Fuzzy set

Summary

In mathematics, fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, (Salii 1965) defined a more general kind of structure called an "L-relation", which he studied in an abstract algebraic context; fuzzy relations are special cases of L-relations when L is the unit interval $[0, 1]$. They are now used throughout fuzzy mathematics, having applications in areas such as linguistics (De Cock Bodenhofer Kerre 2000), decision-making (Kuzmin 1982), and clustering (Bezdek 1978).