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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