Image Processing Reference
In-Depth Information
ν
=
06
.,
ν
=
03
.,
ν
=
02
.,
ν
=
05
.
a
a
a
a
1
2
3
4
Then
⎛
1
/
λ
1
/
λ
⎞
⎛
⎞
⎛
⎞
4
4
⎜
∏
(
)
w
∏
(
)
w
⎟
j
j
⎜
μ
λ
⎟
⎜
λ
⎟
GIFWA
w
(,,
aaa
,
…
=− −
, )
a
1
1
,
11 1
−− −
(
1
−
ν
)
123
n
a
a
j
j
⎝
⎠
⎝
⎠
j
=
1
j
=
1
⎝
⎠
⎡
⎤
1101 10
−− ×−
(
.
202
)
.
(
.
4
203
)
.
×− ×−
( .) (
1 06 102
2 01
.
. )) ,
20412
. /
⎢
⎢
⎢
⎥
⎥
⎥
⎥
(
202
.
203
.
=
1 11106
− −−− ×−−
(( .))
(
1
(
103
. ))
× −−
)
2 04
12
/
201
.
.
⎢
×−−
(( .))
1102 1105
(
(
. ))
⎣
⎦
= (. ,.
000
333
3959)
3.5.2 Generalized Intuitionistic Fuzzy Ordered
Weighted Averaging Operator
Similar to the generalized intuitionistic fuzzy ordered weighted averaging
(GIFOWA) operator and following a similar type of procedure as the fuzzy
ordered weighting operator, let
a
j
μν
with (
j
= 1, 2, 3, …,
n
) be a collec-
tion of intuitionistic fuzzy values; then
=
(,
)
a
a
j
j
(
)
1
/
λ
λ
λ
λ
λ
GIFOWA
w
(,,
aaa
,
, )
a
=
wa wa wa
⊕
⊕
⊕ ⊕
wa
…
123
n
1
σ
()
1
2
σ
()
2
3
σ
()
3
nn
σ
(
)
⎛
1
/
λ
⎛
⎞
n
⎜
⎜
∏
(
)
w
⎜
⎜
j
⎟
⎟
λ
=− −
1
1
μ
,
a
σ
()
j
⎝
⎠
j
=
1
⎝
1
/
λ
⎞
⎛
⎞
n
∏
1
(
)
w
⎟
⎟
j
⎜
⎜
⎟
⎟
λ
(3.16)
11 11
−− −−
(
ν
)
a
j
σ
(()
⎝
⎠
j
=
⎠
where
w
= (
w
1
,
w
2
, …,
w
n
)
T
is an associated weight vector, and
∑
1
and λ > 0
σ
= (1, 2, 3, …,
n
), and
a
σ(
i
)
is the
j
th largest value in the set (
a
1
,
a
2
, …,
a
n
) such
that
a
σ(
i
)
≥
a
σ(
i
−1)
.
n
w
j
=
j
=
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