Information Technology Reference
In-Depth Information
Table 11.9 Decision table after reducing attribute c
U
a b d e
1
2
3
4
5
6
7
8
1 0 2 0
0 1 1 2
2 0 1 1
1 1 2 2
1 0 0 1
2 2 1 1
2 1 1 2
0 1 0 1
Then, we reduce the attribute values in Table 11.9. For the third decision rule
a
2
b
0
→d
1
e
1
, it is a consistent decision rule. a
2
, b
0
are core values, because a
2
→d
1
e
1
after deleting b
0
and b
0
→d
1
e
1
after deleting a
2
are both inconsistent rule.
For the second decision rule a
0
b
1
→d
1
e
2
, it is an inconsistent decision rule and a
0
is its core value. The reason is that, the decision attribute values determined by
a
0
b
1
are {d
1
e
2
, d
0
e
1
}, and after deleting b
1
, the decision attribute values
determined by a
0
are also {d
1
e
2
, d
0
e
1
}. However, if a
0
is deleted, the decision
attribute values determined by b
1
are also {d
1
e
2
, d
2
e
2
, d
0
e
1
}. So, a
0
cannot be
reduced. With this method, the resulting core values of each decision rule are
showed in Table 11.10.
Table 11.10 Core values of the decision rules in Table 11.9
U
a b d e
1 0 2 0
0
1 2
2 0 1 1
1 1 2 2
1 0 0 1
2 1 1
2 1 1 2
0
0 1
Therefore, we get the reducts of all attribute values as Table 11.11.
Suppose θ and Ψ are the logic formulas for conditions and decisions
respectively, and θ→Ψ is a decision rule. We use |Ψ| to represent the object set
satisfying formula Ψ in S. We can attach a value to each decision rule, which is
called rough operator of the rule. The operator is defined as: µ(θ, Ψ)=K(|θ
∧Ψ|)/K(|θ|), and the form of the operator's rule is: θ→mΨ, m=µ(θ, Ψ). In the
definition, K(S) represents the cardinal number of S, which has the same
1
2
3
4
5
6
7
8
