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With the netting method, we have the following clustering results (Wang et al.
2011):
Using Zhang et al. (2007)'s method, we first construct the intuitionistic fuzzy
similarity matrix based on the data in Table 2.18 .
(
1
,
0
)
(
0
.
41
,
0
.
08
)(
0
.
33
,
0
.
24
)(
0
.
43
,
0
.
08
)(
0
.
63
,
0
.
08
)
(
0
.
41
,
0
.
08
)
(
1
,
0
)
(
0
.
41
,
0
.
08
)(
0
.
49
,
0
.
16
)(
0
.
36
,
0
.
14
)
(
0
.
33
,
0
.
24
)(
0
.
41
,
0
.
08
)
(
1
,
0
)
(
0
.
46
,
0
.
08
)(
0
.
35
,
0
.
08
)
(
0
.
43
,
0
.
08
)(
0
.
49
,
0
.
16
)(
0
.
46
,
0
.
08
)
(
1
,
0
)
(
0
.
49
,
0
.
00
)
( 0 . 63 , 0 . 08 )( 0 . 36 , 0 . 14 )( 0 . 35 , 0 . 08 )( 0 . 49 , 0 . 00 )
( 1 , 0 )
Z =
(
)
( 0 . 55 , 0 . 0 )( 0 . 41 , 0 . 14 )( 0 . 43 , 0 . 36 )( 0 . 43 , 0 . 08 )( 0 . 30 , 0 . 08 )
(
0
.
38
,
0
.
14
)(
0
.
57
,
0
.
08
)(
0
.
22
,
0
.
16
)(
0
.
33
,
0
.
22
)(
0
.
27
,
0
.
22
)
( 0 . 35 , 0 . 0 )( 0 . 49 , 0 . 16 )( 0 . 33 , 0 . 08 )( 0 . 67 , 0 . 00 )( 0 . 36 , 0 . 08 )
(
0
.
46
,
0
.
08
)(
0
.
43
,
0
.
14
)(
0
.
25
,
0
.
29
)(
0
.
33
,
0
.
08
)(
0
.
27
,
0
.
08
)
( 0 . 38 , 0 . 14 )( 0 . 55 , 0 . 00 )( 0 . 46 , 0 . 08 )( 0 . 35 , 0 . 00 )( 0 . 43 , 0 . 24 )
(
0
.
43
,
0
.
24
)(
0
.
57
,
0
.
22
)(
0
.
49
,
0
.
08
)(
0
.
63
,
0
.
14
)(
0
.
46
,
0
.
16
0
.
57
,
0
.
08
)(
0
.
41
,
0
.
14
)(
0
.
43
,
0
.
14
)(
0
.
49
,
0
.
16
)(
0
.
57
,
0
.
22
)
(
0
.
22
,
0
.
16
)(
0
.
43
,
0
.
36
)(
0
.
25
,
0
.
29
)(
0
.
33
,
0
.
08
)(
0
.
49
,
0
.
08
)
(
0
.
33
,
0
.
22
)(
0
.
43
,
0
.
08
)(
0
.
33
,
0
.
08
)(
0
.
67
,
0
.
00
)(
0
.
63
,
0
.
14
)
(
0
.
27
,
0
.
22
)(
0
.
30
,
0
.
08
)(
0
.
27
,
0
.
08
)(
0
.
36
,
0
.
08
)(
0
.
46
,
0
.
16
)
( 1 , 0 )
( 0 . 38 , 0 . 22 )( 0 . 55 , 0 . 00 )( 0 . 33 , 0 . 08 )( 0 . 22 , 0 . 22 )
(
0
.
38
,
0
.
22
)
(
1
,
0
)
(
0
.
38
,
0
.
08
)(
0
.
34
,
0
.
21
)(
0
.
36
,
0
.
22
)
( 0 . 55 , 0 . 00 )( 0 . 38 , 0 . 08 )
( 1 , 0 )
( 0 . 33 , 0 . 16 )( 0 . 22 , 0 . 36 )
(
0
.
33
,
0
.
08
)(
0
.
35
,
0
.
22
)(
0
.
33
,
0
.
16
)
(
1
,
0
)
(
0
.
43
,
0
.
08
)
( 0 . 22 , 0 . 22 )( 0 . 36 , 0 . 22 )( 0 . 22 , 0 . 36 )( 0 . 43 , 0 . 08 )
( 1 , 0 )
In order to get the clustering result with Zhang et al. (2007)'s method, we should
get the equivalent matrix. By the composition operations of similarity matrices, we
have
(
,
)
(
.
,
.
)(
.
,
.
)(
.
,
.
)(
.
,
.
)
1
0
0
43
0
08
0
43
0
08
0
49
0
00
0
63
0
08
(
0
.
43
,
0
.
08
)
(
1
,
0
)
(
0
.
49
,
0
.
08
)(
0
.
57
,
0
.
08
)(
0
.
49
,
0
.
08
)
(
0
.
43
,
0
.
08
)(
0
.
49
,
0
.
08
)
(
1
,
0
)
(
0
.
49
,
0
.
08
)(
0
.
46
,
0
.
08
)
(
0
.
49
,
0
.
00
)(
0
.
57
,
0
.
08
)(
0
.
49
,
0
.
08
)
(
1
,
0
)
(
0
.
49
,
0
.
00
)
(
)
( 0 . 46 , 0 . 08 )( 0 . 57 , 0 . 08 )( 0 . 41 , 0 . 08 )( 0 . 49 , 0 . 08 )( 0 . 38 , 0 . 08 )
(
0
.
63
,
0
.
08
)(
0
.
49
,
0
.
08
)(
0
.
46
,
0
.
08
)(
0
.
49
,
0
.
00
)
(
1
,
0
Z 2
=
Z
Z
=
)
( 0 . 46 , 0 . 08 )( 0 . 55 , 0 . 08 )( 0 . 41 , 0 . 08 )( 0 . 43 , 0 . 08 )( 0 . 46 , 0 . 08 )
(
0
.
55
,
0
.
0
)(
0
.
43
,
0
.
08
)(
0
.
43
,
0
.
08
)(
0
.
43
,
0
.
08
)(
0
.
55
,
0
.
08
)
( 0 . 46 , 0 . 08 )( 0 . 57 , 0 . 08 )( 0 . 49 , 0 . 08 )( 0 . 63 , 0 . 08 )( 0 . 49 , 0 . 08 )
0
.
43
,
0
.
0
)(
0
.
49
,
0
.
08
)(
0
.
46
,
0
.
08
)(
0
.
67
,
0
.
00
)(
0
.
49
,
0
.
00
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