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FUZZY LOGIC

Fuzzy logic is an alternative to Boolean logic, allowing a much broader response instead of just true and false, though they both use the eight basic logic gates. Fuzzy logic allows a response within the range of 0.0 to 1.0 where 0.0 is absolute falsity and 1.0 is absolute truth. This system is useful in situations that are vague or imprecise. Let's use the following example: the question "Is it cold outside?" Using the Boolean system it would think, "if the temperature (variable) is below -5ºC then it is cold, but if it is above -5ºC it is not cold." As you can see, this is not a suitable method to decide whether it is cold outside. Fuzzy logic gets around this problem by applying degrees of truth or falsity in comparison to a predefined variable. For our example we can say that -25ºC is very cold and 10ºC is warm. Therefore if the temperature is -18ºC the statement "it is cold outside," has a 0.8 degree of correctness, meaning "there is an eighty percent degree of coldness outside." Using fuzzy terminology, a 0.8 degree of correctness means, "more or less, it is cold outside."

Though fuzzy logic is still quite a young field, many of its ideas originated in the time of the ancient Greeks. The "Laws of Thought" were posited. One of these, the "Law of the Excluded Middle," states that every proposition must either be True or False. Even when Parminedes proposed the first version of this law (around 400 B.C.) there were strong and immediate objections. For example, Heraclitus proposed that things could be simultaneously true and not true. Plato probably made one of the most important contributions to fuzzy logic by demonstrating that there is a third region beyond true and false. In the 1900's Lukasiewicz was the first to propose a systematic alternative to the bi-valued logic, which Aristotle had formulated. Lukasiewicz had created a tri-valued logic, where there is a true (2), a false (0) and a possible (1) response. He then experimented with a four-valued logic and declared that it is possible to create an infinite-valued logic. The advantage of this was not realized until 1965 when Lotfi A. Zadeh publish the paper "Fuzzy Sets" which describe the mathematics of fuzzy set theory and in turn also described fuzzy logic (which is mentioned above). Zadeh also formulated the concept of fuzzy control that allows a small set of intuitive rules to be used in order to control the operation of electronic devices such as home appliances. Fuzzy control allows the appliance to adapt automatically to different conditions. For instance, a vacuum cleaner would apply more suction to an especially dirty area. Another prominent feature of the fuzzy system is its ability to define hedges.

Hedges are used to keep the fuzzy logic similar to natural language. Using the temperature example from above, if there is a 0.5 or less degree of correctness, then it is not very cold. If the degree of correctness is 0.8 or above, it is very cold. Though fuzzy logic has proved to be very useful in appliances and electronics, it has not been accepted very well in the Artificial Intelligence community. Many researchers question the consistency and validity of the methods used to 'reason' with fuzzy logic.