Information Technology Reference
In-Depth Information
1
1
Y
Z
3
3
200*
−
Y
Z
0
0
H
=
arctan
1
1
X
Y
3
3
500*
−
X
Y
0
0
1
3
Y
V
=
116*
−
16
Y
0
2
2
1
1
1
1
X
Y
Y
Z
3
3
3
3
C
=
500
x
−
+
200
x
−
X
Y
Y
Z
0
0
0
0
where
0
X Y Z
are the values for pure white.
, ,
0
0
r ough Set Attribute r eduction
In an information system, there often exist some condition attributes that do not provide any additional
information about the objects in
U.
So, we should remove those attributes since the complexity and cost
of the decision process can be reduced if those condition attributes are eliminated (Bazan, Skowron, &
Synak, , 1994; Kryszkiewicz & Rybinski, 1994; Stefanowski, 1993; Zhong & Skowron, 2000).
Definition 2 (Reduct).
Given a classification task mapping a set of variables
C
to a set of labeling
D,
a
reduct is defined as any
R
⊆
C,
such that
( , )
C D
=
( , ).
R D
Definition 3 (Reduct Set).
Given a classification task mapping a set of variables
C
to a set of la-
beling
D
, a reduct set is defined with respect to the power set
P
(
C
) as the set
R
⊆
P
such that
( )
C
R A
= ∈ =
P
That is, the reduct set is the set of all possible reducts of the equivalence
relationship denoted by
C
and
D
.
{
( ): ( , )
C
A D
( , )}.
C D
Definition 4 (Significance).
Given
, , and an object ,
P Q
x
∈
, the significant
( , )
x
P Q
of
x
in the equivalence
relation denoted by
P
and
Q
is
( , )
x
P Q
=
( , )
P Q
−
(
P x Q
−
{ }, ).
Definition 5 (Minimal Reduct).
Given a classification task mapping a set of variables
C
to a set of
labeling
D
, and
R
, the reduct set for this problem space, a minimal reduct is defined as any reduct
R
such that
| | | |,
≤ ∀ ∈
That is, the minimal reduct is the reduct of least cardinality for the equivalence
relationship denoted by
C
and
D
.
R A A R
.
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