Image Processing Reference
In-Depth Information
With λ
= 1, GIFHA reduces to the intuitionistic fuzzy hybrid averaging
(IFHA) operator:
⎛
⎞
n
n
∏∏
(
)
w
j
w
⎜
⎜
⎟
⎟
IFHA
w
(
aaa
,
,
,
…=−
,
a
)
1
1
−
μ
,
ν
j
,
ω
123
n
a
a
σ
()
j
σ
()
j
⎝
⎠
j
=
1
j
=
1
An example is given to show the computation of IFHA for the five intuition-
istic values.
Example 3.3
Let us consider five intuitionistic fuzzy values
a
1
= (0.2, 0.6),
a
2
= (0.4, 0.2),
a
3
= (0.5, 0.6),
a
4
= (0.5, 0.4),
a
5
= (0.7, 0.2) and
weight vector be ω = (0.25, 0.20, 0.15, 0.18, 0.22)
T
of
a
j
(
j
= 1, 2, 3, 4, 5) and λ
= 2
Solution
Using the formula λ
a
= (1 − (1 − μ
a
)
λ
,
v
a
λ
), λ > 0,
The weighted intuitionistic fuzzy values are obtained as
ana
=
ω5
a
j
j
j
j
j
a
1
5025
*.
5025
*.
=−−
[( .) ,. ][.
1102
06
=
0
243
,
0
.
528
]
a
2
[( .) ,. ][., .]
1104
502
*.
02 00
5 02
*.
42
=−−
=
a
3
5015
*.
5015
*.
=−−
[( .) ,. ][.
1105
06
=
0 4054 0 6817
,
.
]
a
4
5018
*.
5018
*.
=−−
[( .) ,. ][.
1105
04
=
0 4641 0 4384
,
.
]
a
5
5022
*.
5022
*.
=−−
[( .) ,. ][.
1107
02
=
0 7340 0 1703
,
.
]
Now, the scores of
aj
j
(
=
12345
are computed as
,,,,
)
( )
sa
=
0 243 0 528
.
−
.
= −
0 285
.
, ()
sa
= −= =
04 02 02
.
.
.
, ()
sa
0 405
.
4406817
−
.
= −
0 2763
.
,
1
2
3
sa
() .
=
0 4641 0 4384
−
.
=
0 0257
.
, () .
sa
=
0 734
0001703
−
.
=
0 5637
.
4
5
As
sa sa sa sa sa
() () () () ()
> > > >
,
5
2
4
3
1
So,
a
=
(. ,. ),
0 7340 0 1703
a
=
(.,.),
0402
a
=
(. ,.
0 4641 04
384
),
σ
()
1
σ
()
2
σ
()
3
a
=
(. ,. ),
0 4054 0 6817
a
=
(
0
.
243
,
0
.
528
)
σ
()
4
σ
()
5
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