Databases Reference
In-Depth Information
item
I
j
,
f
(
i
)
jl
is
v
(
i
)
j
's fuzzy membership value in region
R
jk
,and
) is the number of active linguistic terms for
I
j
.
STEP 3.2: For each item region
R
jk
, calculate its scalar cardinality on the
transactions as follows:
l
(=
|
I
j
|
n
f
(
i
)
count
jk
=
jk
.
i
=1
STEP 3.3: For each
R
jk
,1
, check whether its
count
j
k
over
n
is larger than or equal to the minimum support
threshold
α
.If
R
jk
satisfies the above condition, put it in the
set of large 1-itemsets (
L
1
). That is:
≤
j
≤
m
and 1
≤
k
≤|
I
j
|
L
1
=
{
R
jk
|
count
jk
/n
≥
α,
1
≤
j
≤
mand
1
≤
k
≤|
I
j
|}
.
STEP 3.4: Set the fitness value of the chromosome as the sum of the fuzzy
supports (the scalar cardinalities / n) of the fuzzy regions in
L
1
divided by suitability(
C
q
). That is:
f
(
C
q
)=
X
∈
L
1
fuzzy support
(
X
)
suitability
(
C
q
)
.
STEP 4: Execute crossover operations on each population.
STEP 5: Execute mutation operations on each population.
STEP 6: Using the selection criteria to choose individuals in each population
for the next generation.
STEP 7: If the termination criterion is not satisfied, go to Step 3; otherwise,
do the next step.
STEP 8: Gather the sets of membership functions, each of which has the
highest fitness value in its population.
The sets of the best membership functions gathered from each population
are then used to mine fuzzy association rules from the given quantitative data-
base. Our fuzzy mining algorithm proposed in [5] is then adopted to achieve
this purpose. It first transforms each quantitative value into a fuzzy set of
linguistic terms using the derived membership functions. It then calculates
the scalar cardinality of each linguistic term on all the transaction data. The
mining process based on fuzzy counts is then performed to find fuzzy asso-
ciation rules. The details of the fuzzy mining algorithm [5] are described as
follows.
The algorithm for mining fuzzy association rules:
INPUT: A set of
n
quantitative transaction data, each with
m
item values, a
set of membership functions, a predefined minimum support thresh-
old
α
, a predefined confidence threshold
λ
, and the large 1-itemset
L
1
from the phase of mining membership functions.
