Information Technology Reference
In-Depth Information
If a decision rule is inconsistent, we should first calculate the core value of its
condition attributes. That is to say, delete a value of attribute value from the table
and test whether the decision attribute values determined by the values of
condition attributes are same before and after deletion. If not, the value is a core
value. After the calculation of core values, the second step is to get the reduct of
the condition attribute values. Then, some condition attribute values are
combined with the core values, and the decision attribute values determined by
the resulting condition attribute values are tested whether they are different with
the original set of decision attribute values and whether each condition attribute
value can be omitted.
In the following, we will illustrate how to use the method to reduce an
inconsistent decision table.
Consider a knowledge representation system illustrated by Table 11.8.
Table 11.8 A knowledge representation system
U
a b c d e
1
2
3
4
5
6
7
8
1 0 2 2 0
0 1 1 1 2
2 0 0 1 1
1 1 0 2 2
1 0 2 0 1
2 2 0 1 1
2 1 1 1 2
0 1 1 0 1
Here, C={a, b, c} and D={d, e} are condition attribute set and decision
attribute set respectively. Because U|C={{1,5}, {2,8}, {3}, {4}, {6}, {7}},
U|D={{1}, {2,7}, {3,6}, {4}, {5,8}}, POSC(D)={{3}, {4}, {6}, {7}} and
rC(D)=4/8≠1, table 11.8 is inconsistent.
After deleting attribute a, U|(C
{a})={{1,5}, {2,7,8}, {3}, {4}, {6}}, POSC
{a}(D) ={{3}, {4}, {6}} POSC(D), so attribute a can not be omitted; after
deleting attribute b, U|(C
{b})={{1,5}, {2,8}, {3,6}, {4}, {7}}, POSC
{b}(D)
={{3}, {4}, {6},{7}}=POSC(D), so attribute b is not omissible; after deleting
attribute c, U|(C
{c})={{1,5}, {2,8}, {3}, {4}, {6}, {7}}, POSC
{c}(D)
={{3}, {4}, {6},{7}}=POSC(D) , so attribute c is not omissible.
From these results, we can get the condition attribute core of table 11.8 is a,
and there are two reducts {a, b} and {a, c}. Table 11.9 is the table after reducing
attribute c from the original decision table.
