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λ
choose the confidence level
from the biggest one to the smallest one in the associ-
ation matrix. After that, in terms of the chosen confidence level
λ
, we construct the
corresponding
-cutting matrix. With this principle, the clustering results come into
being, the smaller the confidence level
λ
λ
is, the more detailed the clustering will be.
2.7.3 Numerical Example
Example 2.8
(Zhao et al. 2012b) A military equipment development team needs to
cluster five combat aircrafts according to their operational effectiveness. In order to
group these combat aircrafts
y
i
(
with respect to their comprehensive
functions, a team of military experts have been set up to provide their assessment
information on
y
i
i
=
1
,
2
,...,
5
)
(
i
=
1
,
2
,...,
5
)
. The attributes which are considered here in
assessment of
y
i
are: (1)
G
1
is the aircraft power; (2)
G
2
is the
fire power (a military capability to direct force at an enemy); (3)
G
3
is the capacity
for target detection; (4)
G
4
is the controlling ability; (5)
G
5
is the survivability; (6)
G
6
is the range of voyage; and (7)
G
7
is the electronic countermeasure effect. The
military experts evaluate the performances of the combat aircrafts
y
i
(
(
i
=
1
,
2
,...,
5
)
i
=
1
,
2
,...,
5
)
according to the attributes
G
j
(
j
=
1
,
2
,...,
7
)
, and gives the data as follows:
y
1
={
G
1
,
0
.
5
,
0
.
3
,
G
2
,
0
.
6
,
0
.
3
,
G
3
,
0
.
4
,
0
.
3
,
G
4
,
0
.
8
,
0
.
1
,
G
5
,
0
.
7
,
0
.
2
,
G
6
,
0
.
5
,
0
.
2
,
G
7
,
0
.
4
,
0
.
3
}
y
2
={
G
1
,
0
.
6
,
0
.
2
,
G
2
,
0
.
5
,
0
.
3
,
G
3
,
0
.
5
,
0
.
2
,
G
4
,
0
.
6
,
0
.
2
,
G
5
,
0
.
6
,
0
.
3
,
G
6
,
0
.
6
,
0
.
3
,
G
7
,
0
.
5
,
0
.
2
}
y
3
={
G
1
,
0
.
7
,
0
.
1
,
G
2
,
0
.
6
,
0
.
3
,
G
3
,
0
.
7
,
0
.
2
,
G
4
,
0
.
5
,
0
.
3
,
G
5
,
0
.
5
,
0
.
2
,
G
6
,
0
.
5
,
0
.
2
,
G
7
,
0
.
6
,
0
.
3
}
y
4
={
G
1
,
0
.
4
,
0
.
3
,
G
2
,
0
.
7
,
0
.
2
,
G
3
,
0
.
5
,
0
.
3
,
G
4
,
0
.
6
,
0
.
2
,
G
5
,
0
.
7
,
0
.
1
,
G
6
,
0
.
4
,
0
.
3
,
G
7
,
0
.
7
,
0
.
2
}
y
5
={
G
1
,
0
.
6
,
0
.
2
,
G
2
,
0
.
6
,
0
.
3
,
G
3
,
0
.
6
,
0
.
2
,
G
4
,
.
,
.
,
G
5
,
.
,
.
,
G
6
,
.
,
.
,
G
7
,
.
,
.
}
0
5
0
3
0
8
0
1
0
6
0
1
0
6
0
1
Suppose that the weights of the attributes
G
j
(
j
=
1
,
2
,...,
7
)
are equal, now we
utilize Algorithm 2.12 to group these combat aircrafts
y
i
(
i
=
1
,
2
,...,
5
)
:
Step 1
Use Eq. (
2.160
) to compute the association coefficients of the IFSs
y
i
(
i
=
1
,
2
,...,
5
)
, and then construct an association matrix
C
=
(
c
ij
)
5
×
5
, where
c
ij
=
c
3
(
y
i
,
y
j
),
i
,
j
=
1
,
2
,...,
5:
⎛
⎞
1
.
000 0
.
964 0
.
917 0
.
952 0
.
947
⎝
⎠
0
.
964 1
.
000 0
.
948 0
.
941 0
.
963
C
=
0
.
917 0
.
948 1
.
000 0
.
946 0
.
957
0
.
952 0
.
941 0
.
946 1
.
000 0
.
957
0
.
947 0
.
963 0
.
957 0
.
957 1
.
000
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