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⎛
⎝
⎞
⎠
(
1
,
0
)(
0
.
7
,
0
.
2
)(
0
.
7
,
0
.
1
)(
0
.
5
,
0
.
3
)(
0
.
5
,
0
.
4
)
(
0
.
7
,
0
.
2
)(
1
,
0
)(
0
.
7
,
0
.
1
)(
0
.
6
,
0
.
1
)(
0
.
6
,
0
.
3
)
Z
=
(
0
.
7
,
0
.
1
)(
0
.
7
,
0
.
1
)(
1
,
0
)(
0
.
6
,
0
.
1
)(
0
.
5
,
0
.
5
)
(
0
.
5
,
0
.
3
)(
0
.
6
,
0
.
1
)(
0
.
6
,
0
.
1
)(
1
,
0
)(
0
.
6
,
0
.
3
)
(
0
.
5
,
0
.
4
)(
0
.
6
,
0
.
3
)(
0
.
5
,
0
.
5
)(
0
.
6
,
0
.
3
)(
1
,
0
)
Step 2 Choose the confidence levels properly, and get the corresponding clustering
results with the direct method:
(1) When 0
.
7
<μ λ 1
≤
1
.
0, by Eq. ( 2.210 ), we know that there is no value z ij
y i ] ( 1 )
in R such that z ij
= λ 1 , i.e.,
[
= φ
. Thus, each car is clustered into one type:
Z
{
y 1 } , {
y 2 } , {
y 3 } , {
y 4 }
and
{
y 5 }
.
(2) When 0
.
6
<μ λ 2 ≤
0
.
7, we have the following two cases:
(i) z 13
=
z 23
= (
0
.
7
,
0
.
1
)
: In this case, by Eq. ( 2.209 ), we know that y 1 ,
y 2 and
y 3 can be clustered into one type:
{
y 1 ,
y 2 ,
y 3 }
. Then, by Step 2 of the clustering
method, we get that the cars y i (
i
=
1
,
2
,
3
,
4
,
5
)
are clustered into three types:
{
y 1 ,
y 2 ,
y 3 } , {
y 4 }
and
{
y 5 }
.
: In this case, y 1 and y 2 can be clustered into one type. Thus,
by Step 2 of the clustering method, we know that the cars y i
(ii) z 12 = (
0
.
7
,
0
.
2
)
(
i
=
1
,
2
,
3
,
4
,
5
)
are
also clustered into three types:
{
y 1 ,
y 2 ,
y 3 } , {
y 4 }
and
{
y 5 }
.
(3) When 0
.
5
<μ λ 3 ≤
0
.
6, we have the following two cases:
: In this case, y 2 , y 3 and y 4 can be clustered into one
type. Then, merging the clustering results of (1) and (2), we can see that the cars
y i (
(i) z 24
=
z 34
= (
0
.
6
,
0
.
1
)
=
,
,
,
,
)
{
y 1 ,
y 2 ,
y 3 ,
y 4 }
{
y 5 }
i
1
2
3
4
5
are clustered into two types:
and
.
= (
.
,
.
)
: In this case, y 2 and y 5 can be clustered into one type.
Then, merging the clustering results above, it can be obtained that the cars y i (
(ii) z 25
0
6
0
3
i
=
1
,
2
,
3
,
4
,
5
)
are clustered into one type:
{
y 1 ,
y 2 ,
y 3 ,
y 4 ,
y 5 }
.
Compared with Zhang et al. (2007)'s method, we can know that the direct method
with less calculation amount can have better clustering results.
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