Databases Reference
In-Depth Information
attributes
B
are the same. For example if
r
2
=[(
a
2
,
1)
∗
(
a
3
,
4)
−→
(
d,
1)],
then
r
1
/
.
In our example, we get the following optimal rules which support is greater
or equal to 2:
(
b,
3)
{
a
2
,a
3
}
=
r
2
/
{
a
2
,a
3
}
∗
(
c,
2)
−→
(
d,H
), (
a,
1)
∗
(
b,
1)
−→
(
d,L
),
(
a,
1)
∗
(
c,
1)
−→
(
d,L
), (
b,
1)
∗
(
c,
0)
−→
(
d,H
),
(
d,H
)
Now, let us assume that (
a,v
(
a,
1)
−→
w
) denotes the fact that the value of
attribute
a
has been changed from
v
to
w
. Similarly, the term (
a,v
−→
w
)(
x
)
means that
a
(
x
)=
v
has been changed to
a
(
x
)=
w
. Saying another words,
the property (
a,v
) of object
x
has been changed to property (
a,w
).
Let
S
=(
U,A
St
∪A
Fl
∪{d}
) is a decision table and rules
r
1
,
r
2
have been
extracted from
S
. The notion of e-action rule was given in [13]. Its definition
is given below. We assume here that:
•
−→
B
St
is a maximal subset of
A
St
such that
r
1
/B
St
=
r
2
/B
St
•
d
(
r
1
)=
k
1
,
d
(
r
2
)=
k
2
and
k
1
≤
k
2
•
(
∀
a
∈
[
A
St
∩
L
(
r
1
)
∩
L
(
r
2
)])[
a
(
r
1
)=
a
(
r
2
)]
•
(
∀
i
≤
q
)(
∀
e
i
∈
[
A
St
∩
[
L
(
r
2
)
−
L
(
r
1
)]])[
e
i
(
r
2
)=
u
i
]
•
(
∀
i
≤
r
)(
∀
c
i
∈
[
A
Fl
∩
[
L
(
r
2
)
−
L
(
r
1
)]])[
c
i
(
r
2
)=
t
i
]
•
(
∀
i
∈
p
)(
∀
b
i
∈
[
A
Fl
∩
L
(
r
1
)
∩
L
(
r
2
)])[[
b
i
(
r
1
)=
v
i
]&[
b
i
(
r
2
)=
w
i
]]
Let
A
St
∩
L
(
r
1
)
∩
L
(
r
2
)=
B
.By(
r
1
,r
2
) -e-action rule on
x
∈
U
we mean
the expression
r
:
[
{
a
=
a
(
r
1
):
a
∈
B
}
(
e
1
=
u
1
)
∧
(
e
2
=
u
2
)
∧
...
∧
(
e
q
=
u
q
)
∧
(
b
1
,v
1
−→
w
1
)
∧
(
b
2
,v
2
−→
w
2
)
∧
...
∧
(
b
p
,v
p
−→
w
p
)
∧
(
c
1
,
−→
t
1
)
∧
(
c
2
,
−→
t
2
)
∧
...
∧
(
c
r
,
−→
t
r
)](
x
)=
⇒
[(
d,k
1
−→
k
2
)](
x
)
Object
x
∈
U
supports (
r
1
,r
2
)-e-action rule
r
in
S
=(
U,A
St
∪
A
Fl
∪{
d
}
),
if the following conditions are satisfied:
•
(
∀
i
≤
p
)[
∀
b
i
∈
L
(
r
)][
b
i
(
x
)=
v
i
]
∧
d
(
x
)=
k
1
•
(
∀
i
≤
p
)[
∀
b
i
∈
L
(
r
)][
b
i
(
y
)=
w
i
]
∧
d
(
y
)=
k
2
•
(
∀
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 e-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
)]
∧
