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 that they need not sum to one). This allows for values between 0 and 1, shades of gray, and maybe; it allows partial membership in a set. It is highly related to fuzzy sets and possibility theory. It was introduced in the 1960s by Dr. Lotfi Zadeh of UC Berkeley. Fuzzy logic is controversial. It is widely accepted within the engineering and computer science communities but generally rejected by mathematicians and (in particular) 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.| Table of contents |
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2 Common misconceptions 3 Examples where Fuzzy Logic is used 4 External Links |
Applications: Home appliances and more
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, 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. 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.
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 has also proved a theorem that shows that Bayes' theorem can be derived from the concept of fuzzy subsethood. This should not by any means suggest that all those who study probability accept or even understand fuzzy logic, however; to many, fuzzy logic is still a curiosity.
Fuzzy logic is also sometimes said to be used only in AI, control systems, and/or expert systems (note that these fields can have significant overlap). These are by far the most common applications, but by no means the only possible; fuzzy logic can be applied in any situation requiring the handling of uncertainty.
Common misconceptions
Fuzzy logic has suffered many misconceptions, partly due to its name. "Fuzzy" is said to have negative connotations, usually 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, rather it is an organized and mathematical method of handling inherently uncertain concepts; the concept of "coldness" cannot be expressed in an equation (temperature is a quantity, but "coldness" is not). However, everybody has an idea of what "cold" is, and agrees that something cannot be "cold" at N degrees but "not cold" at N+1 degrees (which is a concept classical logic and equations cannot easily handle).
Examples where Fuzzy Logic is used
Fuzzy logic has also been incorporated into some microcontrollers and microprocessors, for instance, the Motorola 68HC12.