Image Processing Reference
In-Depth Information
where 1 ≤ p < +∞ and
μ
()
x
+−
1
2
ν
() ,
x
μ
()
x
+−
1
2
ν
()
x
Ai
Ai
Bi
Bi
ϕ
()
x
=
ϕ
(
x
)
=
Ai
Bi
7. Hung and Wang [9] suggested some similarity measures that are the
extensions of fuzzy sets which are given as
(
)
1
2
SAB
(,) ax () ()max(
=−
1
μ
x
μ
x
+
ν
x
)
ν
(
x
)
(4.9)
Ai Bi
Ai Bi
i
i
n
1 μ
() () () ()
x
μ
x
+
ν
x
ν
x
Ai Bi Ai Bi
SAB
(,)
=−
1
i
=
(4.10)
n
μ
() () (
x
+
μ
x
+
ν
x
)
+
ν
(
x
)
Ai Bi
A
i
B
i
i
=
1
n
min( ( , ()) min( ( , ())
μ
x
μ
x
+
ν
x
ν
x
1
Ai Bi
Ai Bi
SAB
(,)
=
i
=
1
(4.11)
1
n
N
max(
μ
(
x
), ( )max((), ( )
μ
x
+
ν
x
ν
x
A
i Bi
A
i Bi
i
8. Liang and Shi [12] suggested another similarity measure between
two IFS s with intervals [μ A ( x i ), 1 − ν A ( x i )] and [μ B ( x i ), 1 − ν B ( x i )] a s
n
1
L
p
SAB
(,)
=−
1
( () ( )
ϕ
x
+
ϕ
x
(4.12)
p
IFS
Ai Bi
p
n
i
=
1
where 1 ≤ p < +∞ and
μ
() () ,
x
μ
x
1
ν
()
x
1
ν
()
x
Ai Bi
Ai
Bi
ϕ
()
x
=
ϕ
(
x
)
=
Ai
Bi
2
2
2
9. Liang and Shi [12] suggested another similarity measure. For an IFS
A with intervals [μ A ( x i ), 1 − ν A ( x i )], the median value of the interval is
μ
()(
x
+−
1
2
ν
(
x
))
Ai
Ai
mx
()
=
Ai
With this median value, the interval is divided into two subintervals which
are denoted as
[(), ( ]
μ
xmx
and
[ ( ,
m x
1
− ν
(
x
)]
Ai Ai
Ai
Ai
 
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