Information Technology Reference
In-Depth Information
.
<λ
≤
.
937, then
y
i
(
=
,
,...,
)
(8) If 0
919
0
i
1
2
10
are classified into the follow-
ing eight types:
{
y
1
}
,
{
y
2
}
,
{
y
5
}
,
{
y
6
}
,
{
y
3
,
y
7
}
,
{
y
4
,
y
9
}
,
{
y
8
}
,
{
y
10
}
(9) If 0
.
937
<λ
≤
0
.
968, then
y
i
(
i
=
1
,
2
,...,
10
)
are classified into the follow-
ing nine types:
{
y
1
}
,
{
y
2
}
,
{
y
3
}
,
{
y
5
}
,
{
y
6
}
,
{
y
7
}
,
{
y
8
}
,
{
y
4
,
y
9
}
,
{
y
10
}
(10) If 0
.
968
<λ
≤
1, then
y
i
(
i
=
1
,
2
,...,
10
)
are classified into the following
ten types:
{
y
1
}
,
{
y
2
}
,
{
y
3
}
,
{
y
4
}
,
{
y
5
}
,
{
y
6
}
,
{
y
7
}
,
{
y
8
}
,
{
y
9
}
,
{
y
10
}
, then
we first need to transform all the given IFSs (see Table
2.2
) into the interval-valued
fuzzy sets, listed in Table
2.3
(Xu et al. 2008).
After that, we utilize Eq. (
2.11
) (without loss of generality, here we let
If we utilize Algorithm 2.1 to cluster the ten new cars
y
i
(
i
=
1
,
2
,...,
10
)
λ
=
2
,
β
1
=
β
2
=
β
3
=
1
/
3
)
to calculate the intuitionistic fuzzy similarity degrees of
y
i
(
i
=
1
,
2
,...,
10
)
, and then construct the intuitionistic fuzzy similarity matrix
R
=
(
˜
r
ij
)
10
×
10
:
Table 2.3
The transformed car data set
G
1
G
2
G
3
G
4
G
5
G
6
[
μ
y
i
(
G
1
),
[
μ
y
i
(
G
2
),
[
μ
y
i
(
G
3
),
[
μ
y
i
(
G
4
),
[
μ
y
i
(
G
5
),
[
μ
y
i
(
G
6
),
1
−
v
y
i
(
G
1
)
]1
−
v
y
i
(
G
2
)
]1
−
v
y
i
(
G
3
)
]1
−
v
y
i
(
G
4
)
]1
−
v
y
i
(
G
5
)
]1
−
v
y
i
(
G
6
)
]
y
1
[0.30, 0.60]
[0.20, 0.30]
[0.40, 0.50]
[0.80, 0.90]
[0.40, 0.50]
[0.20, 0.30]
y
2
[0.40, 0.70]
[0.50, 0.90]
[0.60, 0.80]
[0.20, 0.30]
[0.30, 0.40]
[0.70, 0.80]
y
3
[0.40, 0.80]
[0.60, 0.90]
[0.80, 0.90]
[0.20, 0.40]
[0.30, 0.30]
[0.50, 0.80]
y
4
[0.30, 0.60]
[0.90, 1.00]
[0.80, 0.90]
[0.70, 0.90]
[0.10, 0.20]
[0.20, 0.20]
y
5
[0.80, 0.90]
[0.70, 0.80]
[0.70, 1.00]
[0.40, 0.90]
[0.80, 0.80]
[0.40, 0.40]
y
6
[0.40, 0.70]
[0.30, 0.50]
[0.20, 0.40]
[0.70, 0.90]
[0.50, 0.60]
[0.30, 0.40]
y
7
[0.60, 0.60]
[0.40, 0.80]
[0.70, 0.80]
[0.30, 0.40]
[0.30, 0.30]
[0.60, 0.90]
y
8
[0.90, 0.90]
[0.70, 0.80]
[0.70, 0.90]
[0.40, 0.50]
[0.40, 0.50]
[0.80, 1.00]
y
9
[0.40, 0.60]
[1.00, 1.00]
[0.90, 0.90]
[0.60, 0.80]
[0.20, 0.30]
[0.10, 0.20]
y
10
[0.90, 0.90]
[0.80, 1.00]
[0.60, 0.70]
[0.50, 0.80]
[0.80, 0.90]
[0.60, 0.60]
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