Sidebar: The history of fuzzy logic

When Aristotle and his predecessors devised their theories of logic and mathematics, they came up with the so-called Law of the Excluded Middle, which states that every proposition must either be true or false. Grass is either green or not green; it clearly cannot be both green and not green. But not everyone agreed, and Plato indicated there was a third region, beyond true and false, where these opposites "tumbled about."

In the Aristotelian world view, logic dealt with two values. In the 19th century, George Boole created a system of algebra and set theory that could deal mathematically with such two-valued logic, mapping true and false to 1 and 0, respectively. Then in the early 20th century, Jan Lukasiewicz proposed a three-valued logic (true, possible, false), which never gained wide acceptance.

In 1965, Lotfi A. Zadeh of the University of California at Berkeley published "Fuzzy Sets," which laid out the mathematics of fuzzy set theory and, by extension, fuzzy logic. Zadeh had observed that conventional computer logic couldn't manipulate data that represented subjective or vague ideas, so he created fuzzy logic to allow computers to determine the distinctions among data with shades of gray, similar to the process of human reasoning.

Although, the technology was introduced in the U.S., U.S. and European scientist and researchers largely ignored it for years, perhaps because of its unconventional name. They refused to take seriously something that sounded so childlike. Some mathematicians argued that fuzzy logic was merely probability in disguise. But fuzzy logic was readily accepted in Japan, China and other Asian countries. The greatest number of fuzzy researchers today are found in China, with over 10,000 scientists. Japan, though considered at the leading edge of fuzzy studies, has fewer people engaged in fuzzy research. A decade ago, the Chinese University of Hong Kong surveyed consumer products using fuzzy logic, producing a 100-plus-page report listing washing machines, camcorders, microwave ovens and dozens of other kinds of electrical and electronic products.

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