Information Technology Reference
In-Depth Information
Table 7.2
The decision
table in Table
7.1
with the
generalized decision function
Car
Pr
Ma
Sa
Ev
∂
C
u
1
High
High
Low
Unacc
{unacc}
u
2
Med
Med
Med
Unacc
{unacc, acc}
u
3
Med
Med
Med
Acc
{unacc, acc}
u
4
Med
High
Low
Acc
{acc}
u
5
Med
Med
High
Acc
{acc, good}
u
6
Med
Med
High
Good
{acc, good}
u
7
Low
Med
Med
Good
{good}
u
1
u
2
u
3
u
4
u
5
u
6
u
7
u
1
∅
C
C
{
Pr
}
C
C
C
u
2
C
∅
∅
{
Ma
,
Sa
}{
Sa
}
{
Sa
}
{
Pr
}
∅
∅
{
,
}{
}
{
}
{
}
u
3
C
Ma
Sa
Sa
Sa
Pr
u
4
{
}{
,
}{
,
}
∅{
,
}{
,
}
Pr
Ma
Sa
Ma
Sa
Ma
Sa
Ma
Sa
C
u
5
C
{
Sa
}
{
Sa
}{
Ma
,
Sa
}
∅
∅{
Pr
,
Sa
}
u
6
C
{
Sa
}
{
Sa
}{
Ma
,
Sa
}
∅
∅{
Pr
,
Sa
}
u
7
C
{
Pr
}
{
Pr
}
C
{
Pr
,
Sa
}{
Pr
,
Sa
}
∅
The discernibility functions
F
L
and
F
L
for the decision table are calculated as:
F
L
Pr
Ma
Sa
Pr
Ma
Sa
Pr
Ma
Pr
Sa
(
,
,
)
=
m
ij
˜
c
=
(
)
∧
(
∨
)
=
(
∧
)
∨
(
∧
),
c
∈
i
=
1
,
4
,
7
j
=
i
Pr
Ma
Sa
Pr
Sa
Pr
Sa
F
U
(
,
,
)
=
m
ij
˜
=
(
)
∧
(
)
=
(
∧
).
c
c
∈
i
,
j
|
i
=
j
,(
i
,
j
)
=
(
2
,
3
),(
3
,
2
),(
5
,
6
),(
6
,
5
)
Therefore, there are two L-reducts {Pr, Ma} and {Pr, Sa}, and one U-reduct {Pr, Sa}.
In this case, we would select the U-reduct {Pr, Sa}, because we obtain the same
size of reducts even if we select the other L-reduct.
7.3 Structure-Based Attribute Reduction in Variable
Precision Rough Set Models
7.3.1 Rough Membership Function
The reason why decision tables are inconsistent is not only lack of knowledge (con-
dition attributes) related to the decision attribute but also noise in observation of
attribute values. In the latter case, the classical RSMwould not be very useful because
it does not permit any errors in the classification of objects into the lower approxi-
mations.
Search WWH ::
Custom Search