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Table 2.6 The characteristics of the suppliers
G 1
G 2
G 3
G 4
G 5
G 6
y 1
(0.61,0.32)
(0.24,0.53)
(0.14,0.76)
(0.77,0.18)
(0.36,0.62)
(0.54,0.42)
y 2
(0.18,0.65)
(0.81,0.17)
(0.12,0.84)
(0.62,0.24)
(0.21,0.68)
(0.43,0.37)
y 3
(0.62,0.11)
(0.26,0.62)
(0.33,0.25)
(0.91,0.08)
(0.22,0.75)
(0.12,0.86)
y 4
(0.45,0.35)
(0.62,0.24)
(0.74,0.15)
(0.41,0.52)
(0.18,0.81)
(0.32,0.65)
y 5
(0.13,0.76)
(0.26,0.75)
(0.24,0.68)
(0.81,0.12)
(0.74,0.13)
(0.55,0.36)
y 6
(0.32,0.45)
(0.45,0.25)
(0.73,0.24)
(0.62,0.36)
(0.12,0.82)
(0.22,0.75)
y 7
(0.55,0.35)
(0.24,0.75)
(0.03,0.84)
(0.39,0.61)
(0.49,0.28)
(0.85,0.14)
y 8
(0.65,0.25)
(0.38,0.45)
(0.92,0.06)
(0.24,0.57)
(0.82,0.17)
(0.04,0.92)
divide the suppliers into several groups in the supply markets, which is based on a
variety of different factors. It aims at implementing the different supplier strategies
according to the different types of suppliers.
,
The six factors which are considered here in assessing the suppliers are: (1) G 1 :
Prices; (2) G 2 : Product quality; (3) G 3 : The degree of market impacting; (4) G 4 :
After-sales service; (5) G 5 : Current assets efficiency; and (6) G 6 : Deliveries. Assume
that the characteristics of the suppliers y i (
A purchasing company wants to classify its eight suppliers y i (
i
=
1
,
2
,...,
8
)
i
=
1
,
2
,...,
8
)
with respect to the factors
G j
(
j
=
1
,
2
,...,
6
)
are represented by the IFSs, shown as in Table 2.6 (Xu et al.
2011).
In what follows, we utilize the intuitionistic fuzzy orthogonal clustering algorithm
to classify the eight suppliers, which involves the following steps (Xu et al. 2011):
Step 1 By Eqs. ( 2.125 ) and ( 2.131 ), we first calculate y 1 ·
y 2 = (
.
,
.
), (
y 1 ◦
0
62
0
24
c
y 2 )
= (
.
,
.
),
(
y 1 ,
y 2 ) = (
.
,
.
)
, and then calculate the others in a
similar way. Consequently, we get the intuitionistic fuzzy similarity matrix:
0
75
0
14
R
0
62
0
24
⎛
⎝
⎞
⎠
(
1
,
0
)
(
0
.
62
,
0
.
24
)(
0
.
62
,
0
.
26
)(
0
.
45
,
0
.
36
)(
0
.
68
,
0
.
24
)(
0
.
62
,
0
.
36
)(
0
.
55
,
0
.
35
)(
0
.
45
,
0
.
38
)
(
0
.
62
,
0
.
24
)
(
1
,
0
)
(
0
.
62
,
0
.
24
)(
0
.
62
,
0
.
24
)(
0
.
62
,
0
.
24
)(
0
.
62
,
0
.
25
)(
0
.
43
,
0
.
37
)(
0
.
37
,
0
.
45
)
(
0
.
62
,
0
.
26
)(
0
.
62
,
0
.
24
)
(
1
,
0
)
(
0
.
45
,
0
.
25
)(
0
.
62
,
0
.
26
)(
0
.
62
,
0
.
25
)(
0
.
55
,
0
.
35
)(
0
.
62
,
0
.
25
)
(
0
.
45
,
0
.
36
)(
0
.
62
,
0
.
24
)(
0
.
45
,
0
.
25
)
(
1
,
0
)
(
0
.
36
,
0
.
52
)(
0
.
73
,
0
.
24
)(
0
.
45
,
0
.
41
)(
0
.
65
,
0
.
32
)
R
=
( 0 . 68 , 0 . 24 )( 0 . 62 , 0 . 24 )( 0 . 62 , 0 . 26 )( 0 . 36 , 0 . 52 )
( 1 , 0 )
( 0 . 45 , 0 . 36 )( 0 . 55 , 0 . 28 )( 0 . 45 , 0 . 38 )
(
0
.
62
,
0
.
36
)(
0
.
62
,
0
.
25
)(
0
.
62
,
0
.
25
)(
0
.
73
,
0
.
24
)(
0
.
45
,
0
.
36
)
(
1
,
0
)
(
0
.
39
,
0
.
45
)(
0
.
73
,
0
.
24
)
( 0 . 55 , 0 . 35 )( 0 . 43 , 0 . 37 )( 0 . 55 , 0 . 35 )( 0 . 45 , 0 . 41 )( 0 . 55 , 0 . 28 )( 0 . 39 , 0 . 45 )
( 1 , 0 )
( 0 . 55 , 0 . 38 )
(
0
.
45
,
0
.
38
)(
0
.
37
,
0
.
45
)(
0
.
62
,
0
.
25
)(
0
.
65
,
0
.
32
)(
0
.
45
,
0
.
38
)(
0
.
73
,
0
.
24
)(
0
.
55
,
0
.
38
)
(
1
,
0
)
(λ, δ)
Step 2 Take the different values of the confidence level
from the elements
of R , and determine the
= ( (λ,δ) r ij ) 8 × 8 of R by using
Eq. ( 2.130 ) under the different values of the confidence level
(λ, δ)
-cutting matrix
R
(λ,δ)
(λ, δ)
.
Then we classify the suppliers y i (
i
=
1
,
2
,...,
8
)
by the orthogonal principles.
Concretely, we have
 
 
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