Fuzzy set operations

A fuzzy set operation is an operation on fuzzy sets. These operations are generalization of crisp set operations. There is more than one possible generalization. The most widely used operations are called standard fuzzy set operations. There are three operations: fuzzy complements, fuzzy intersections, and fuzzy unions.Let A and B be fuzzy sets that A,B ⊆ U, u is any element (e.g. value) in the U universe: u ∈ U.μA(x) is defined as the degree to which x belongs to A. Let ∁A denote a fuzzy complement of A of type c. Then μ∁A(x) is the degree to which x belongs to ∁A, and the degree to which x does not belong to A. (μA(x) is therefore the degree to which x does not belong to ∁A.) Let a complement ∁A be defined by a functionThe intersection of two fuzzy sets A and B is specified in general by a binary operation on the unit interval, a function of the form The union of two fuzzy sets A and B is specified in general by a binary operation on the unit interval function of the formAggregation operations on fuzzy sets are operations by which several fuzzy sets are combined in a desirable way to produce a single fuzzy set.