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(
r
i
)
of
r
i
by using Xu and Yager (2006)'s ranking
method, and obtain the priority of the alternatives according to the ranking of
r
i
(
Step 3
Calculate the scores
S
, the bigger the value
r
i
, the better the alternative
y
i
.
Now we utilize Example 1.7 to illustrate the proposed method. To obtain the most
preferred supplier(s), the following steps are given:
i
=
1
,
2
,...,
m
)
Step 1
Aggregate the intuitionistic fuzzy values
r
i
of the supplier
y
i
by the
GHIFWA operator (without loss of generality, let
γ
=
2 and
λ
=
2
)
:
r
1
=
(
0
.
4439
,
0
.
2936
),
r
2
=
(
0
.
4231
,
0
.
2475
),
r
3
=
(
0
.
5348
,
0
.
3099
)
r
4
=
(
0
.
4904
,
0
.
3971
),
r
5
=
(
0
.
4226
,
0
.
2733
),
r
6
=
(
0
.
4351
,
0
.
1708
)
Step 2
Calculate the scores
S
(
r
i
)
of
r
i
by using Xu and Yager (2006)'s ranking
method:
S
(
r
1
)
=
0
.
1502
,
S
(
r
2
)
=
0
.
1756
,
S
(
r
3
)
=
0
.
2248
S
(
r
4
)
=
0
.
0933
,
S
(
r
5
)
=
0
.
1493
,
S
(
r
6
)
=
0
.
2643
Since
S
(
r
6
)>
S
(
r
3
)>
S
(
r
2
)>
S
(
r
1
)>
S
(
r
5
)>
S
(
r
4
)
we can obtain the priority of the suppliers
y
i
(
i
=
1
,
2
,...,
6
)
:
y
6
y
3
y
2
y
1
y
5
y
4
are assigned different values, the scores of the suppliers
obtained are different, and the rankings of the suppliers are also different, some cases
can be found in Tables
1.14
and
1.15
(Xia and Xu 2011), when the GHIFWA and
GHIFWG operators are used, respectively.
To investigate the variation trends of the scores and the rankings of the suppliers
with the change of the values of the parameters
As the parameters
λ
and
γ
, we use figures to illustrate
these issues. Figures
1.18
,
1.19
,
1.20
,
1.21
,
1.22
and
1.23
(Xia and Xu 2011) give
the scores of suppliers obtained by the GHIFWA operator as
λ
and
γ
λ
and
γ
are assigned
values between 0 and 10.
It is noted that the scores increase as
.
Figures
1.24
,
1.25
,
1.26
,
1.27
,
1.28
,
1.29
,
1.30
,
1.31
,
1.32
,
1.33
,
1.34
and
1.35
(Xia
and Xu 2011) give the scores of suppliers obtained by the GHIFWG operator as
λ
increases, but not suitable for
γ
λ
and
γ
are assigned values between 0 and 10. It is noted that the scores decrease as
λ
. Therefore, the proposed aggregation operators
with parameters can provide the decision makers (or experts) more choices and thus
are more flexible than the existing ones, because we can choose different values
according to the practical problems, which is worthy to be further studied in the
future.
increases, but not suitable for
γ
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