Fuzzy logic
Fuzzy logic is a superset 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 which are very similar to probabilities, except they need not add up to 100%. This allows for values between 0 and 1, shades of gray, and maybe; it allows partial membership in a set. It is related to fuzzy sets and possibility theory. It was introduced in 1965 by Dr. Lotfi Zadeh of Berkeley.
Fuzzy logic is controversial: it is widely accepted within the engineering and computer science communities, but generally rejected by mathematicians and statisticians. Critics argue that it cannot be a superset of ordinary set theory since membership functions are defined in terms of conventional sets. Others argue that it is unscientific by the standards of Karl Popper, since set membership values are not empirically verifiable. One problem with these arguments are that all internally consistant information systems, including boolean or bivalent logic, cannot be claimed to be totally empirically verifiable. Logical truths, like 1 + 1 = 2, are 100% true within the system of math. But do these "truths" correspond perfectly to the observed world? Define one apple, or anything, from its opposite. You only have incomplete data to compare, and you have uncertainty challenging every claim you make, since you are not all-knowing. In essence, by Karl Popper's standards, no science has ever been completely undertaken.
Applications
Fuzzy logic can be used to control household appliances such as washing machines (which sense load size and detergent concentration and adjust their wash cycles accordingly) and refrigerators.
A basic application might quantify where a limited range applies to a smooth spectrum, for instance, in temperature measurement for anti-lock brakes to function properly. Truth values derived from the specific temperature are mapped to a series of candidate quantities. These quantities can then be used to determine a separate function in accordance with the graduated value scheme.
In this image, cold, warm, and hot are identities mapped to a temperature scale. A point on that scale is represented by two "truth values" — one in each of the two nearest identities. As the temperature rises, its "truth value" in the cold category declines, while its "truth value" in the warmer category rises.
The AND, OR, and NOT operators of boolean logic exist in fuzzy logic, usually defined as the minimum, maximum, and complement; when they are defined this way, the are called the Zadeh operators, because they were first defined as such in Zadeh's original papers. So for the fuzzy variables x and y:
NOT x = (1 - truth(x))
x AND y = minimum(truth(x), truth(y))
x OR y = maximum(truth(x), truth(y))
There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as "very", or "somewhat", which modify the meaning of a set using a mathematical formula.
Common misconceptions
Fuzzy logic has suffered many misconceptions, partly due to its name. "Fuzzy" often has negative connotations, either suggesting something cute or something imprecise; the latter sometimes causes people to equate "fuzzy logic" with "imprecise logic". However, fuzzy logic is not any less precise than any other form of logic: it is an organized and mathematical method of handling inherently imprecise concepts. The concept of "coldness" cannot be expressed in an equation, because although temperature is a quantity, "coldness" is not. However, people have an idea of what "cold" is, and agree that something cannot be "cold" at N degrees but "not cold" at N+1 degrees — a concept classical logic cannot easily handle due to the principle of bivalence.
Another common misconception is that fuzzy logic is a new way of expressing probability. However, Bart Kosko has shown that probability is a subset of fuzzy logic, as probability only handles one kind of uncertainty. He also proved a theorem demonstrating that Bayes' theorem can be derived from the concept of dynamic logic, control system, expert system, artificial intelligence, Combs method, Fuzzy Control Language.
Examples where Fuzzy Logic is used
Fuzzy logic has also been incorporated into some microcontrollers and microprocessors, for instance, the
