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corresponds to a decision rule. Thus for calculating the core of a decision rule's
condition attributes, we should first delete the values of condition attributes in the
row from the table, and then add some condition attribute values to the core. The
resulting condition attribute values can ensure the consistency of tables, and each
condition attribute values are not omissible. If there exist reduplicate rows in the
reduced tables, the rows should be deleted also, because they represent the same
decision rule.
For example, considering the first decision rule
a 1 c 2 e 0 in Table 11.5,
a 1 is
the core value. Because rule
a 1 e 0 (after deleting
c 2 ) is true and rule
c 2 e 0 (after
deleting
a 1 cannot be reduced. With this method, all core values of
every decision rules in Table 11.5 are illustrated as Table 11.6.
a 1 ) is false,
Table 11.6 The Core Vlues of Table 11.5
A
U a
c
e
u 1
1
0
u 2
1
1
u 3
2
0
u 4
0
2
2
After calculating all core values, each decision rule is reduced. For example,
the first decision rule has a reduct a1→e0, because the decision rule can ensure
the consistency of table. Thus, we can get the reduced table of Table 11.5.
Table 11.7 Reduced table of Table 11.5
A
U a
c
e
u 1
1
×
0
u 2
×
1
1
u 3
2
×
0
u 4
0
2
2
The corresponding decision algorithm is:
a
a
e
c
e
a 0 c
e
2
1
2
0
1
1
2
4 . Importance of Attributes
As mentioned before, reduction is an important concept in rough set theory,
which can be used for data analysis. However, the calculation of all reducts is an
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