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In-Depth Information
Table 2.1
The characteristics of the ten new cars
G
1
G
2
G
3
G
4
G
5
G
6
y
1
(0.3,0.5)
(0.6,0.1)
(0.4,0.3)
(0.8,0.1)
(0.1,0.6)
(0.5,0.4)
y
2
(0.6,0.3)
(0.5,0.2)
(0.6,0.1)
(0.7,0.1)
(0.3,0.6)
(0.4,0.3)
y
3
(0.4,0.4)
(0.8,0.1)
(0.5,0.1)
(0.6,0.2)
(0.4,0.5)
(0.3,0.2)
y
4
(0.2,0.4)
(0.4,0.1)
(0.9,0)
(0.8,0.1)
(0.2,0.5)
(0.7,0.1)
y
5
(0.5,0.2)
(0.3,0.6)
(0.6,0.3)
(0.7,0.1)
(0.6,0.2)
(0.5,0.3)
Step 1
By Eq. (
2.11
), we construct the intuitionistic fuzzy similarity matrix (with-
out loss of generality, let
λ
=
2
,β
1
=
β
2
=
β
3
=
1
/
3
)
:
We first calculate
λ
d
∗
(
1
√
3
[
2
2
2
1
−
y
1
,
y
2
)
=
1
−
max
{|
0
.
3
−
0
.
6
|
+|
0
.
5
−
0
.
3
|
+|
0
.
2
−
0
.
1
|
,
2
2
2
2
2
2
|
.
−
.
|
+|
.
−
.
|
+|
.
−
.
|
,
|
.
−
.
|
+|
.
−
.
|
+|
.
−
.
|
,
0
6
0
5
0
1
0
2
0
3
0
3
0
4
0
6
0
3
0
1
0
3
0
3
2
2
2
2
2
2
|
0
.
8
−
0
.
7
|
+|
0
.
1
−
0
.
1
|
+|
0
.
1
−
0
.
2
|
,
|
0
.
1
−
0
.
3
|
+|
0
.
6
−
0
.
6
|
+|
0
.
3
−
0
.
1
|
,
1
2
2
2
2
|
0
.
5
−
0
.
4
|
+|
0
.
4
−
0
.
3
|
+|
0
.
1
−
0
.
3
|
}]
=
0
.
78
λ
d
1
√
3
[
2
2
2
∗
(
y
1
,
y
2
)
=
min
{|
0
.
3
−
0
.
6
|
+|
0
.
5
−
0
.
3
|
+|
0
.
2
−
0
.
1
|
,
2
2
2
2
2
2
|
0
.
6
−
0
.
5
|
+|
0
.
1
−
0
.
2
|
+|
0
.
3
−
0
.
3
|
,
|
0
.
4
−
0
.
6
|
+|
0
.
3
−
0
.
1
|
+|
0
.
3
−
0
.
3
|
,
2
2
2
2
2
2
|
0
.
8
−
0
.
7
|
+|
0
.
1
−
0
.
1
|
+|
0
.
1
−
0
.
2
|
,
|
0
.
1
−
0
.
3
|
+|
0
.
6
−
0
.
6
|
+|
0
.
3
−
0
.
1
|
,
2
2
2
2
|
0
.
5
−
0
.
4
|
+|
0
.
4
−
0
.
3
|
+|
0
.
1
−
0
.
3
|
}]
=
0
.
08
, similarly, we can calculate the other intuitionistic fuzzy
similarity degrees, and then get the intuitionistic fuzzy similarity matrix:
Thus,
z
12
=
(
0
.
78
,
0
.
08
)
⎛
⎝
⎞
⎠
(
,
)
(
.
,
.
)(
.
,
.
)(
.
,
)(
.
,
.
)
1
0
0
78
0
02
0
72
0
02
0
64
0
0
63
0
08
(
0
.
78
,
0
.
02
)
(
1
,
0
)
(
0
.
78
,
0
.
08
)(
0
.
71
,
0
.
08
)(
0
.
71
,
0
)
=
(
0
.
72
,
0
.
08
)(
0
.
78
,
0
.
08
)
(
1
,
0
)
(
0
.
67
,
0
.
14
)(
0
.
59
,
0
.
08
)
Z
(
0
.
64
,
0
)(
0
.
71
,
0
.
08
)(
0
.
67
,
0
.
14
)
(
1
,
0
)
(
0
.
63
,
0
.
08
)
(
0
.
63
,
0
.
08
)(
0
.
71
,
0
)(
0
.
59
,
0
.
08
)(
0
.
63
,
0
.
08
)
(
1
,
0
)
Step 2
Calculate
⎛
⎝
⎞
⎠
(
1
,
0
)
[
0
.
78
,
0
.
92
]
(
0
.
78
,
0
.
08
)(
0
.
71
,
0
)(
0
.
71
,
0
.
08
)
(
0
.
78
,
0
.
08
)
(
1
,
0
)
(
0
.
78
,
0
.
08
)(
0
.
71
,
0
.
08
)(
0
.
71
,
0
)
Z
2
=
Z
◦
Z
=
(
0
.
78
,
0
.
08
)(
0
.
78
,
0
.
08
)
(
1
,
0
)
(
0
.
71
,
0
.
08
)(
0
.
71
,
0
.
08
)
(
0
.
71
,
0
)(
0
.
71
,
0
.
08
)(
0
.
71
,
0
.
08
)
(
1
,
0
)
(
0
.
71
,
0
.
08
)
(
0
.
71
,
0
.
08
)(
0
.
71
,
0
)(
0
.
71
,
0
.
08
)(
0
.
71
,
0
.
08
)
(
1
,
0
)
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