Databases Reference
In-Depth Information
Membership
value
Low
Middle
High
1
Quantity
03 45
9 1 3
Fig. 3.
An example of a possible set of membership functions for Item
milk
Control Genes
Parametric Genes
11134559 19 3∞
c
112
c
111
c
111
c
113
c
122
c
121
c
133
c
132
c
133
Low
Middle
High
Fig. 4.
The chromosome representation for the set of membership functions in Fig. 3
Item
I
j
can be represented as a bit string of
b
j
1
b
j
2
···
b
jT
,where
T
is the
maximum possible number of linguistic terms. The bit
b
ji
indicates whether
the
i
-th membership function is active or not. If
b
ji
=1,the
i
-th membership
function is active, meaning it will be used in the later fuzzy mining process. If
b
ji
= 0, it is inactive. All the individuals in the same population thus have the
same string length. Below, an example is given to demonstrate the process of
encoding membership functions.
Example 1.
Assume there are four items in a transaction database: milk,
bread, cookies and beverage. Also assume a possible set of membership func-
tions for Item milk is given as shown in Fig. 3.
There are three active linguistic terms,
Low
,
Middle
,and
High
, for this
item. According to the proposed encoding scheme, the individual for repre-
senting the set of membership functions in Fig. 3 is encoded as shown in Fig. 4.
In Fig. 4, the three bits in the control genes have value 1, representing the
three membership functions are active. The membership function of
Low
for
milk is encoded as (3, 4, 5) according to Fig. 3. Similarly, the membership
functions for
Middle
and
High
are respectively encoded as (5, 9, 13) and
(9, 13,
). The parametric genes are then the catenation of the three tuples.
In another case, if the control genes of the chromosome become (1, 0, 1) during
the evolution, then only two active membership functions,
Low
and
High
, will
be used for the item. The proposed model can thus learn the number of labels
for a variable according to the coding scheme.
∞
