Information Technology Reference
In-Depth Information
to
u
with respect to criteria
A
”. For
u
U
, its dominating set and its dominated set
with respect to
A
are defined, respectively, by:
∈
D
A
(
u
∈
u
,
u
)
={
U
|
(
u
)
∈
D
A
}
,
D
A
(
u
∈
u
)
∈
u
)
={
U
|
(
u
,
D
A
}
.
The dominating set
D
A
(
(resp. the dominated set
D
A
(
u
)
u
)
) is the set of the objects
dominating (resp. dominated by)
u
under
A
.
Since decision classes are ordered
X
1
<
X
2
<
···
<
X
p
, one can define an
upward union of decision classes
X
i
and a downward union of decision classes
X
i
with respect to each class
X
i
,
i
∈
V
d
, as follows:
X
i
X
i
=
X
j
,
=
X
j
.
j
≥
i
j
≤
i
For convenience,
X
0
=
X
p
+
1
=∅
.Wehave
X
i
X
i
−
1
.
=
U
\
Example 10
Consider a decision table
given in Table
7.7
.
This table shows student evaluation in a school. The objects are seven students, i.e.,
U
D =
(
U
,
C
∪{
d
}
,
{
V
a
}
)
. The condition attributes are scores of mathematics (Ma),
physics (Ph) and literature (Li), while the decision attribute (
d
) is a comprehensive
evaluation (E). Namely,
C
={
u
1
,
u
2
,...,
u
7
}
E. We may assume that the better
scores in all subjects student takes, the better comprehensive evaluation he/she gets.
Let
A
=
{Ma, Ph, Li} and
d
=
{Ma, Ph}. The dominance relation
D
A
is described as the following
matrix. Symbol
=
indicates that the corresponding row object
u
i
and column object
u
j
is in the dominance relation, i.e.,
∗
(
u
i
,
u
j
)
∈
D
A
.
u
1
u
2
u
3
u
4
u
5
u
6
u
7
u
1
∗∗∗∗∗∗∗
u
2
∗∗∗∗∗∗∗
u
3
∗∗∗∗∗
u
4
∗
∗
u
5
∗∗∗
u
6
∗∗∗
u
7
∗
Table 7.7
A decision table
of student records
Student
Ma
Ph
Li
E
u
1
Good
Good
Good
Good
u
2
Good
Good
Med
Med
u
3
Med
Good
Med
Good
u
4
Bad
Med
Good
Med
u
5
Med
Bad
Med
Bad
u
6
Med
Bad
Bad
Med
u
7
Bad
Bad
Bad
Bad
Search WWH ::
Custom Search