Geoscience Reference
In-Depth Information
I.3
Defuzzification methods
There are various methods of
defuzzification,
whereby a fuzzy set is represented by a
single crisp value. Two commonly used methods are the
centre-of-area method
and the
max-membership method
. In the former (also called
centroid method
) the defuzzified
value
x
*
is defined as the value within the range of the base value for which the area
under the graph of the membership function,
"
X
(x),
is divided into two equal sub-areas.
This value is calculated by the formula
(I.21)
The latter method, also know as
height method,
seeks for the value corresponding to the
maximum membership, i.e.
(I.22)
Figure I.3.
A membership function showing the defuzzification values by
centre-of-area
method and the
max-membership
method.
An example of defuzzification by the method of
centre-of-area
and the method of
max-
membership
are shown in Figure I.3. If the membership function is defined by a triangular
shape, the defuzzification by the centre of area method reduces to a simple form as
(I.23)
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