Databases Reference
In-Depth Information
•
(
∀
j
≤
p
)[
a
j
∈
(
A
St
∩
L
(
r
2
))][
a
j
(
x
)=
u
j
]
•
(
∀
j
≤
p
)[
a
j
∈
(
A
St
∩
L
(
r
2
))][
a
j
(
y
)=
u
j
]
•
Object
x
supports rule
r
1
•
Object
y
supports rule
r
2
By the support of an extended action rule
r
in
S
, denoted by
Sup
S
(
r
), we
mean the set of all objects in
S
supporting
R
. In other words, the set of all
objects in
S
supporting
r
has the property
(
a
1
=
u
1
)
∧
(
a
2
=
u
2
)
∧
...
∧
(
a
q
=
u
q
)
∧
(
b
1
=
v
1
)
∧
(
b
2
=
v
2
)
∧
...
∧
(
b
p
=
v
p
)
(
d
=
k
1
).
By the confidence of R in S, denoted by
Conf
S
(
r
), we mean
[
Sup
S
(
r
)
/Sup
S
(
L
(
r
))][
Conf
(
r
2
)].
In order to find the confidence of (
r
1
,r
2
)-E-action rule in
S
, we divide
the number of objects supporting (
r
1
,r
2
)-action rule in
S
by the number of
objects supporting left hand side of (
r
1
,r
2
)-E-action rule times the confidence
of the second classification rule
r
2
in
S
.
∧
4 Discovering E-Action Rules
In this section we present a new algorithm for discovering E-action rules.
Initially, we partition the set of rules discovered from an information system
S
=(
U,A
St
∪
), where
A
St
is the set of stable attributes,
A
Fl
is
the set of flexible attributes and,
V
d
=
A
Fl
∪{
d
}
is the set of decision
values, into subsets of rules defining the same decision value. Saying another
words, the set of rules
R
discovered from
S
is partitioned into
{
d
1
,d
2
,...,d
k
}
{
R
i
}
i
:1
≤i≤k
,
where
R
i
=
for any
i
=1
,
2
,...,k
. Clearly, the objects
supporting any rule from
R
i
form subsets of
d
−
1
(
{
r
∈
R
:
d
(
r
)=
d
i
}
).
Let us take Table 1 as an example of a decision system
S
. We assume
that
a
,
c
are stable attributes and
b
,
d
are flexible. The set
R
of certain rules
extracted from
S
is given below:
1. (
a,
0)
{
d
i
}
−→
(
d,L
), (
c,
0)
−→
(
d,L
)
2. (
b,R
)
−→
(
d,L
), (
c,
1)
−→
(
d,L
)
3. (
b,P
)
−→
(
d,L
), (
a,
2)
∗
(
b,S
)
−→
(
d,H
)
4. (
b,S
)
(
d,H
)
We partition this set into two subsets
R
1
=
∗
(
c,
2)
−→
{
[(
a,
0)
−→
(
d,L
)]
,
[(
c,
0)
−→
(
d,L
)]
,
[(
b,R
)
−→
(
d,L
)]
,
[(
c,
1)
−→
(
d,L
)]
,
[(
b,P
)
−→
(
d,L
)]
}
and
R
2
=
{
.
Assume now that our goal is to re-classify some objects from the class
d
−
1
(
[(
a,
2)
∗
(
b,S
)
−→
(
d,H
)]
,
[(
b,S
)
∗
(
c,
2)
−→
(
d,H
)]
}
) into the class
d
−
1
(
{
d
i
}
{
d
j
}
). In our example, we assume that
d
i
=(
d,L
)
and
d
j
=(
d,H
).
First, we represent the set
R
as a table (see Table 2). The first column of
this table shows objects in
S
supporting the rules from
R
(each row represents
