Image Processing Reference
In-Depth Information
4.5 Intuitionistic Fuzzy Information Measure
If
p
and
q
are two probability distributions for two random variables, the
cross-entropy measure of
p
and
q
is defined as [11]
( )ln
()
()
px
qx
=
∑
Ipq
(,)
p x
It measures the amount of discrimination of
p
and
q
. Lin [13] proposed a
modified cross-entropy measure as
px
px
()
∑
Kpq
(,)
=
p x
( )ln
(4.19)
(
12
/
) () (
+
12
/
) ()
qx
In an analogous manner, Vlachos and Sergiadis [20] defined information of
discrimination in terms of the membership and non-membership degrees as
μ
μ
()
()
a
b
A
IAB
(,) n
=
ij
B
ij
In order to define the cross entropy using
IFS
, information carried by both
membership and non-membership degrees is calculated.
Information carried out as a result of the membership degree is
μ
μ
()
()
x
x
=
∑
Ai
IAB
ʹ
(,)
μ
(
x
)ln
Ai
Bi
This is the expected information of discrimination of
A
against
B.
Likewise,
the information due to the non-membership degree is
ν
ν
()
()
x
x
=
∑
Ai
I AB
ʹʹ
non
(,)
ν
(
x
)ln
Ai
Bi
So, information of discrimination in favour of
A
against
B
[20] is
n
μ
μ
()
()
x
x
ν
ν
()
()
x
x
∑
Ai
Ai
I AB
ʹ
(,)
=
μ
(
x
)ln
+
ν
()ln
x
IFS
A
i
Ai
Bi
Bi
i
=
1
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