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Fig. 14.4 Algorithm for fuzzifying numeric attributes.
The only parameters that need to be determined are the set of
k
centers
M
=
. The centers can be found using the algorithm presented
in Figure 14.4. Note that in order to use the algorithm, a monotonic
decreasing learning rate function should be provided.
{
m
1
,...,m
k
}
14.6.2
Inducing of Fuzzy Decision Tree
The induction algorithm of fuzzy decision tree is presented in Figure 14.5.
The algorithm measures the classification ambiguity associated with each
attribute and splits the data using the attribute with the smallest classifica-
tion ambiguity. The classification ambiguity of attribute
a
i
with linguistic
terms
v
i,j
,j
=1
,...,k
on fuzzy evidence
S
, denoted as
G
(
a
i
|
S
), is the
weighted average of classification ambiguity calculated as:
k
G
(
a
i
|
S
)=
w
(
v
i,j
|
S
)
ยท
G
(
v
i,j
|
S
)
,
(14.8)
j
='1
where
w
(
v
i,j
|
S
) is the weight which represents the relative size of
v
i,j
and
is defined as:
M
(
v
i,j
|
S
)
w
(
v
i,j
|
S
)=
k
S
)
.
(14.9)
M
(
v
i,k
|
S
)=
g
(
p
(
C|v
i,j
)), which is measured based on the possibility distribution vector
p
(
C|v
i,j
)=(
p
(
c
1
|
The
classification ambiguity of
v
i,j
is defined
as
G
(
v
i,j
|
v
i,j
)
,...,p
(
c
|
k
|
|
v
i,j
))
.
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