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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