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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
v 2 ), (
g
,
w 1
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
v 2 ) (
g
,
w 1 ) ]
is an action term that consists of two atomic action
terms, namely
(
f
,
v 1
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 )
F , and Dom
(
t 1 )
Dom
(
t 2 ) =∅
.
=
[ (
,
v 1
v 2 ) (
,
w 2 ) ]⃒ (
,
d 1
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
v 2 ) (
g
,
w 2 ) ]⃒ (
d
,
d 1
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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