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In example 11.1, the decision table illustrated by Table 11.1 can be
decomposed to the following two sub-tables:
Table 11.12 Totally consistent decision table
U
a b c d e
3
4
6
7
2 0 0 1 1
1 1 0 2 2
2 2 0 1 1
2 1 1 1 2
Table 11.13 Totally inconsistent decision table
U
a b c d e
1
2
5
8
1 0 2 2 0
0 1 1 1 2
1 0 2 0 1
0 1 1 0 1
For Table 11.12,
U|C
={{3}, {4}, {6}, {7}},
U|D
={{3,6}, {4}, {7}},
POS
C
(D)={{3}, {4}, {6}, {7}} and
r
C
(D)=4/4=1, so Table 11.12 is totally
consistent and the decision rules in this table are all consistent.
For Table 11.13,
)=0/4=0,
so Table 11.6 is totally inconsistent and the decision rules in this table are all
inconsistent.
For Table 11.12, we reduce it and the resulting reducts of condition attributes
are {
U
|
C
={{1, 5}, {2,8}},
U
|
D
={{1}, {2}, {5,8}},
r
C
(
D
a
,
b
}, {
a
,
c
} and {
b
,
c
}. Suppose the final reduct is {
a, b
}, then its
corresponding decision table is as Table 11.14.
Table 11.14 Decision table after reducing attribute c from Table 11.11
U
a b d e
3
4
6
7
2 0 1 1
1 1 2 2
2 2 1 1
2 1 1 2
After reducing the condition attribute values in Table 11.13, the resulting
decision algorithm is:
