Information Technology Reference
In-Depth Information
Step 1
Construct the intuitionistic fuzzy distance matrix and the fuzzy graph
where each node is associated to a sample to be clustered which is expressed by IFS:
(1) Calculate the distances
d
ij
=
d
y
i
,
y
j
(
i
,
j
=
1
,
2
,...,
6
)
by Eq. (
2.111
):
d
(
y
1
,
y
3
)
=
d
(
y
3
,
y
1
)
=
0
.
1225
,
d
(
y
1
,
y
4
)
=
d
(
y
4
,
y
1
)
=
0
.
117
d
(
y
1
,
y
5
)
=
d
(
y
5
,
y
1
)
=
0
.
1725
,
d
(
y
1
,
y
6
)
=
d
(
y
6
,
y
1
)
=
0
.
1115
d
(
y
2
,
y
3
)
=
d
(
y
3
,
y
2
)
=
0
.
1225
,
d
(
y
2
,
y
4
)
=
d
(
y
4
,
y
2
)
=
0
.
128
d
(
y
2
,
y
5
)
=
d
7
(
y
5
,
y
2
)
=
0
.
1
,
d
(
y
2
,
y
6
)
=
d
7
(
y
6
,
y
2
)
=
0
.
194
d
(
y
3
,
y
4
)
=
d
(
y
4
,
y
3
)
=
0
.
1045
,
d
(
y
3
,
y
5
)
=
d
(
y
5
,
y
3
)
=
0
.
1
d
(
y
3
,
y
6
)
=
d
(
y
6
,
y
3
)
=
0
.
0715
,
d
(
y
4
,
y
5
)
=
d
(
y
5
,
y
4
)
=
0
.
1095
d
(
y
4
,
y
6
)
=
d
(
y
6
,
y
4
)
=
0
.
088
,
d
(
y
5
,
y
6
)
=
d
(
y
6
,
y
5
)
=
0
.
1715
then we get the intuitionistic fuzzy distance matrix as follows:
⎛
⎝
⎞
⎠
00
.
245 0
.
1225 0
.
117 0
.
1725 0
.
1115
.
.
.
.
.
0
245
0
0
1225 0
128
0
10
194
.
.
.
.
.
0
1225 0
1225
0
0
1045
0
10
0715
=
D
0
.
117 0
.
128 0
.
1045
0
0
.
1095 0
.
088
0
.
1725
0
.
10
.
10
.
1095
0
0
.
1715
0
.
1115 0
.
194 0
.
0715 0
.
088 0
.
1715
0
=
V
D
with 6 nodes associated to the samples
(2) Draw the fuzzy graph
G
,
y
i
(
to be clustered and every edge between
y
i
and
y
j
having theweight
d
ij
, which is an element of the intuitionistic fuzzy distance matrix
D
i
=
1
,
2
,...,
6
)
d
ij
)
6
×
6
and
denotes the dissimilarity degree between the samples
y
i
and
y
j
(see Fig.
2.7
) (Zhao
et al. 2012a).
=
(
=
V
D
by Kruskal method
,
Step 2
Compute the MST of the fuzzy graph
G
(Kruskal 1956):
(1) Arrange the edges of
G
in order from the smallest weight to the largest one:
d
36
<
d
46
<
d
35
=
d
25
<
d
34
<
d
45
<
d
16
<
d
14
<
d
13
=
d
23
<
d
24
<
d
56
<
d
15
<
d
26
<
d
52
(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
46
between
y
4
and
y
6
.
(4) Select the edge with the smallest weight from the rest e
dg
es which do not form
a circuit with those already chosen, we can choose the edge
E
35
between
y
3
and
y
5
.
(5) Repeat the proces
s
(4) until five edges have been selected. Thus we get the
MST of the fuzzy graph
G
=
V
D
(see Fig.
2.8
) (Zhao et al. 2012a).
,
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