Image Processing Reference
In-Depth Information
Since
s
(
a
4
) >
s
(
a
3
) >
s
(
a
2
) >
s
(
a
1
) >
s
(
a
5
),
a
=
(.,.),
0701
a
=
(.,.),
0602
a
=
(.,.),
0403
σ
()
1
σ
()
2
σ
()
3
a
=
(.
02
, , .),
06
a
σ
=
( .,.)
0107
σ
()
4
()
5
Now, from the definition of IFOWA
⎛
⎞
n
n
∏∏
(
)
w
⎜
⎜
j
w
⎟
⎟
(,,
aaa
,
…
=− −
, )
a
n
1
1
μ
,
ν
j
123
a
a
σ
()
j
σ
()
j
⎝
⎠
j
=
1
j
=
1
(
⎡
⎤
0 112
.
0 236
.
0 304
.
11107
−− ×− ×−
(
. )
(
106
.)
(
1 04
. )
⎢
⎢
⎢
⎥
⎥
⎥
)
0 236
.
0 112
.
=
×− ×
(
102
. )
(
1
−
01
.)
,
0 112
.
0 236
.
0 304
.
0 236
.
0 112
.
01
.
×
02
.
×
03
.
×
06
.
×
07
.
⎣
⎦
=
( 435 3122)
000
.
,
.
3.5.3 Generalized Intuitionistic Fuzzy Hybrid Averaging Operator
The GIFWA operator weighs only intuitionistic fuzzy values, and GIFOWA
weighs only the ordered positions of intuitionistic fuzzy values. To over-
come the limitation, the generalized intuitionistic fuzzy hybrid averaging
(GIFHA) operator is introduced, which weighs both intuitionistic fuzzy val-
ues and its ordered position.
A GIFHA operator of dimension '
n
' with an associated vector
w
=
(
w
1
,
w
2
, …,
w
n
)
T
and
∑
n
w
j
=
1
σ
()
is the
j
th largest of the weighted intu-
,
a
j
j
=
1
itionistic fuzzy values
=ω
,
j
= 1, 2, 3, …,
n
and ω = (ω
1
, ω
2
, ω
3
, …, ω
n
)
T
is the weight vector of
a
j
(
j
= 1, 2, 3, …,
n
) and
aa na
j
(
)
j
jj
∑
n
ω
j
=
1
and λ > 0 is given as
j
=
1
(
)
1
/
λ
aaa
a
wa wa wa
λ
λ
λ
w
a
λ
GIFHA
w
(
,
,
,
…= ⊕
,
)
⊕
⊕
n
n
n
,
ω
123
1
σ
( )
1
2
σ
( )
2
3
σ
( )
3
σ
()
1
/
λ
⎛
⎛
⎞
n
(
)
w
∏
j
⎜
⎜
⎜
⎜
λ
⎟
⎟
=− −
1
1
μ
λ
,
a
()
j
⎝
⎠
j
=
1
⎝
1
/
λ
⎞
⎛
⎞
w
n
(
)
j
⎛
⎜
λ
⎞
⎟
∏
⎟
⎟
⎜
⎜
⎟
⎟
11 1
−− −
1
−
ν
λ
(3.17)
a
()
j
⎝
⎠
j
=
1
⎠
where
.
a
σ
μν
σ
=
(
,
)
()
j
a
a
()
j
σ
()
j
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