Databases Reference
In-Depth Information
OUTPUT: A set of fuzzy association rules.
STEP 1: IF
L
1
is not null, then do the next step; otherwise, exit the algo-
rithm.
STEP 2: Set
r
=1,where
r
is used to represent the number of items kept in
the current large itemsets.
STEP 3: Join the large itemsets
L
r
to generate the candidate set
C
r
+1
in
a way similar to that in the a priori algorithm except that two
regions (linguistic terms) belonging to the same attribute can not
simultaneously exist in an itemset in
C
r
+1
. Restated, the algorithm
first joins
L
r
and
L
r
under the condition that
r
-1 items in the two
itemsets are the same and the other one is different. It then keeps
in
C
r
+1
the itemsets which have all their sub-itemsets of
r
items
existing in
L
r
and do not have any two items
R
jp
and
R
jq
(
p
=
q
)
of the same attribute
R
j
.
STEP 4: Do the following substeps for each newly formed (
r
+1)-itemset
s
with items (
s
1
,s
2
,...,s
r
+1
)in
C
r
+1
:
STEP 4.1: Calculate the fuzzy value of each transaction data
D
(
i
)
in
s
as
f
(
i
)
=
f
(
i
)
f
(
i
)
f
(
i
)
s
r
+1
,where
f
(
i
)
s
j
is the membership
value of
D
(
i
)
in region
s
j
. If the minimum operator is used for
the intersection, then:
∧
s
2
∧
,...,
∧
s
s
1
f
(
i
)
s
=
Min
r
+1
j
=1
f
(
i
)
s
j
STEP 4.2: Calculate the scalar cardinality
count
s
of
s
in the transac-
tions as:
n
f
(
i
s
.
count
s
=
i
=1
STEP 4.3: If
count
s
is larger than or equal to the predefined minimum
support value
α
, put
s
in
L
r
+1
.
STEP 5: IF
L
r
+1
is null, then do the next step; otherwise, set
r
=
r
+1and
repeat Steps 2-4.
STEP 6: Construct association rules for each large
q
-itemset
s
with items
(
s
1
,s
2
,...,s
q
),
q
2, using the following substeps:
STEP 6.1: Form each possible association rule as follows:
≥
s
1
∧
...
∧
s
k−
1
∧
s
k
+1
∧
...
∧
s
q
→
s
k
where
k
=1 to
q
.
STEP 6.2: Calculate the confidence values of all association rules using:
i
=1
f
(
i
)
s
i
=1
f
(
i
)
f
(
i
)
s
k−
1
,f
(
i
)
f
(
i
)
s
1
∧
...
∧
s
k
+1
∧
...
∧
s
q
STEP 7: Output the association rules with confidence values larger than or
equal to the predefined confidence threshold
λ
.
