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Fig. 2.5
The intuitionistic
fuzzy graph
Fig. 2.6
The MST of the
intuitionistic fuzzy graph
and then we sort all the intuitionistic fuzzy weights as follows:
(2) Select the edge with the smallest weight, that is the edge
E
36
between
y
3
and
y
6
.
(3) Select the edge with the smallest weight from the rest edges, that is the edge
E
35
between
y
3
and
y
5
.
(4) Select the edge with the smallest from the rest e
d
ges which do not forma circuit
with those already chosen (we can choose the edge
E
46
between
y
4
and
y
6
)
. Repeat
(4) until five edges have been selected. Thus we get the MST of the intuitionistic
fuzzy graph
V
D
(see Fig.
2.6
) (Zhao et al. 2012a).
,
Step 3
Group the nodes (sample points) into clusters: by choosing a threshold
λ
and cutting down all the edges of the MST with the weights greater than
λ
, we can
get a certain number of sub-trees (clusters).
(1) If
λ
=
d
16
=
(
0
.
057
,
0
.
892
)
, then we get
{
y
1
,
y
2
,
y
3
,
y
4
,
y
5
,
y
6
}
.
(2) If
λ
=
d
25
=
(
0
.
071
,
0
.
918
)
, then we get
{
y
1
}
,
{
y
2
,
y
3
,
y
4
,
y
5
,
y
6
}
.
{
y
1
}
,
{
y
2
}
,
{
y
6
}
(3) If
λ
=
d
46
=
(
0
.
057
,
0
.
914
)
, then we get
y
3
,
y
4
,
y
5
,
.
{
y
1
}
,
{
y
2
}
,
{
y
4
}
,
{
y
6
}
(4) If
λ
=
d
35
=
(
0
.
071
,
0
.
929
)
, then we get
y
3
,
y
5
,
.
{
y
1
}
,
{
y
2
}
,
{
y
4
}
,
{
y
5
}
,
{
y
6
}
(5) If
λ
=
d
36
=
(
0
,
0
.
894
)
, then we get
y
3
,
.
λ
=
(
,
)
{
y
1
}
,
{
y
2
}
,
{
y
3
}
,
{
y
4
}
,
{
y
5
}
,
{
y
6
}
(6) If
.
Furthermore, we use Algorithm 2.10 to cluster these battle projects
y
j
(
0
1
, then we get
=
j
1
,
2
,...,
6
)
as follows:
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