Fuzzy Set - Definition

Definition

A fuzzy set is a pair where is a set and

For each the value is called the grade of membership of in For a finite set the fuzzy set is often denoted by

Let Then is called not included in the fuzzy set if is called fully included if and is called a fuzzy member if The set is called the support of and the set is called its kernel. The function is called the membership function of the fuzzy set

Sometimes, more general variants of the notion of fuzzy set are used, with membership functions taking values in a (fixed or variable) algebra or structure of a given kind; usually it is required that be at least a poset or lattice. These are usually called L-fuzzy sets, to distinguish them from those valued over the unit interval. The usual membership functions with values in are then called -valued membership functions. These kinds of generalizations were first considered in 1967 by Joseph Goguen, who was a student of Zadeh.

Read more about this topic:  Fuzzy Set

Famous quotes containing the word definition:

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.
    Samuel Taylor Coleridge (1772–1834)

    It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.”
    Jane Adams (20th century)