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where
w
= (
w
1
,
w
2
, …,
w
n
)
T
is the weight vector of
a
j
(
j
= 1, 2, 3, …,
n
), and
w
j
∑
n
1
and λ > 0. To compute generalized intuitionistic fuzzy weighted
averaging (GIFWA), the first two terms of Equation 3.15, that is, for
n
= 2, are
computed, that is,
=
j
=
1
λ
λ
wa wa
11
⊕
22
(
)
(
)
λ
λ
λ
λ
λ
λ
a
=
μ
,
11
− −
(
ν
),
a
=
μ
,
11
− −
(
ν
)
1
a
a
2
a
a
1
1
2
2
Then
(
)
λ
λ
w
λ
w
wa
11
11
=−−
(
μ
) ,( (
11
−
−
ν
) )
1
1
a
a
1
1
(
)
(
)
w
(
)
w
2
2
λ
λ
λ
wa
22
11
=−−
μ
,
11
−−
(
ν
)
a
a
2
2
⎡
⎢
(
)
−−
w
(
)
w
⎤
⎡
⎢
(
)
w
(
)
w
⎤
⎥
1
1
2
2
λ
λ
λ
λ
λ
λ
wa wa
11 22
11 11
⊕= −−
μ
,
(
ν
)
⎥
⊕−−
11
μ
,
11
−−
(
ν
)
a
a
a
a
1
1
2
2
(
)
⋅ −−
(
)
⎡
(
)
+− −
w
(
)
−−−
w
(
a
)
w
(
)
w
⎤
1
2
1
2
λ
λ
λ
λ
11 11
−−
μ
μ
11
μ
11
μ
,
⎢
⎢
⎢
⎢
a
a
a
⎥
⎥
⎥
⎥
1
2
1
2
=
(
)
⋅ −−
w
(
)
w
1
2
λ
λ
11
−−
(
ν
)
11
(
ν
)
⎣
a
a
⎦
1
2
⎡
(
)
−−
w
(
)
−+ −
w
(
)
w
⎤
1
2
1
λ
λ
λ
21
−−
μ
1
μ
1
1
μ
a
a
a
⎢
⎢
⎢
⎢
⎢
⎢
⎥
⎥
⎥
⎥
⎥
⎥
1
2
1
(
)
−−
w
(
)
⋅ −
w
(
)
w
2
1
2
λ
λ
λ
=
+−
1
μ
1
μ
1
μ
,
a
a
a
2
1
2
(
)
−−
w
(
)
w
1
2
λ
⋅
λ
11
−−
(
ν
)
11
(
ν
)
a
a
1
2
⎣
⎦
(
)
⋅ −
w
(
)
−−
w
(
)
⋅ −−
w
(
)
w
1
2
1
2
λ
λ
λ
λ
=− −
11 1
μ
μ
,
1
(
1
ν
)
1
(
1
ν
)
a
a
a
a
1
2
1
2
2
2
(
)
(
)
w
w
λ
λ
=− −
1
1
μ
,
11
−−
(
ν
)
a
a
=
1
=
1
Then by the induction method,
⎛
⎞
n
n
∏
∏
(
)
w
j
⎜
⎜
w
⎟
⎟
wa wa wa
λ
⊕⊕⊕⊕ =− −
λ
λ
w
nn
λ
1
1
μ
λ
,
(
11
−−
(
ν
) )
λ
j
11
22 33
a
a
j
j
⎝
⎠
j
=
1
j
=
1
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