Database Reference
In-Depth Information
Fig. 14.5 Fuzzy decision tree induction.
Given
v
i,j
, the possibility of classifying an object to class
c
l
can be
defined as:
S
(
v
i,j
,c
l
)
max
k
p
(
c
l
|
v
i,j
)=
S
(
v
i,j
,c
k
)
,
(14.10)
where
S
(
A, B
) is the fuzzy subsethood that was defined in Definition 14.5.
The function
g
(
p
) is the possibilistic measure of ambiguity or non-specificity
andisdefinedas:
g
(
p
)=
|p|
(
p
i
−
p
i
+1
)
·
ln(
i
)
,
(14.11)
i
=1
where
p
∗
=(
p
1
,...,p
|p|
) is the permutation of the possibility distribution
p
sorted such that
p
i
≥
p
i
+1
.
All the above calculations are carried out at a predefined significant
level
α
. An instance will take into consideration of a certain branch
v
i,j
only if its corresponding membership is greater than
α
. This parameter is
used to filter out insignificant branches.
After partitioning the data using the attribute with the smallest
classification ambiguity, the algorithm looks for non-empty branches.
For each non-empty branch, the algorithm calculates the truth level of
classifying all instances within the branch into each class. The truth level
is calculated using the fuzzy subsethood measure
S
(
A, B
).
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