هنگرد ِ پرزوار hangard-e porzvâr
*Fr.: ensemble flou*
A set of → *truth value*s in → *fuzzy logic*
that does not have sharp boundaries. Instead, set members have degrees of membership.
If the value of 1 is assigned to objects entirely within the set and a 0 is assigned
to objects outside of the set, then any object partially in the set will have a value
between 0 and 1. This contrast with → *crisp set*s
in → *classical logic*
where members assume a precise value of 1 or 0. Fuzzy sets were first introduced by
Lotfi A. Zadeh (1965) and defined as follows.
Let X be a space of points, with a generic element of X denoted by *x*. Thus X = {*x*}.
A fuzzy set A in X is characterized by a → *membership function*
*f*_{A}(*x*)
which associates with each point in X a real number in the interval [0,1], with the
values of *f*_{A}(*x*) at *x* representing the "grade of membership"
of *x* in A. Thus, the nearer the value of *f*_{A}(*x*)
to unity, the higher the grade of membership of *x* in A.
Generally, the intersection operations of fuzzy sets are the expansion of that
operation on → *nonfuzzy set*s. In other words, operations on
nonfuzzy sets are a particular case of operations on fuzzy sets. → *fuzzy*; → *set*. |