Information Technology Reference
In-Depth Information
Atomic action terms model a single feature values transition pattern, but it does
not model the association between feature values transition patterns.
Definition 2
(
Action terms
) are defined as the smallest collection of expressions for
a decision system
S
such that:
•
If
t
is an atomic action term in
S
, then
t
is an action term in
S
.
•
If
t
1
,
t
2
are action terms in
S
and
∧
is a 2-argument functor called composition,
then
t
1
∧
t
2
is a candidate action term in
S
.
•
If
t
is a candidate action term in
S
and for any two atomic action terms
(
f
,
v
1
ₒ
v
2
), (
g
,
w
1
ₒ
w
2
)
contained in
t
we have
f
=
g
, then
t
is an action term in
S
.
Assuming that
S
is given, we will say from now on,
action term
instead of
action
term in S
.
Definition 3
(
Domain of an action term
) The domain
Dom
of an action term
t
is the set of features listed in the atomic action terms contained in
t
. For example,
t
(
t
)
=[
(
f
,
v
1
ₒ
v
2
)
∧
(
g
,
w
1
)
]
is an action term that consists of two atomic action
terms, namely
(
f
,
v
1
ₒ
v
2
)
and
(
g
,
w
1
)
. Therefore,
Dom
(
t
)
={
f
,
g
}
.
Action rules are expressions that take the following form:
r
=[
t
1
⃒
t
2
]
, where
t
1
,
t
2
are action terms. The interpretation of the action rule
r
is that by triggering
the action term
t
1
, we would get, as a result, the changes of states in action term
t
2
.
We also assume that
Dom
(
t
1
)
∪
Dom
(
t
2
)
ↆ
F
, and
Dom
(
t
1
)
∩
Dom
(
t
2
)
=∅
.
=
[
(
,
v
1
ₒ
v
2
)
∧
(
,
w
2
)
]⃒
(
,
d
1
ₒ
d
2
)
] means that by
changing the state of feature
f
from
v
1
to
v
2
, and by keeping the state of feature
g
as
w
2
, we would observe a change in attribute
d
from the state
d
1
to
d
2
, where
d
is
commonly referred to as the decision attribute.
For example,
r
[
f
g
d
9.3.1 Action Rules Evaluation
In [
8
] it was observed that each action rule can be seen as a composition of two classi-
fication rules. For instance, the rule
r
=
[
[
(
f
,
v
1
ₒ
v
2
)
∧
(
g
,
w
2
)
]⃒
(
d
,
d
1
ₒ
d
2
)
]
is a composition of
r
1
=[
(
f
,
v
1
)
∧
(
g
,
w
2
)
]ₒ
(
d
,
d
1
)
and
r
2
=[
(
f
,
v
2
)
∧
(
g
,
w
2
)
]ₒ
(
. Also, the definition
of support (
Sup
) and confidence (
Conf
) of an action rule is based on support and
confidence of classification rules (see below).
Assume that action rule
r
is a composition of two classification rules
r
1
and
r
2
.
Then [
8
]:
d
,
d
2
)
. This fact can be recorded by the equation
r
=
r
(
r
1
,
r
2
)
•
Sup
(
r
)
=
min
{
card
(
sup
(
r
1
)),
card
(
sup
(
r
2
))
}
,
•
Conf
(
r
)
=
conf
(
r
1
)
·
conf
(
r
2
)
,
where
conf
(
r
1
)
and
conf
(
r
2
)
are the respective confidences of classification rules
r
1
and
r
2
.
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