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Table 6.1 Probabilistic decision table
E i
a 1
a 2
a 3
Region
P
(
E i
)
P
(
X
|
E i
)
E 0
1
1
1
BND
0.0520
0.78
E 1
1
1
0
NEG
0.1354
0.02
E 2
1
0
1
POS
0.1562
0.99
E 3
1
0
0
BND
0.1562
0.36
E 4
0
1
1
NEG
0.1406
0.11
E 5
0
1
0
BND
0.1093
0.41
E 6
0
0
1
NEG
0.1562
0.27
E 7
0
0
0
POS
0.0941
0.85
rough set model, using absolute approximation regions. Another related issue is that
the probabilistic decision tables can be structured into parent-child linear hierarchies,
in which a parent boundary region provides a basis to form an approximation space
for the child decision table [ 31 ]. In this way, the exponential growth of decision
tables caused by the increase in the number of attributes can be effectively controlled
without reducing the quality of rough approximations.
6.4.3 Classification Tables
An intermediate step leading to the probabilistic decision table is the creation of
the classification table , as illustrated in Table 6.2 . The classification table associates
combinations of condition attribute values, for each elementary set E
U
/
C , with
a pair of corresponding P
probability measures. In the example
Table 6.2 , the partitioning of U is obtained in terms of conditional attributes C
(
E
)
and P
(
X
|
E
)
=
{
, with the connected probabilistic measures. The information contained
in the classification table can then be used to build rough approximations of any
target set X
a 1 ,
a 2 ,
a 3 }
D , based on pre-set values of the precision control lower and upper
limit parameters l and u .
U
/
Table 6.2 Classification table
E i
P ( E i )
P ( X | E i )
a 1
a 2
a 3
E 0
1
1
1
0.0520
0.78
E 1
1
1
0
0.1354
0.02
E 2
1
0
1
0.1562
0.99
E 3
1
0
0
0.1562
0.36
E 4
0
1
1
0.1406
0.11
E 5
0
1
0
0.1093
0.41
E 6
0
0
1
0.1562
0.27
E 7
0
0
0
0.0941
0.85
 
 
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