Fuzzy Set
The notion of a fuzzy set is a generalization of a classic set, defined in mathematics by a characteristic function, 
, which assigns number 1 to every element x from X, if x belongs to A, and 0 if x does not belong to A.
Fuzzy set A, as a subset of a certain space of consideration X, is determined by a membership function, 
, which assigns a real number in the interval [0,1] to every element 
, 
. The values of function 
represent membership degrees of particular elements x in A (Zadeh, 1965).
Fuzzy set A in a space of consideration, 
, is denoted by a set of pairs
(1) where the membership function can be given in some analytic form, e.g.
(2)When the space of consideration is a finite set, 
, fuzzy set A is denoted as a sum of elements with the membership degrees, in the following form
.
(3)