Information Technology Reference
In-Depth Information
⎛
⎝
⎞
⎠
(
0
.
5
,
0
.
1
,
0
.
4
)(
0
.
6
,
0
.
2
,
0
.
2
)(
0
.
8
,
0
.
1
,
0
.
1
)(
0
.
5
,
0
.
4
,
0
.
1
)
(
0
.
6
,
0
.
3
,
0
.
1
)(
0
.
6
,
0
.
2
,
0
.
2
)(
0
.
7
,
0
.
2
,
0
.
1
)
--
R
(
3
,
4
)
=
(
0
.
6
,
0
.
4
,
0
)(
0
.
7
,
0
.
1
,
0
.
2
)(
0
.
6
,
0
.
1
,
0
.
3
)
--
(
0
.
8
,
0
.
1
,
0
.
1
)(
0
.
7
,
0
.
1
,
0
.
2
)(
0
.
7
,
0
.
2
,
0
.
1
)(
0
.
7
,
0
.
1
,
0
.
2
)
where “--” means that there are no elements for the second and the third layers each
of which has only three attributes.
Below we shall use Zhang and Xu (2012)'s method to aggregate the given infor-
mation: We first analyze the importance of the considered attributes. Here we adopt
the method introduced by Xu (2006) to construct the reciprocal judgment matrix
J
l
corresponding to the attributes in the
l
th layer,
l
4, and then construct
the reciprocal judgment matrix
J
of the layers in this system. After that, we use Xu
(2006)'s model to get the weight vectors
w
l
=
1
,
2
,
3
,
of the attributes in the
l
th layer and the weight vector
w
of the layers as follows, respectively:
(
l
=
1
,
2
,
3
,
4
)
T
T
T
w
=
(
0
.
2
,
0
.
3
,
0
.
4
,
0
.
1
)
,
w
1
=
(
0
.
3
,
0
.
3
,
0
.
2
,
0
.
2
)
,
w
2
=
(
0
.
5
,
0
.
2
,
0
.
3
)
T
T
w
3
=
(
0
.
4
,
0
.
4
,
0
.
2
)
,
w
4
=
(
0
.
4
,
0
.
2
,
0
.
2
,
0
.
2
)
Thenwe aggregate the information on the attributes in each layer by calculating the
membership degree
μ
(
k
)
l
, the non-membership degree
v
(
k
)
l
(
y
j
)
(
y
j
)
and the hesitancy
π
(
k
)
l
degree
(
y
j
)
corresponding to the
l
th layer of the system
y
j
and the expert
e
k
:
4
μ
(
1
)
1
(
y
1
)
=
1
μ
r
(
1
,
1
)
w
1
,
j
=
0
.
6
×
0
.
3
+
0
.
7
×
0
.
3
+
0
.
7
×
0
.
2
+
0
.
7
×
0
.
2
=
0
.
67
1
,
j
j
=
4
v
(
1
)
1
(
y
1
)
=
v
r
(
1
,
1
)
1
w
1
,
j
=
0
.
3
×
0
.
3
+
0
.
2
×
0
.
3
+
0
.
1
×
0
.
2
+
0
.
1
×
0
.
2
=
0
.
19
,
j
j
=
1
π
(
1
)
1
(
y
1
)
=
1
−
μ
(
1
)
(
y
1
)
−
v
(
1
)
(
y
1
)
=
1
−
0
.
67
−
0
.
19
=
0
.
14
1
1
Similarly, we can get the membership degrees, the non-membership degrees and
the hesitancy degrees of the other layers, and all the aggregated results corresponding
to the expert
e
k
are contained in the intuitionistic fuzzy matrix
R
(
k
)
, listed as follows
(Zhang and Xu 2012):
⎛
⎝
⎞
⎠
(
0
.
67
,
0
.
19
,
0
.
14
)(
0
.
71
,
0
.
17
,
0
.
12
)(
0
.
78
,
0
.
14
,
0
.
08
)(
0
.
64
,
0
.
14
,
0
.
22
)
(
.
,
.
,
.
)(
.
,
.
,
.
)(
.
,
.
,
.
)(
.
,
.
,
.
)
0
62
0
19
0
19
0
65
0
17
0
18
0
70
0
20
0
10
0
58
0
18
0
24
R
(
1
)
=
(
.
,
.
,
.
)(
.
,
.
,
.
)(
.
,
.
,
.
)(
.
,
.
,
.
)
0
62
0
19
0
19
0
78
0
17
0
05
0
64
0
20
0
16
0
60
0
16
0
24
(
0
.
62
,
0
.
19
,
0
.
19
)(
0
.
62
,
0
.
17
,
0
.
21
)(
0
.
64
,
0
.
20
,
0
.
16
)(
0
.
74
,
0
.
16
,
0
.
10
)
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