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1.6.3 An Approach to Intuitionistic Fuzzy Multi-Attribute
Decision Making
For a multi-attribute decision making under intuitionistic fuzzy environment, let
Y
and
G
be defined as in Sect.
1.2.4
. To evaluate the performance of the alternative
y
i
under the attribute
G
j
, the expert is required to provide not only the information that
the alternative
y
i
satisfies the attribute
G
j
, but also the information that the alternative
y
i
doesn't satisfy the attribute
G
j
. These two part information can be expressed by
μ
ij
and
v
ij
which denote the degrees that the alternative
y
i
satisfies the attribute
G
j
and doesn't satisfy the attribute
G
j
, then the performance of the alternative
y
i
under
the attribute
G
j
can be expressed by an IFV
α
ij
=
(μ
ij
,
v
ij
)
with the condition that
0
1. When all the performances of the alternatives are
provided, the intuitionistic fuzzy decision matrix
B
≤
μ
ij
,
v
ij
≤
1 and
μ
ij
+
v
ij
≤
v
ij
)
m
×
n
can be constructed. To obtain the ranking of the alternatives, the following steps can
be given (Xia et al. 2012c):
=
(μ
ij
,
=
(
b
ij
)
m
×
n
Step 1
Transform the intuitionistic fuzzy decision matrix
B
=
(
b
ij
)
n
×
n
into the
normalized intuitionistic fuzzy decision matrix
R
=
(
r
ij
)
n
×
n
, where
b
ij
,
for benefit attribute G
i
r
ij
=
,
i
=
1
,
2
,...,
m
,
j
=
1
,
2
,...,
n
(1.239)
b
ij
,
for cost attribute G
i
Step 2
Aggregate the intuitionistic fuzzy values
r
i
(
i
=
1
,
2
,...,
m
)
of the
alternatives
y
i
(
i
=
1
,
2
,...,
m
)
by the HIFWA operator:
n
⊕
r
i
=
ATS
−
IFWA
(
r
i
1
,
r
i
2
,...,
r
in
)
=
w
j
r
ij
,
i
=
1
,
2
,...,
m
(1.240)
j
=
1
or the HIFWG operator:
n
⊗
r
w
j
ij
r
i
=
ATS
−
IFWG
(
r
i
1
,
r
i
2
,...,
r
in
)
=
,
i
=
1
,
2
,...,
m
(1.241)
j
=
1
of
b
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
(
b
i
)
, the bigger the
r
i
, the better the alternative
y
i
.
To illustrate the proposed method, we give an example adapted from Chen (2011)
as follows:
i
=
1
,
2
,...,
m
)
Example 1.7
The purchasing manager in a small enterprise considers various cri-
teria (or attributes) involving: (1)
G
1
: financial factors (e.g., economic performance,
financial stability); (2)
G
2
: performance (e.g., delivery, quality, price); (3)
G
3
: tech-
nology (e.g., manufacturing capability, design capability, ability to cope with tech-
nology changes); and (4)
G
4
: organizational culture and strategy (e.g., feeling of
trust, internal and external integration of suppliers, compatibility across levels and
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