Information Technology Reference
In-Depth Information
Table 11.3 and 11.4 can be reduced. For example, Table 11.3 can be reduced to a
Table 11.5 as follows.
Table 11.5 The Reduction of Table 11.3
A
U
a
c
e
u
1
1
2
0
u
2
0
1
1
u
3
2
2
0
u
4
0
2
2
3
.
Reduction of Attribute Values
For decision tables, the reduction of attribute values is processed on decision
rules. It is to reduce the unnecessary conditions of each decision rules in decision
algorithms respectively with decision logic. The reduction is not the unitary
attribute reduction. It is a reduction on each decision rule. The redundant attribute
values in a decision rule are reduced, which make the decision algorithm smaller.
In previous sections, we have defined that, if θ is a
P
-basic formula and
R
⊆
P
,
then
θ
|R
denotes a
R
-basic formula that is generated by deleting all elementary
formulas from θ.
θ→Ψ is a
P
PQ
-rule and
a
∈
P
, if and only if |=
S
θ→Ψ implicates |=
S
θ|(
{
a
})→
Ψ. At this time, we call that attribute
a
is omissible in θ→Ψ. Otherwise,
attribute
is not omissible in θ→Ψ.
In rule θ→Ψ, if all attributes are not omissible, then θ→Ψ is independent. If
θ→Ψ is independent, and |=
S
θ→Ψ implicates |=
S
θ|(
a
P
{
a
})→Ψ, then attribute
subset
is called as the reduct of θ→Ψ. If R is the reduct of θ→Ψ, θ
|R
→Ψ is
called as reduced.
The set of all attributes in
θ→Ψ that are not omissible is called as the core of
θ→Ψ, and it is denoted as CORE(θ→Ψ).
Proposition 11.10
R
⊆
P
CORE(P
→
Q)=
∩
RED(P
→
Q),
Here, RED(P
→
Q) is the reduction set of P
→
Q .
As we said, the reduction of decision rules is that using decision logic to
reduce the unnecessary conditions of each decision rule in decision algorithms.
That is, calculate the core and reducts of each decision rule.
The reduction of attribute values in decision tables (the reduction of decision
rules) is actually processed on condition attributes. Each row of decision table
