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t
i
c
i
a
n
i
n
f
u
t
u
r
e
r
e
s
e
a
r
c
h
w
o
r
k
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as:
Sectio
n
2
co
n
tai
n
s
t
h
e
in
tr
o
d
u
cto
r
y
d
ef
i
n
itio
n
o
f
f
u
zz
y
s
u
b
f
ield
an
d
r
elate
d
r
esu
lt
w
h
ic
h
p
la
y
a
k
e
y
r
o
le
f
o
r
o
u
r
f
u
r
t
h
er
d
is
c
u
s
s
io
n
.
I
n
Sectio
n
3
w
e
d
ef
i
n
e
-
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
s
,
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
s
an
d
also
p
r
o
v
e
t
h
at
le
v
el
s
u
b
s
et
o
f
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
is
s
u
b
f
ield
o
f
f
ield
,
an
d
v
ice
v
er
s
a.
I
n
Sect
io
n
4,
w
e
p
r
o
v
e
t
h
at
t
h
e
p
r
o
d
u
ct
o
f
t
w
o
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
s
is
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
a
n
d
d
ev
elo
p
s
o
m
e
r
es
u
lts
o
f
t
h
e
p
r
o
d
u
ct
o
f
t
w
o
co
m
p
le
x
f
u
zz
y
s
u
b
f
iel
d
s
.
T
h
e
i
m
a
g
e
an
d
in
v
er
s
e
i
m
a
g
e
o
f
co
m
p
lex
f
u
z
z
y
s
u
b
f
ield
u
n
d
er
f
ield
h
o
m
o
m
o
r
p
h
is
m
is
d
escr
ib
ed
in
Sec
t
io
n
5
.
2.
P
RE
L
I
M
I
NARIE
S
W
e
r
ec
all
f
ir
s
t
th
e
ele
m
e
n
tar
y
n
o
tio
n
o
f
f
u
zz
y
s
et
s
an
d
f
u
zz
y
s
u
b
f
ield
w
h
ich
p
la
y
a
k
e
y
r
o
le
f
o
r
o
u
r
f
u
r
t
h
er
an
al
y
s
is
.
Def
ini
t
io
n (
2
.
1
)
[
1
]:
A
f
u
zz
y
s
et
o
f
a
n
o
n
e
m
p
t
y
s
e
t
is
a
m
ap
p
in
g
Def
ini
t
io
n (
2
.
2
)
[6
]:
A
f
u
zz
y
s
u
b
s
et
o
f
a
f
ield
is
ca
lled
a
f
u
z
z
y
s
u
b
f
ield
i
f
1.
{
}
2.
{
}
3.
Def
ini
t
io
n
(
2
.
3
)
[
1
2
]:
A
co
m
p
lex
f
u
zz
y
s
et
o
f
u
n
i
v
er
s
e
o
f
d
is
co
u
r
s
e
is
id
en
tify
w
i
th
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
an
d
is
d
ef
in
ed
as
{
|
|
}
T
h
is
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
r
ec
eiv
e
all
m
e
m
b
er
s
h
ip
v
alu
e
f
r
o
m
t
h
e
u
n
it
cir
cle
o
f
co
m
p
l
ex
p
la
n
e,
w
h
er
e
√
b
o
th
an
d
ar
e
r
ea
l
v
alu
ed
s
u
c
h
th
at
an
d
.
T
h
r
o
u
g
h
o
u
t
th
is
p
ap
er
w
e
ta
k
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
co
m
p
le
x
f
u
zz
y
s
ets
an
d
s
u
ch
as
an
d
,
r
esp
ec
tiv
el
y
.
Def
ini
t
io
n (
2
.
4
)
[
2
0
]
L
et
{
(
)
}
b
e
a
f
u
zz
y
s
u
b
s
et.
T
h
en
t
h
e
s
et
{
(
)
}
is
ca
lled
a
-
f
u
zz
y
s
u
b
s
et.
Def
ini
t
io
n (
2
.
5
)
[
2
0
]
:
L
et
an
d
b
e
C
F
S o
f
.
T
h
en
1
.
A
co
m
p
lex
f
u
zz
y
s
et
is
h
o
m
o
g
e
n
eo
u
s
co
m
p
lex
f
u
zz
y
s
et
,
if
f
o
r
all
,
w
e
h
a
v
e
if
an
d
o
n
l
y
i
f
2
.
A
co
m
p
lex
f
u
zz
y
s
et
is
h
o
m
o
g
e
n
eo
u
s
co
m
p
lex
f
u
zz
y
s
et
w
it
h
,
if
f
o
r
all
,
w
e
h
a
v
e
if
an
d
o
n
l
y
if
.
I
n
th
i
s
p
ap
er
w
e
ta
k
e
co
m
p
lex
f
u
zz
y
s
e
t
as
h
o
m
o
g
en
eo
u
s
co
m
p
le
x
f
u
zz
y
s
et.
Def
ini
t
io
n
(
2
.
6
)
[
1
4
]
L
et
b
e
c
o
m
p
le
x
f
u
zz
y
s
et
s
o
f
s
et
f
o
r
a
ll
.
T
h
e
co
m
p
le
m
e
n
t
o
f
co
m
p
l
ex
f
u
zz
y
s
et
is
s
p
ec
i
f
ied
b
y
a
f
u
n
c
tio
n
{
}
{
}
Def
ini
t
io
n
2
.
7
[
1
4
]
L
et
an
d
t
w
o
co
m
p
le
x
f
u
zz
y
s
ets
o
f
u
n
i
v
er
s
e
o
f
d
i
s
co
u
r
s
e
.
T
h
e
C
ar
tesi
an
p
r
o
d
u
ct
o
f
co
m
p
le
x
f
u
zz
y
s
et
s
an
d
is
d
e
f
i
n
ed
b
y
a
f
u
n
ctio
n
{
}
{
}
T
heo
re
m
2
.
8
:
I
n
ter
s
ec
tio
n
o
f
t
w
o
f
u
zz
y
s
u
b
f
ie
ld
o
f
f
ield
is
f
u
zz
y
s
u
b
f
ield
o
f
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
21
,
No
.
2
,
Feb
r
u
ar
y
2
0
2
1
:
1
0
48
-
10
56
1050
Def
ini
t
io
n
2
.
9
:
L
et
b
e
a
h
o
m
o
m
o
r
p
h
i
s
m
.
L
et
an
d
b
e
tw
o
co
m
p
le
x
f
u
zz
y
s
et
o
f
an
d
.
T
h
e
i
m
a
g
e
an
d
p
r
e
-
i
m
ag
e
o
f
an
d
r
esp
ec
tiv
el
y
a
n
d
d
ef
i
n
ed
as
1.
{
{
2.
(
)
3.
P
RO
P
E
RT
I
E
S
O
F
CO
M
P
L
E
X
F
U
Z
Z
Y
SUB
F
I
E
L
D
T
h
is
s
ec
tio
n
d
e
v
o
ted
th
e
s
tu
d
y
o
f
-
f
u
zz
y
s
u
b
f
ield
a
n
d
co
m
p
l
ex
f
u
zz
y
s
u
b
f
ield
s
.
W
e
also
f
o
u
n
d
t
h
at
a
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
g
e
n
er
ates
t
w
o
f
u
zz
y
s
u
b
f
ield
s
.
W
e
also
s
h
o
w
t
h
at
lev
e
l
s
u
b
s
et
o
f
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
f
o
r
m
s
u
b
f
ie
ld
o
f
f
ield
.
W
e
d
ef
in
e
t
h
e
co
n
ce
p
t
o
f
d
ir
ec
t
p
r
o
d
u
ct
o
f
co
m
p
lex
f
u
zz
y
s
u
b
f
ield
an
d
p
r
o
v
e
th
at
d
ir
ec
t
p
r
o
d
u
ct
o
f
t
w
o
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
s
i
s
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
an
d
in
v
e
s
ti
g
ate
s
o
m
e
f
u
n
d
a
m
en
ta
l p
r
o
p
er
ties
o
f
th
es
e
f
ield
s
.
Def
ini
t
io
n
3
.
1
:
L
et
{
(
)
}
b
e
a
-
f
u
z
z
y
s
e
t
o
f
f
ie
ld
is
ca
lled
-
f
u
zz
y
s
u
b
f
ield
o
f
,
f
o
r
all
,
if
1.
{
}
2.
{
}
3.
.
T
heo
re
m
3
.
2
:
L
et
{
(
)
}
b
e
-
f
u
zz
y
s
et
o
f
.
T
h
en
is
-
f
u
zz
y
s
u
b
f
ield
if
an
d
o
n
l
y
i
f
is
f
u
zz
y
s
u
b
f
ield
.
Def
ini
t
io
n 3
.
3
: A
co
m
p
le
x
f
u
z
z
y
s
et
o
f
f
ield
is
ca
lled
co
m
p
l
ex
f
u
zz
y
s
u
b
f
ield
o
f
if
1.
{
}
,
2.
{
}
,
3.
,
f
o
r
all
.
T
heo
re
m
3
.
4
:
L
et
{
(
)
}
b
e
co
m
p
lex
f
u
zz
y
s
et
o
f
f
ie
ld
.
T
h
en
is
a
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
o
f
if
f
:
1.
T
h
e
f
u
zz
y
s
et
{
(
)
}
is
a
f
u
zz
y
s
u
b
f
i
eld
.
2.
T
h
e
-
f
u
zz
y
s
et
{
(
)
}
is
a
-
f
u
zz
y
s
u
b
f
ield
.
P
ro
o
f
: Su
p
p
o
s
e
th
at
b
e
co
m
p
l
ex
f
u
zz
y
s
u
b
f
ield
,
f
o
r
all
,
th
en
w
e
h
av
e
{
}
{
}
{
}
{
}
As
is
h
o
m
o
g
e
n
eo
u
s
,
{
}
an
d
{
}
Mo
r
eo
v
er
,
{
}
{
}
{
}
{
}
I
m
p
lies
t
h
at
{
}
an
d
{
}
Mo
r
eo
v
er
,
(
)
I
m
p
lies
t
h
at
an
d
.
Hen
ce
an
d
ar
e
f
u
zz
y
s
u
b
f
ield
an
d
-
f
u
zz
y
s
u
b
f
ield
,
r
esp
ec
ti
v
e
l
y
.
C
o
n
v
er
s
el
y
,
s
u
p
p
o
s
e
th
a
t
an
d
is
f
u
zz
y
s
u
b
f
ield
an
d
-
f
u
zz
y
s
u
b
f
ield
.
T
h
en
w
e
h
a
v
e
{
}
an
d
{
}
{
}
an
d
{
}
,
an
d
As
A
is
h
o
m
o
g
e
n
eo
u
s
,
So
,
{
}
}
{
}
{
}
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
A
n
o
te
o
n
co
mp
lex
fu
z
z
y
s
u
b
fi
eld
(
Mu
h
a
mma
d
Gu
lz
a
r
)
1051
Mo
r
eo
v
er
,
{
}
{
}
{
}
{
}
A
l
s
o
,
(
)
.
Hen
ce
,
is
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
.
T
heo
re
m
3
.
5
:
I
n
ter
s
ec
tio
n
o
f
t
w
o
co
m
p
le
x
f
u
zz
y
s
u
b
f
ie
ld
o
f
f
ield
is
also
co
m
p
le
x
f
u
zz
y
s
u
b
f
ield
o
f
.
P
ro
o
f
:
L
et
{
(
)
}
an
d
{
(
)
}
b
e
t
w
o
co
m
p
lex
f
u
zz
y
s
u
b
f
ield
o
f
.
No
te
th
a
t,
an
d
ar
e
f
u
zz
y
s
u
b
f
ield
an
d
-
f
u
zz
y
s
u
b
f
ield
.
Fro
m
th
eo
r
e
m
(
3
.
2
)
an
d
(
2
.
9
)
,
w
e
h
av
e
an
d
ar
e
f
u
zz
y
s
u
b
f
ield
an
d
-
f
u
zz
y
s
u
b
f
ield
.
C
o
n
s
id
er
,
{
}
{
}
{
}
{
}
.
Mo
r
eo
v
er
,
{
}
{
}
{
}
T
h
er
ef
o
r
e,
{
}
.
T
h
u
s
,
(
)
Hen
ce
,
p
r
o
v
ed
o
u
r
clai
m
.
T
heo
re
m
3
.
6
:
I
f
{
(
)
}
is
a
co
m
p
lex
f
u
zz
y
s
u
b
f
ie
ld
o
f
f
ield
,
.
T
h
en
1.
,
2.
,
w
h
er
e
an
d
is
id
en
ti
t
y
ele
m
e
n
t
o
f
P
ro
o
f
:
(
1
)
.
C
o
n
s
id
er
,
(
)
{
}
{
}
{
}
{
}
As
is
h
o
m
o
g
e
n
eo
u
s
T
h
u
s
,
,
an
d
.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
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n
esia
n
J
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lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
21
,
No
.
2
,
Feb
r
u
ar
y
2
0
2
1
:
1
0
48
-
10
56
1052
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I
n
d
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n
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n
J
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E
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N:
2502
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4752
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
21
,
No
.
2
,
Feb
r
u
ar
y
2
0
2
1
:
1
0
48
-
10
56
1054
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1
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
A
n
o
te
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n
co
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lex
fu
z
z
y
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b
fi
eld
(
Mu
h
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d
Gu
lz
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r
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1055
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T
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4
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5
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[1
]
L
.
A
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fo
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.
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