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1.2.4 Approaches to Multi-Attribute Group Decision Making
with Intuitionistic Fuzzy Information
Xu (2011) utilized the intuitionistic fuzzy power aggregation operators to multi-
attribute group decision making with intuitionistic fuzzy information:
For a multi-attribute group decision making problem with intuitionistic fuzzy
information, let
Y
={
y
1
,
y
2
,...,
y
n
}
be a set of
n
alternatives,
G
={
G
1
,
G
2
,...,
G
m
}
T
, with
a set of
m
attributes, whose weight vector is
w
=
(
w
1
,
w
2
,...,
w
m
)
m
, and
i
=
1
w
i
w
i
≥
0
,
i
=
1
,
2
,...,
=
1, and let
E
={
e
1
,
e
2
,...,
e
s
}
be a set of
s
T
, with
experts, whose weight vector is
η
=
(η
1
,η
2
,...,η
s
)
η
k
≥
0
,
k
=
1
,
2
,...,
s
,
and
k
=
1
η
k
=
b
(
k
)
ij
1. Let
B
(
k
)
=
(
)
m
×
n
be an intuitionistic fuzzy decision matrix,
where
b
(
k
)
ij
t
(
k
)
ij
f
(
k
)
ij
,π
(
k
)
ij
=
(
,
)
is an attribute value provided by the expert
e
k
, denoted
by an IFV, where
t
(
k
)
ij
indicates the degree that the alternative
y
j
satisfies the attribute
G
i
, while
f
(
k
)
indicates the degree that the alternative
y
j
does not satisfy the attribute
ij
π
(
k
)
ij
G
i
, and
indicates the uncertainty degree of the alternative
y
j
to the attribute
G
i
,
such that
t
(
k
)
ij
f
(
k
)
ij
t
(
k
)
ij
f
(
k
)
ij
,π
(
k
)
ij
t
(
k
)
ij
f
(
k
)
ij
∈[
0
,
1
]
,
∈[
0
,
1
]
,
+
≤
1
=
1
−
−
,
i
=
1
,
2
,...,
m
;
j
=
1
,
2
,...,
n
(1.49)
are of the same type, then the attribute
values do not need normalization. Whereas, there are generally benefit attributes
(i.e., the bigger the attribute values the better) and cost attributes (i.e., the smaller
the attribute values the better) in multi-attribute decision making. In such cases, we
may transform the attribute values of cost type into the attribute values of benefit
type, then
B
(
k
)
=
(
If all the attributes
G
i
(
i
=
1
,
2
,...,
m
)
b
(
k
)
ij
)
m
×
n
can be transformed into the intuitionistic fuzzy decision
r
(
k
)
ij
matrix
R
(
k
)
=
(
)
m
×
n
, where
⎨
b
(
k
)
ij
,
for benefit attribute G
i
r
(
k
)
ij
=
(μ
(
k
)
ij
v
(
k
)
ij
,π
(
k
)
ij
b
(
k
)
ij
c
,
)
=
,
j
=
1
,
2
,...,
n
⎩
,
for cost attribute G
i
(1.50)
where
b
(
k
)
ij
c
, such that
b
(
k
)
ij
c
is the complement of
b
(
k
)
ij
f
(
k
)
ij
t
(
k
)
ij
,π
(
k
)
ij
=
(
,
)
,
π
(
k
)
ij
t
(
k
)
ij
f
(
k
)
ij
−
μ
(
k
)
ij
v
(
k
)
ij
clearly,
=
1
−
−
=
1
−
.
Then, we can utilize the IFPWA (or IFPWG) operator to develop an approach to
multi-attribute group decision making with intuitionistic fuzzy information, which
involves the following steps (Xu 2011):
Approach 1.1
Step 1
Calculate the supports:
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