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where
"
Ã
(x)
is the grade of membership (or degree of belief) of
x
in
Ã
. The function
!
Ã
(x)
is called the
membership function
of
Ã
. A membership function (Fig. 2.4) maps every
element of the universal set
X
to the interval [0, 1], i.e.
"
Ã
(x)
:
X
[0,1]
(2.13)
Figure 2.4.
A normal (trapezoidal) membership function. (See Appendix I for
the definition of a normal membership function.)
Basic
operations on fuzzy sets
As in classical sets
union, intersection
and
complement
are the three basic and most often
used operations in fuzzy sets. Given two fuzzy sets
Ã
and
the union, intersection and
complement operations are represented as:
(2.14)
(2.15)
(2.16)
The union and intersection of two fuzzy sets
Ã
and
(Fig. 2.5) and the complement of
Ã
are illustrated in Figure 2.6(a-c).
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