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Centre of gravity method (COG)
This approach has its origin in the idea to select a value
that, on average, would lead to the smallest error in the sense of
a criterion. If
is chosen, and the best value is , then
the error is
. Thus, to determine
the least squares
method can be used. As weights for each square
,
one can take the grade of membership
with which
is a reasonable value. As a result one has to find

(16.4) 
Differentiating with respect to the unknown
and equating
the derivative to zero, the formula

(16.5) 
is obtained, which determines the value of the abscissa of the
centre of gravity of the area below the membership function
.
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Christian Schmid 20050509