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Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory to deal with reasoning that is approximate rather than precise. In binary sets with binary logic, in contrast to fuzzy logic named also crisp logic, the variables may have a membership value of only 0 or 1. Just as in fuzzy set theory with fuzzy logic the set membership values can range (inclusively) between 0 and 1, in fuzzy logic the degree of truth of a statement can range between 0 and 1 and is not constrained to the two truth values {true (1), false (0)} as in classic predicate logic. And when linguistic variables are used, these degrees may be managed by specific functions, as discussed below.The term "fuzzy logic" emerged in the development of the theory of fuzzy sets by Lotfi Zadeh. The first paper on Fuzzy Logic (defined as a multivalued logic based upon set theory) was published by R.H. Wilkinson in 1963 following his first proposals in his 1961 Electrical Engineering master thesis. He was the first one to redefine the earlier multivalued logics in terms of set theory. The main purpose of his paper was to show how any mathematical function could be simulated using hardwired analog electronic circuits based upon what he called analog logic. He did this by first creating various linear voltage ramps which were then selected in a "logic block" using diodes and resistor circuits which implemented the maximum and minimum Fuzzy Logic rules of the INCLUSIVE OR and the AND operations respectively. He called his logic analog logic.In 1965 Lotfi Zadeh (then an Electrical Engineering systems professor) axiomatized the logic of Wilkinson without the electrical circuits and without giving Wilkinson any credit. Fuzzy Logic has been applied to diverse fields from control theory to artificial intelligence, yet still remains controversial among most statisticians who prefer probabilistic logic[citation needed] and some control engineers who prefer traditional two valued logic.
