from an expert. For example, a rule for operating an air conditioner may state: If the outside temperature is high and the humidity is high, then the air conditioner setting should be very high. …

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