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(λ, δ) = (
,
)
(
,
)
(1) If
1
0
, then each pair of the column vectors of the
1
0
-cutting
(
=
,
,...,
)
matrix
R are orthogonal. Thus the suppliers y i
i
1
2
8
are clustered
(
1
,
0
)
into eight classes:
{ y 1 } , { y 2 } , { y 3 } , { y 4 } , { y 5 } , { y 6 } , { y 7 } , { y 8 }
.
(2) If
(λ, δ) = (
0
.
73
,
0
.
24
)
, then we get the
(
0
.
73
,
0
.
24
)
-cutting matrix:
⎛
⎝
⎞
⎠
(
1
,
0
)(
0
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
(
0
,
0
)(
1
,
0
)(
0
,
0
)(
0
,
0
)(
0
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
(
0
,
1
)(
0
,
0
)(
1
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
(
0
,
1
)(
0
,
0
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
0
,
1
)
R
=
( 0 . 73 , 0 . 24 )
(
0
,
0
)(
0
,
0
)(
0
,
1
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
(
0
,
1
)(
0
,
1
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
1
,
0
)
(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
1
,
0
)(
0
,
1
)
(
,
)(
,
)(
,
)(
,
)(
,
)(
.
)(
,
)(
,
)
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
Calculating the inner products of all pairs of the column vectors of ( 0 . 73 , 0 . 24 ) R ,
we know that
r 1 , ( 0 . 73 , 0 . 24 )
r 2 , ( 0 . 73 , 0 . 24 )
r 3 , ( 0 . 73 , 0 . 24 )
r 5 and
r 7
(
0
.
73
,
0
.
24
)
(
0
.
73
,
0
.
24
)
; ( 0 . 73 , 0 . 24 ) r 4 , ( 0 . 73 , 0 . 24 ) r 6 and
are orthogonal to each other column of
R
(
0
.
65
,
0
.
32
)
r 8 are non-orthogonal. Then the suppliers y i
(
i
=
1
,
2
,...,
8
)
are clus-
(
0
.
73
,
0
.
24
)
tered into six classes:
{
y 1 } , {
y 2 } , {
y 3 } , {
y 5 } , {
y 7 } , {
y 4 ,
y 6 ,
y 8 }
.
(3) If
(λ, δ) = (
0
.
68
,
0
.
24
)
, then we get the
(
0
.
68
,
0
.
24
)
-cutting matrix:
⎛
⎞
(
1
,
0
)(
0
,
0
)(
0
,
1
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
⎝
⎠
(
0
,
0
)(
1
,
0
)(
0
,
0
)(
0
,
0
)(
0
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
(
0
,
1
)(
0
,
0
)(
1
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
(
0
,
1
)(
0
,
0
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
0
,
1
)
R
=
(
0
.
68
,
0
.
24
)
(
1
,
0
)(
0
,
0
)(
0
,
1
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
0
,
1
)(
0
,
1
)
(
0
,
1
)(
0
,
0
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
1
.
0
)
(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
1
,
0
)(
0
,
1
)
(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
0
,
1
)(
1
,
0
)(
0
,
1
)(
1
,
0
)
R ,
we can see that ( 0 . 68 , 0 . 24 ) r 1 is non-orthogonal to both ( 0 . 68 , 0 . 24 ) r 3 and ( 0 . 68 , 0 . 24 ) r 5 ;
Calculating the inner products of all pairs of the column vectors of
(
0
.
68
,
0
.
24
)
r 4 is non-orthogonal to both
r 6 and
r 8 ; ( 0 . 68 , 0 . 24 )
r 3 ,
(
0
.
68
,
0
.
24
)
(
0
.
68
,
0
.
24
)
(
0
.
68
,
0
.
24
)
r 2 and
r 7 are orthogonal to each other column of
R . Then
(
0
.
68
,
0
.
24
)
(
0
.
68
,
0
.
24
)
(
0
.
68
,
0
.
24
)
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 }
For the case where
(λ, δ) = (
0
.
65
,
0
.
32
)
, we can also get the above clustering
result.
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