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Thursday, July 19, 2007

The Fuzzy Logic

Fuzzy logic is an extension of Boolean logic dealing with the concept of partial truth. Whereas classical logic holds that everything can be expressed in binary terms (0 or 1, black or white, yes or no), fuzzy logic replaces Boolean truth values with degrees of truth.

Degrees of truth are often confused with probabilities, although they are conceptually distinct, because fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition. Fuzzy logic allows for set membership values between and including 0 and 1, shades of gray as well as black and white, and in its linguistic form, imprecise concepts like "slightly", "quite" and "very". Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory. It was introduced in 1965 by Prof. Lotfi Zadeh at the University of California, Berkeley.

Fuzzy logic is controversial despite wide acceptance: it is rejected by some control engineers for validation and other reasons, and by some statisticians who hold that probability is the only rigorous mathematical description of uncertainty. Critics also argue that it cannot be a superset of ordinary set theory since membership functions are defined in terms of conventional sets.

Many people would note that fuzzy logic sounds good, but how is it being used. A good example is a fuzzy washing machine. Using yes and no logic to make a washing machine that would automatically handle all the controls on a load of wash, would add hundreds of dollars to the cost of the machine. Dozens of special sensors and the equivalent of a small computer would have to be added to the machine. The fuzzy washing machines being sold in Japan for the last few years cost about twenty dollars more, use a handful of inexpensive sensors and a small logic chip. All you have to do to use the machine, in many cases, is put the clothes in and turn it on.
Most scientists refused to look closely at the logic, when it was first talked about. The ideas seemed too radical to them. It took engineers first in Europe, but mainly in Japan to start using fuzzy logic before scientists started to take it seriously.

Other applications of Fuzzy logic such as:

  • Automobile subsystems, such as ABS and cruise control
  • Air conditioners
  • Cameras
  • Digital image processing, such as edge detection
  • Rice cookers
  • Dishwashers
  • Washing machines and other home appliances.

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