Databases Reference
In-Depth Information
where
range
(
R
j
1
,R
j
2
,
,R
jl
) is the coverage range of the active membership
functions,
l
is the number of active membership functions for
I
j
,and
max
(
I
j
)
is the maximum quantity of
I
j
in the transactions.
The usage ratio of membership functions for an item
I
j
is defined as the
number of large-1 itemsets for
I
j
divided by the number of active linguistic
terms. Note that the maximum possible number of large-1 itemsets for an
item is the number of its active linguistic terms. The more the usage ratio is,
the better the derived membership functions are. Thus, the usage factor of
the membership functions for an item
I
j
in the chromosome
C
q
is defined as:
···
l
C
q
max
(
L
C
1
usage factor
(
C
q
)=
,
,
1)
is the active linguistic terms of chromosome
C
q
,and
max
(
L
C
1
where
l
C
q
,
1)
is the maximum of the number of large-1 itemsets and 1.
The suitability of the set of membership functions in a chromosome
C
q
is thus defined as
k
1
∗
coverage factor
(
C
q
)+
k
3
∗
usage factor
(
C
q
), where
k
1
,
k
2
,
k
3
are weighting factors.
The fitness value of a chromosome
C
q
is then defined as:
overlap factor
(
C
q
)+
k
2
∗
X∈L
C
q
1
fuzzy support
(
X
)
f
(
C
q
)=
,
suitability
(
X
)
where
L
C
q
1
is the set of large 1-itemsets obtained by using the set of mem-
bership functions in
C
q
,and
fuzzy support
(
X
) is the fuzzy support of the
1-itemset
X
derived from
C
q
in the given transaction database.
The suitability factor used in the fitness function can reduce the occurrence
of the two bad kinds of membership functions shown in Fig. 5, where the first
one is too redundant, and the second one is too separate. It can also help
generate an appropriate number of membership functions for an item.
The overlap factor in
suitable
(
C
q
) is designed for avoiding the first bad
case, and the coverage factor is for the second one.
Using the fuzzy-supports of the linguistic terms in the large 1-itemsets can
achieve a trade-off between execution time and rule interestingness. Usually,
(a)
Redundant membership functions
(b)
Separate membership functions
Low Middle
High
Low
Middle
High
0
5
89
0
5
20
25
Quantity
Quantity
Fig. 5.
Two bad sets of membership functions
