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from the elements of
R
∗
,
λ
and then take the different values of the confidence level
by which we classify the suppliers
y
i
(
=
,
,...,
)
i
1
2
8
. Concretely, we have
(1)If0
.
73
<λ
≤
1, then the suppliers
y
i
(
i
=
1
,
2
,...,
8
)
are clustered into
eight classes:
{
y
1
}
,
{
y
2
}
,
{
y
3
}
,
{
y
4
}
,
{
y
5
}
,
{
y
6
}
,
{
y
7
}
,
{
y
8
}
(2) If 0
.
68
<λ
≤
0
.
73, then the suppliers
y
i
(
i
=
1
,
2
,...,
8
)
are clustered into
six classes:
{
y
1
}
,
{
y
2
}
,
{
y
3
}
,
{
y
5
}
,
{
y
7
}
,
{
y
4
,
y
6
,
y
8
}
(3)If0
.
62
<λ
≤
0
.
68, then the suppliers
y
i
(
i
=
1
,
2
,...,
8
)
are clustered into
four classes:
{
y
1
,
y
5
}
,
{
y
2
}
,
{
y
3
}
,
{
y
7
}
,
{
y
4
,
y
6
,
y
8
}
(4)If0
.
55
<λ
≤
0
.
62, then the suppliers
y
i
(
i
=
1
,
2
,...,
8
)
are clustered into
two classes:
{
y
1
,
y
2
,
y
3
,
y
4
,
y
5
,
y
6
,
y
8
}
,
{
y
7
}
(5) If 0
≤
λ
≤
0
.
55, then the suppliers
y
i
(
i
=
1
,
2
,...,
8
)
are of the same class:
{
y
8
}
y
1
,
y
2
,
y
3
,
y
4
,
y
5
,
y
6
,
y
7
,
From the above numerical analysis, we can see that the intuitionistic fuzzy orthog-
onal clustering algorithm and the transitive closure clustering algorithm derive the
same clustering results under the different confidence levels. Since the intuitionistic
fuzzy similarity matrix generally does not has the transitivity property, and thus, the
transitive closure clustering algorithm needs to derive the intuitionistic fuzzy equiva-
lence matrix after the finite times of compositions of the intuitionistic fuzzy similarity
matrix, and then get the
, by which the
considered objects are clustered. However, the composition process of the transitive
closure clustering algorithm is somewhat cumbersome, and is not easy to calculate;
while the intuitionistic fuzzy orthogonal clustering algorithm only needs to derive
the
λ
-cutting matrix under the confidence level
λ
-cutting matrix of the intuitionistic fuzzy similarity matrix according to the
confidence level
(λ, δ)
, and then directly clusters the considered objects by judging
the orthogonality of the column vectors of the cutting matrix. The intuitionistic fuzzy
orthogonal clustering algorithm does not need to take time to derive the intuitionistic
fuzzy equivalence matrix, and is very easy to be implemented on a computer, and
thus, it is more straightforward and convenient than the transitive closure clustering
algorithm in practical applications.
(λ, δ)
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