Image Processing Reference
In-Depth Information
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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