Lotfi A. Zadeh
A fuzzy set is a pair (A,m) where A is a set and .
For each , m(x) is the grade of membership of x. If A = {x1,...,xn} the fuzzy set (A,m) can be denoted {m(x1) / x1,...,m(xn) / xn}.
An element mapping to the value 0 means that the member is not included in the fuzzy in an arbitrary fixed algebra or structure L; usually it is required that L be at set, 1 describes a fully included member. Values strictly between 0 and 1 characterize the fuzzy members.[4] The set is called the support of the fuzzy set (A,m) and the set is called the kernel of the fuzzy set (A,m).
Sometimes, a more general definition is used, where membership functions take values least a poset or lattice. The usual membership functions with values in [0, 1] are then called [0, 1]-valued membership functions. This generalization was first considered in 1967 by Joseph Goguen, who was a student of Zadeh.[
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