Database Reference
In-Depth Information
For each
v
i,j
when
j
=2
,...,k
−
1 has a triangular membership function
as follows:
0
x
≤
m
j−
1
m
j−
1
m
j
−
x
−
m
j−
1
<x
≤
m
j
m
j−
1
µ
v
i,j
(
x
)=
.
(14.6)
m
j
+1
−
x
m
j
<x<m
j
+1
m
j
+1
−
m
j
0
x
≥
m
j
+1
Finally, the membership function of the last linguistic term
v
i,k
is:
0
x ≤ m
k−
1
m
k−
1
m
k
−
x
−
m
k−
1
<x
≤
m
k
µ
v
i,k
(
x
)=
.
(14.7)
m
k−
1
1
x
≥
m
k
Figure 14.3 illustrates the creation of four groups defined on the age
attribute: “young”, “early adulthood”, “middle-aged” and “old age”. Note
that the first set (“young”) and the last set (“old age”) have a trapezoidal
form which can be uniquely described by the four corners. For example,
the “young” set could be represented as (0
,
0
,
16
,
32). In between, all other
sets (“early adulthood” and “middle-aged”) have a triangular form which
can be uniquely described by the three corners. For example, the set “early
adulthood” is represented as (16
,
32
,
48).
1
0.9
0.8
0.7
Young
Early adulthood
Middle-aged
Old Age
0.6
0.5
0.4
0.3
0.2
0.1
0
10
30
50
70
Age
Fig. 14.3 Membership function for various groups in the age attribute.
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