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(
I
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)
Vo
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7
,
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.
1
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Feb
r
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ar
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201
7
,
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9
I
SS
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2088
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co
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1.
I
NT
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D
UCT
I
O
N
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e
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e
m
an
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f
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en
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tie
s
.
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tr
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m
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ab
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Fu
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th
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[9
-
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th
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f
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atic
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t
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to
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[
1
]
.
Mo
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[
2
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d
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1
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4
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.
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[
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
7
:
3
2
4
–
329
325
2.
SO
F
T
S
E
T
F
UN
DAM
E
N
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A
L
S
I
n
th
i
s
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tio
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s
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th
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f
u
n
d
a
m
en
tals
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ex
p
lai
n
ed
.
2
.
1
.
I
nfo
r
m
a
t
io
n
Sy
s
t
e
m
in
So
f
t
Set
I
n
r
elatio
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al
d
atab
ase
r
elatio
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s
ar
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k
n
o
w
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s
tab
les
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d
a
r
elatio
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is
t
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e
co
m
b
in
at
io
n
o
f
r
o
w
s
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d
co
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m
n
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I
n
th
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m
e
w
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y
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n
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o
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m
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y
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s
i
m
ilar
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elatio
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elatio
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at
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ase.
An
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m
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a
s
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t set is a
q
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ad
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p
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i.e
.
4
-
t
u
p
les [
1
]
,
[
4
]
,
[
5]
S =
(
U,
A
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f
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[
1
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U
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An
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2
.
2
.
I
ntr
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du
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n t
o
So
f
t
s
et
T
he
o
ry
So
f
t
s
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is
a
s
i
m
p
le
m
at
h
e
m
atica
l
to
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th
at
d
ea
ls
w
it
h
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co
llectio
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o
f
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p
r
o
x
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m
ate
b
e
h
av
io
r
o
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d
escr
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tio
n
o
f
o
b
j
ec
ts
.
I
t
is
a
p
ar
am
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to
o
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to
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w
it
h
ap
p
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x
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ate
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a
te
d
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ca
n
d
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id
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t
w
o
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.
F
ir
s
t
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is
a
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o
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is
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n
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te
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1
]
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I
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m
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a
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m
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n
s
tr
u
cted
an
d
d
ef
in
e
s
th
e
n
o
tio
n
o
f
an
e
x
ac
t
s
o
lu
tio
n
o
f
t
h
i
s
m
o
d
el.
A
cla
s
s
ical
m
o
d
el
is
g
en
er
al
l
y
u
s
ed
to
f
in
d
th
e
ex
ac
t
s
o
lu
tio
n
s
i.e
.
t
h
is
t
y
p
e
o
f
m
o
d
el
is
u
s
ed
f
o
r
p
r
ec
is
e
v
alu
e.
I
n
m
at
h
e
m
atica
l
m
o
d
el
it
i
s
a
to
u
g
h
tas
k
to
o
b
tai
n
th
e
e
x
ac
t
s
o
l
u
tio
n
f
o
r
t
h
e
i
m
p
r
ec
is
e
v
a
lu
e
s
.
So
,
it
i
s
m
o
r
e
r
el
iab
le
an
d
ea
s
y
to
d
ef
i
ne
a
n
ap
p
r
o
x
i
m
ate
s
o
l
u
tio
n
f
ir
s
t
a
n
d
th
e
n
t
h
e
s
o
l
u
tio
n
is
ca
lcu
lated
.
T
h
e
s
o
f
t
s
et
th
eo
r
y
h
a
s
g
iv
e
n
a
n
o
p
p
o
s
ite
ap
p
r
o
ac
h
to
s
o
lv
e
t
h
ese
t
y
p
es
o
f
p
r
o
b
le
m
s
.
I
n
t
h
e
i
n
iti
al
d
escr
ip
tio
n
o
f
a
n
o
b
j
ec
t
it
h
as
an
ap
p
r
o
x
i
m
ate
v
alu
e
a
n
d
i
t
d
o
es
n
o
t
r
eq
u
ir
ed
to
in
tr
o
d
u
ce
th
e
n
o
tio
n
o
f
e
x
a
ct
s
o
lu
tio
n
.
T
h
ese
t
y
p
es
o
f
co
n
d
itio
n
s
o
n
ap
p
r
o
x
i
m
ate
b
eh
a
v
io
r
ar
e
n
o
t
p
r
esen
t
in
s
o
f
t
s
et
t
h
eo
r
y
.
T
h
is
p
r
o
p
er
t
y
m
a
k
es
s
o
f
t
s
et
th
eo
r
y
r
elia
b
le,
s
i
m
p
le
a
n
d
co
m
f
o
r
tab
le
t
o
ap
p
ly
in
a
n
y
r
ea
l
w
o
r
ld
ap
p
licatio
n
s
.
W
it
h
t
h
e
h
elp
o
f
w
o
r
d
s
,
s
e
n
te
n
ce
s
,
n
u
m
b
er
s
,
f
u
n
ctio
n
s
t
h
e
p
ar
a
m
et
er
izatio
n
o
f
s
o
f
t
s
et
ca
n
b
e
ex
p
r
ess
ed
.
I
n
th
e
w
h
o
le
p
ap
er
U
in
d
icate
s
to
t
h
e
u
n
i
v
er
s
e,
E
i
s
d
e
f
in
ed
b
y
a
s
e
t
o
f
p
ar
a
m
eter
s
a
n
d
P
(
U)
is
t
h
e
p
o
w
er
s
et
o
f
U.
Def
i
n
itio
n
1
.
(
[
1
]
,
[
4
]
)
.
A
p
air
(
F,
E
)
is
ca
lled
a
s
o
f
t
s
et
o
v
er
U,
w
h
er
e
F is
a
m
ap
p
in
g
g
i
v
e
n
b
y
(
)
I
n
o
th
er
w
o
r
d
s
U
is
u
n
iv
er
s
e
in
s
o
f
t
s
et
an
d
it
is
a
p
ar
am
eter
ized
f
a
m
il
y
o
f
s
u
b
s
et
s
o
f
u
n
iv
er
s
e
U.
f
o
r
,
F(e
)
m
a
y
b
e
co
n
s
id
er
ed
as
th
e
s
et
o
f
e
ele
m
e
n
ts
o
f
t
h
e
s
o
f
t
s
et
(
F,
E
)
as
th
e
s
et
o
f
e
ap
p
r
o
x
i
m
ate
ele
m
e
n
ts
o
f
s
o
f
t
s
et
[
1
]
.
Ulti
m
atel
y
,
s
o
f
t set is a
n
o
n
-
cr
is
p
s
e
t
Def
i
n
itio
n
2
.
(
See
[
1
]
)
.
L
et
R
b
e
a
f
a
m
il
y
o
f
eq
u
i
v
ale
n
ce
r
elatio
n
s
an
d
let
.
I
t
is
s
ay
t
h
at
A
i
s
d
is
p
en
s
ab
le
in
R
i
f
I
ND(
R
)
=
I
ND(
R
-
{A
})
[
1
-
2]
,
[
4
]
.
Oth
er
w
i
s
e
A
is
i
n
d
is
p
en
s
ab
le
in
R
.
T
h
e
f
a
m
il
y
R
is
I
n
d
ep
en
d
en
t
if
ea
ch
is
in
d
is
p
en
s
ab
le
in
R
.
o
th
er
w
is
e
R
is
d
ep
en
d
en
t.
Q
s
u
b
s
et
o
f
P
is
a
r
ed
u
ctio
n
o
f
P
if
Q
is
in
d
ep
en
d
en
t
a
n
d
I
ND
(
Q)
=
I
ND
(
P
)
,
th
at
is
to
s
a
y
Q
is
t
h
e
m
i
n
i
m
al
s
u
b
s
et
o
f
P
t
h
at
k
ee
p
s
th
e
class
i
f
icatio
n
ab
ili
t
y
[
7
]
.
T
h
e
s
et
o
f
all
i
n
d
is
p
e
n
s
ab
le
r
elatio
n
s
i
n
P
is
ca
lled
th
e
co
r
e
o
f
P
,
an
d
is
d
en
o
ted
as
C
OR
E
(
P
)
.
C
lear
l
y
,
C
O
R
E
(
P
)
=
∩R
E
D
(
P
)
,
w
h
er
e
R
E
D
(
P
)
is
th
e
f
a
m
il
y
o
f
all
r
ed
u
ctio
n
s
o
f
P
[
2
]
,
[
7
]
,
[
1
0
]
.
Def
i
n
itio
n
3
.
(
See
[
1
]
,
[
8
]
)
.
L
et
(
F,
E
)
b
e
a
s
o
f
t
s
et
o
v
er
th
e
u
n
i
v
er
s
e
U
an
d
.
A
p
ar
am
eter
co
-
o
cc
u
r
r
en
ce
s
et
o
f
an
o
b
j
ec
t
u
ca
n
b
e
d
ef
i
n
ed
as [
8
]
:
(
)
*
(
)
+
Ob
v
io
u
s
l
y
,
(
)
*
(
)
+
Def
i
n
itio
n
4
.
(
See
[
1
]
)
.
L
et
(
F,
E
)
b
e
a
s
o
f
t set o
v
er
th
e
u
n
i
v
e
r
s
e
U
an
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
A
R
ea
l Time
A
p
p
lica
tio
n
o
f S
o
ft S
et
in
P
a
r
a
mete
r
iz
a
tio
n
R
ed
u
ctio
n
fo
r
Dec
is
io
n
Ma
kin
g
…
(
Ja
n
meja
y
P
a
n
t
)
326
Su
p
p
o
r
t o
f
an
o
b
j
ec
t u
is
d
ef
in
ed
b
y
:
(
)
(
*
(
)
+
)
[
1
]
3.
E
XAM
P
L
E
O
F
RE
DUC
T
I
O
N
I
N
SO
F
T
S
E
T
I
n
th
is
e
x
a
m
p
le
th
er
e
i
s
s
o
f
t
s
et
(
F,
E
)
w
h
ich
d
escr
ib
es
th
e
“n
at
u
r
e
o
f
B
ik
e
s
to
p
u
r
c
h
a
s
e”
th
a
t
a
cu
s
to
m
er
is
s
u
p
p
o
s
ed
to
m
a
k
e
a
n
ec
ess
ar
y
ac
tio
n
as a
d
ec
is
io
n
to
b
u
y
.
I
n
t
h
e
s
h
o
w
r
o
o
m
th
e
r
e
ar
e
f
iv
e
t
y
p
e
s
o
f
b
ik
es
ar
e
r
ea
d
y
to
s
ale.
T
h
e
n
atu
r
e
o
f
d
if
f
er
e
n
t
t
y
p
es
o
f
b
ik
es
is
S
m
al
l
b
ik
e,
Me
d
iu
m
b
ik
e,
E
x
p
en
s
i
v
e
b
ik
e,
Seco
n
d
-
h
an
d
b
ik
e,
a
n
d
i
m
p
o
r
ted
b
ik
e.
Su
p
p
o
s
e
w
e
h
a
v
e
s
i
x
b
ik
es
w
h
ich
ar
e
u
n
d
er
co
n
s
id
er
atio
n
,
U
=
{b
1
,
b
2
,
b
3
,
b
4
,
b
5
,
b
6
}
w
h
er
e
,
b
1
,
b
2
,
b
3
,
b
4
,
b
5
,
b
6
a
r
e
b
ik
es u
n
d
er
co
n
s
id
er
atio
n
a
n
d
E
is
a
s
et
o
f
d
ec
is
io
n
p
ar
a
m
eter
s
,
E
=
{e
1
,
e2
,
e3
,
e
4
,
e5
}
[
1
]
w
h
er
e,
Fo
r
th
e
p
ar
am
e
ter
“s
m
a
ll b
ik
e
”,
w
e
h
a
v
e
e1
Fo
r
th
e
p
ar
am
e
ter
“m
ed
i
u
m
b
i
k
e”
,
w
e
h
a
v
e
e2
Fo
r
th
e
p
ar
am
e
ter
“
e
x
p
en
s
i
v
e
b
ik
e”
,
w
e
h
av
e
e3
Fo
r
th
e
p
ar
am
e
ter
“Sec
o
n
d
-
h
a
n
d
b
ik
e”
,
w
e
h
a
v
e
e4
Fo
r
th
e
p
ar
am
e
ter
“
i
m
p
o
r
ted
b
ik
e”
,
w
e
h
a
v
e
e5
C
o
n
s
id
er
th
e
m
ap
p
in
g
(
)
g
iv
e
n
b
y
“
b
i
k
es
(
.
)
”,
Her
e
(
.
)
is
to
b
e
f
illed
in
b
y
o
n
e
o
f
p
ar
a
m
eter
s
[
1
]
Su
p
p
o
s
e
th
at
F (
e1
)
=
{b
2
,
b
3
,
b
4
,
b
5
},
F (
e2
)
=
{b
1
,
b
6
},
F (
e3
)
=
{b
1
,
b
2
,
b
6
},
F (
e4
)
=
{b
1
,
b
2
,
b
3
,
b
4
,
b
5
,
b
6
},
F (
e5
)
=
{b
1
,
b
2
,
b
3
,
b
4
,
b
5
,
b
6
}.
T
h
er
ef
o
r
e,
F
(
e1
)
m
ea
n
s
“
t
h
e
s
ize
o
f
b
i
k
es
ar
e
s
m
all”,
i
ts
f
u
n
ctio
n
al
v
al
u
e
i
s
t
h
e
s
et
is
F
(
e1
)
=
{b
2
,
b
3
,
b
4
,
b
5
,
}.
I
t is th
e
s
o
f
t
s
et
(
F,
E
)
as a
co
llectio
n
o
f
ap
p
r
o
x
i
m
atio
n
s
as
:
(
F,
E
)
=
(
*
*
+
*
+
*
+
*
+
)
T
h
e
s
o
f
t
s
et
(
F,
P
)
is
ca
n
b
e
e
x
p
r
ess
ed
as a
b
i
n
ar
y
tab
le,
a
s
s
h
o
w
n
T
ab
le
1
,
to
s
o
lv
e
t
h
is
p
r
o
b
le
m
[
1
]
.
Fo
r
th
is
h
ij
=
1
if
h
i
F
(
ej
)
th
en
h
ij
=
1
,
o
th
er
w
is
e
h
ij
=
0
,
w
h
er
e
h
ij
ar
e
th
e
en
tr
ies i
n
T
ab
le
1
.
So
a
s
o
f
t
s
et
ca
n
n
o
w
b
e
k
n
o
w
n
a
s
a
k
n
o
w
led
g
e
r
ep
r
esen
ta
tio
n
s
y
s
te
m
.
I
n
t
h
i
s
s
y
s
te
m
we
g
e
n
er
all
y
u
s
e
s
et
o
f
p
ar
a
m
eter
s
i
n
s
tead
o
f
s
e
t
o
f
a
ttrib
u
te
s
.
E
v
er
y
a
p
p
r
o
x
im
a
tio
n
ca
n
d
i
v
id
ed
in
t
o
t
w
o
p
ar
ts
,
f
ir
s
t
a
p
r
ed
icate
p
ar
t
e
an
d
s
ec
o
n
d
o
n
e
is
ap
p
r
o
x
i
m
ate
v
al
u
e
s
et
p
[
1
]
.
f
o
r
ex
a
m
p
le,
f
o
r
th
e
a
p
p
r
o
x
im
a
tio
n
s
m
a
ll
b
ik
e=
{b
2
,
b
3
,
b
4
,
b
5
},
h
av
e
th
e
p
r
ed
icate
n
a
m
e
o
f
b
ik
e
s
w
it
h
s
m
all
s
ize
an
d
th
e
v
alu
e
s
et
is
{b
2
,
b
3
,
b
4
,
b
5
}
[
1
]
.
T
ab
le
1
.
R
ep
r
esen
tatio
n
o
f
s
o
f
t set
w
it
h
th
e
ab
o
v
e
e
x
a
m
p
le
i
n
tab
le
U
e1
e2
e3
e4
e5
b1
0
1
1
1
1
b2
1
0
1
1
1
b3
1
0
0
1
1
b4
1
0
0
1
1
b5
1
0
0
1
1
b6
0
1
1
1
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
7
:
3
2
4
–
329
327
3
.
1
.
Resul
t
a
nd
Di
s
cus
s
io
n
I
n
th
is
s
tep
w
e
id
en
ti
f
y
t
h
at
h
o
w
p
ar
a
m
eter
s
ar
e
d
is
p
en
s
ab
l
e
[
1
]
s
o
af
ter
th
at
w
e
w
o
r
k
o
u
t
to
r
e
d
u
ce
th
e
d
i
m
e
n
s
io
n
o
f
d
ata
f
o
r
th
is
t
ask
p
ar
a
m
eter
s
ca
n
b
e
r
e
m
o
v
e
d
w
it
h
o
u
t a
f
f
ec
ted
th
e
o
r
ig
i
n
al
d
ec
is
io
n
s
[
1
]
.
L
et
u
s
co
n
s
id
er
t
h
e
r
ep
r
e
s
en
ta
tio
n
o
f
s
o
f
t
s
et
(
F,
P
)
in
tab
u
l
ar
f
o
r
m
.
S
u
p
p
o
s
e
Q
is
a
r
ed
u
c
tio
n
o
f
P
,
th
en
t
h
e
n
e
w
s
o
f
t set (
F,
Q)
is
ca
lled
th
e
r
ed
u
ct
s
o
f
t set o
f
t
h
e
s
o
f
t set (
F,
P
)
[
1
]
.
A
l
g
o
r
ith
m
:
Su
p
p
o
s
e
Mr
.
XYZ
s
elec
ts
b
ik
e:
T
h
e
p
r
o
ce
s
s
o
f
s
elec
ti
n
g
a
b
ik
e
m
a
y
h
as t
h
r
ee
b
asic
s
tep
s
a.
So
f
t
s
et
t
h
eo
r
y
ca
n
b
e
u
s
ed
t
o
tr
an
s
f
o
r
m
ed
th
e
d
atase
t
in
t
o
a
B
o
o
lean
-
v
al
u
ed
in
f
o
r
m
ati
o
n
(
as
T
a
b
le
1
)
s
y
s
te
m
a
s
S=
(
U,
A
,
V
(
0
,
1
)
,
f
)
s
o
f
t set t
h
eo
r
y
is
u
s
ed
f
o
r
th
is
co
n
v
er
s
i
o
n
[
1
]
.
b.
T
h
e
n
ex
t p
r
o
ce
s
s
is
I
n
p
u
t
I
n
p
u
t t
h
e
s
o
f
t
s
et
(
F,
E
)
,
I
n
p
u
t t
h
e
s
et
P
o
f
ch
o
ice
p
ar
am
eter
s
o
f
Mr
.
XY
Z
w
h
ic
h
is
a
s
u
b
s
et
o
f
E
.
c.
A
t
f
ir
s
t
th
e
d
ata
s
et
m
u
s
t
b
e
r
ed
u
ce
d
b
y
r
e
m
o
v
i
n
g
d
is
p
en
s
ab
le
ite
m
s
b
e
f
o
r
e
m
a
k
e
a
d
ec
is
io
n
.
W
e
u
s
ed
th
e
s
o
f
t set t
h
eo
r
y
r
ed
u
ce
p
ar
am
e
ter
s
[
1
]
[
4
]
.
Fin
d
all
r
ed
u
ct
-
s
o
f
t
-
s
et
s
o
f
(
F,
P
)
,
c
h
o
o
s
e
o
n
e
r
ed
u
c
t
-
s
o
f
t
-
s
e
t sa
y
(
F,
Q)
o
f
(
F,
P
)
.
3
.
2
.
E
x
pla
na
t
io
n
I
t
is
k
n
o
w
n
th
at
{e
l,
e2
,
e4
,
e
5
}
an
d
{e
2
,
e3
,
e4
,
e5
}
ar
e
t
wo
r
ed
u
cts
o
f
P
=
{e
1
,
e2
,
e3
,
e4
,
e5
}
[
1
]
.
B
u
t a
ctu
all
y
{e
l,
e2
,
e4
,
e5
}
a
n
d
{e
2
,
e3
,
e
4
,
e5
}
a
r
e
n
o
t th
e
r
ed
u
cts o
f
P
=
{e
l,
e2
,
e3
,
e4
,
e
5
}.
T
h
e
f
o
llo
w
i
n
g
d
escr
ip
tio
n
s
w
i
ll e
x
p
lain
t
h
i
s
is
s
u
e.
L
et
u
s
co
n
s
id
er
R
p
is
t
h
e
i
n
d
i
s
ce
r
n
ib
ilit
y
r
elatio
n
[
1
]
[
5
]
p
r
o
d
u
ce
d
b
y
P
=
{e
l,
e2
,
e3
,
e4
,
e5
},
th
en
th
e
p
ar
titi
o
n
d
ef
i
n
ed
b
y
R
p
is
{{
b
1
,
b
6
},
{b
3
,
b
4
,
b
5
},
{b
2
}
}
b
ased
o
n
T
ab
le
-
1.
T
h
e
in
d
is
ce
r
n
ib
ili
t
y
r
elatio
n
a
n
d
th
e
p
ar
titi
o
n
w
o
u
ld
b
e
ch
an
g
ed
i
f
o
n
e
o
f
p
ar
a
m
eter
o
f
{
e1
,
e2
,
e
3
}
is
d
elete
d
f
r
o
m
P
.
s
o
th
u
s
all
o
f
th
e
s
e
th
r
ee
p
ar
a
m
eter
s
ar
e
in
d
is
p
en
s
ab
le
[
1
]
.
T
h
e
p
ar
titi
o
n
w
o
u
ld
b
e
ch
a
n
g
e
d
to
{{
b
1
,
b
6
}
,
{b
2
,
b
3
,
b
4
}
,
{
b
2
}}
,
if
{e
1
}
is
r
em
o
v
ed
f
r
o
m
P
.
T
h
e
p
ar
titi
o
n
w
o
u
ld
b
e
ch
a
n
g
e
d
to
{{
b
1
,
b
6
}
,
{b
3
,
b
4
,
b
5
}
,
{
b
2
}}
,
I
f
{e
2
}
is
r
em
o
v
ed
f
r
o
m
P
.
T
h
e
p
ar
titi
o
n
w
o
u
ld
b
e
ch
a
n
g
e
d
to
{{
b
1
,
b
6
}
,
{b
2
,
b
3
,
b
4
,
b
5
}}
,
if
{e
3
}
is
r
e
m
o
v
ed
f
r
o
m
P
.
T
h
e
p
ar
titi
o
n
R
p
w
o
u
ld
b
e
u
n
c
h
an
g
ed
,
I
f
{e
4
}
is
r
e
m
o
v
ed
f
r
o
m
P
.
T
h
e
p
ar
titi
o
n
R
p
w
o
u
ld
b
e
u
n
c
h
an
g
ed
,
I
f
{e
5
}
is
r
e
m
o
v
ed
f
r
o
m
P
.
So
th
e
co
n
clu
s
io
n
is
if
{e
4
,
e5
}
is
d
elete
d
f
r
o
m
P
,
t
h
en
th
e
i
n
d
is
ce
r
n
ib
ilit
y
r
elatio
n
[
1
]
an
d
th
e
p
ar
titi
o
n
R
p
ar
e
n
o
t v
ar
ian
t,
s
o
b
o
th
o
f
e4
an
d
e5
ar
e
d
is
p
en
s
ab
le
in
P
b
y
De
f
in
itio
n
2
[
1
]
.
So
b
y
De
f
i
n
itio
n
3
,
{e
1
,
e2
,
e
3
}
is
th
e
r
ed
u
ctio
n
o
f
P
=
{e
l,
e2
,
e3
,
e4
,
e
5
)
.
Fr
o
m
T
ab
le
1
i
t
is
p
r
o
v
ed
th
at
e4
an
d
e5
ar
e
n
o
t
r
ele
v
an
t
an
d
is
a
f
f
ec
t
th
e
c
h
o
ices
o
f
t
h
e
b
ik
e
s
i
n
ce
t
h
e
y
ta
k
e
t
h
e
s
a
m
e
v
alu
e
s
f
o
r
ev
er
y
b
ik
e.
So
th
e
Mr
.
XYZ
i
s
r
ea
d
y
to
m
ak
e
a
d
ec
is
io
n
to
p
u
r
ch
a
s
e
b
ik
e
b
ased
o
n
th
e
p
ar
am
e
ter
s
{e
1
,
e2
,
e3
}.
W
e
ca
n
ap
p
l
y
De
f
i
n
itio
n
3
to
p
ar
titi
o
n
th
e
o
b
j
ec
ts
b
ased
o
n
t
h
e
p
ar
a
m
eter
co
-
o
cc
u
r
r
en
c
e
an
d
th
e
s
u
p
p
o
r
t v
alu
e
[
1
]
.
Fo
r
T
a
b
le
1
d
ata
s
et,
th
e
f
o
llo
w
i
n
g
w
ill b
e
th
e
co
-
o
cc
u
r
r
en
c
e:
Co
-
o
cc
u
r
r
en
ce
(
b
1
)
=
{e
2
,
e3
,
e4
,
e5
}
Co
-
o
cc
u
r
r
en
ce
(
b
2
)
=
{e
1
,
e3
,
e4
,
e5
}
Co
-
o
cc
u
r
r
en
ce
(
b
3
)
=
{e
1
,
e4
,
e5
}
Co
-
o
cc
u
r
r
en
ce
(
b
4
)
=
{e
1
,
e4
,
e5
}
Co
-
o
cc
u
r
r
en
ce
(
b
5
)
=
{e
1
,
e4
,
e5
}
Co
-
o
cc
u
r
r
en
ce
(
b
6
)
=
{e
2
,
e3
,
e4
,
e5
}.
T
h
e
s
u
p
p
o
r
t v
alu
e
o
f
ea
ch
o
b
j
ec
t c
an
b
e
g
iv
e
n
,
b
y
D
e
f
i
n
itio
n
4
,
as
Su
p
p
o
r
t (
b
1
)
=4
Su
p
p
o
r
t (
b
2
)
=4
Su
p
p
o
r
t (
b
3
)
=3
Su
p
p
o
r
t (
b
4
)
=3
Su
p
p
o
r
t (
b
5
)
=3
Su
p
p
o
r
t
(
c6
)
=4
T
h
e
d
ata
s
et
ca
n
p
ar
titi
o
n
ed
b
a
s
ed
o
n
th
e
s
u
p
p
o
r
t v
alu
e
o
f
a
n
o
b
j
ec
t g
iv
e
n
b
y
:
{{
b
1
,
b
2
,
b
6
},
{b
3
,
b
4
,
b
5
}
}
W
h
en
t
h
e
p
ar
a
m
e
ter
s
e4
,
e5
ar
e
r
em
o
v
ed
t
h
e
cu
r
r
e
n
t
p
ar
titi
o
n
s
w
o
u
ld
n
o
t
b
e
c
h
an
g
ed
b
u
t
f
o
r
o
th
er
p
ar
am
eter
v
al
u
es
it
w
o
u
ld
b
e
ch
an
g
ed
.
So
t
h
e
co
n
clu
s
io
n
is
e4
an
d
e5
ar
e
t
h
e
r
ed
u
ct
s
f
o
r
t
h
e
s
a
m
p
le
d
ata
s
et
g
iv
e
n
i
n
T
ab
le
1
.
Fo
r
th
e
s
m
all
s
a
m
p
le
s
et
b
o
th
m
e
th
o
d
s
p
r
o
d
u
ce
d
th
e
s
a
m
e
r
ed
u
cts
.
So
th
is
tas
k
is
i
m
p
o
r
tan
t
w
h
e
n
d
ea
lin
g
w
it
h
a
lar
g
e
d
ata
s
e
t
.
T
h
is
m
et
h
o
d
o
r
alg
o
r
ith
m
i
s
also
b
en
e
f
icial
to
m
ea
s
u
r
es
d
if
f
er
e
n
t
t
y
p
e
s
o
f
p
er
f
o
r
m
a
n
ce
s
o
f
a
d
ata
s
et.
Fe
atu
r
e
s
elec
tio
n
is
o
n
e
o
f
t
h
e
i
m
p
o
r
tan
t
m
ea
s
u
r
es b
y
u
s
i
n
g
th
i
s
m
eth
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
A
R
ea
l Time
A
p
p
lica
tio
n
o
f S
o
ft S
et
in
P
a
r
a
mete
r
iz
a
tio
n
R
ed
u
ctio
n
fo
r
Dec
is
io
n
Ma
kin
g
…
(
Ja
n
meja
y
P
a
n
t
)
328
4.
P
E
RF
O
RM
ANCE O
F
SO
F
T
SE
T
O
VE
R
O
T
H
E
R
AP
P
RO
ACH
E
S
W
e
ca
n
n
o
t
u
s
e
class
ical
ap
p
r
o
ac
h
es
to
s
o
lv
e
co
m
p
licate
d
p
r
o
b
lem
s
i
n
en
g
in
ee
r
i
n
g
,
ec
o
n
o
m
ic
s
b
ec
au
s
e
o
f
v
ar
io
u
s
u
n
ce
r
tai
n
ti
es
in
th
e
s
e
ar
ea
.
T
h
er
e
ar
e
th
r
ee
th
eo
r
ies
w
h
ic
h
ca
n
co
n
s
id
e
r
as
m
a
th
e
m
atica
l
to
o
ls
f
o
r
d
ea
lin
g
w
it
h
u
n
ce
r
t
ain
tie
s
[
2
]
.
T
h
ese
th
eo
r
ies
ar
e
p
r
o
b
ab
ilit
y
,
f
u
zz
y
s
et
a
n
d
i
n
ter
v
al
m
at
h
e
m
a
tics
.
E
ac
h
th
eo
r
y
h
a
s
it
s
o
w
n
d
if
f
icu
lt
y
.
T
h
eo
r
y
o
f
p
r
o
b
ab
i
lit
y
ca
n
d
ea
l
o
n
l
y
w
i
th
s
t
o
ch
asti
ca
ll
y
s
tab
le
p
r
o
b
lem
s
[
2
]
.
I
n
ter
v
al
m
at
h
e
m
atics d
ea
ls
t
h
e
er
r
o
r
s
o
f
ca
lcu
l
atio
n
s
b
y
c
o
n
s
tr
u
cti
n
g
a
n
in
ter
v
al
esti
m
ate
f
o
r
th
e
ex
ac
t
s
o
l
u
tio
n
o
f
a
p
r
o
b
le
m
.
T
h
is
m
et
h
o
d
is
u
s
ef
u
l
i
n
m
an
y
ca
s
es
b
u
t
th
i
s
t
h
eo
r
y
is
n
o
t
s
u
f
f
icie
n
tl
y
ad
ap
tab
lef
o
r
p
r
o
b
lem
w
it
h
d
if
f
er
en
t
u
n
ce
r
tai
n
tie
s
[
2
]
.
Fu
zz
y
s
et
is
v
er
p
o
w
er
f
u
l
to
o
l
to
d
ea
l
w
it
h
co
m
p
licated
p
r
o
b
lem
s
b
u
t t
h
er
e
ex
is
t
s
a
d
if
f
ic
u
lt
y
h
o
w
to
s
et
t
h
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
i
n
ea
c
h
p
ar
ticu
la
r
ca
s
e
[
2
]
.
T
h
e
co
n
ce
p
t
o
f
s
o
f
t
th
eo
r
y
is
a
m
ath
e
m
atica
l
to
o
l
f
o
r
d
ea
lin
g
w
it
h
u
n
ce
r
tain
t
ies
w
h
ich
i
s
f
r
ee
f
r
o
m
th
e
ab
o
v
e
d
i
f
f
icu
l
ties
.
I
t
i
s
a
p
ar
am
e
ter
ized
to
o
l
to
d
ea
l
w
ith
ap
p
r
o
x
i
m
ate
v
al
u
e
a
n
d
u
n
ce
r
tai
n
t
y
.
E
ac
h
ap
p
r
o
x
im
a
te
d
escr
ip
tio
n
ca
n
d
iv
id
e
i
n
t
w
o
p
ar
ts
.
Fir
s
t
o
n
e
is
a
p
r
ed
icate
p
ar
t
an
d
s
ec
o
n
d
o
n
e
is
a
n
ap
p
r
o
x
im
a
te
v
al
u
e
s
et
[
1
]
.
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
w
e
d
is
cu
s
s
ed
d
a
ta
u
n
ce
r
tain
t
y
a
n
d
n
o
n
-
cr
is
p
d
ata.
W
e
u
s
ed
So
f
t
s
e
t
th
eo
r
y
t
o
co
n
v
er
t
a
s
m
al
l
d
ata
s
et
to
b
in
ar
y
v
al
u
ed
d
ata
s
et.
W
e
also
d
is
cu
s
s
e
d
h
o
w
to
r
ed
u
ce
th
e
u
n
n
ec
es
s
ar
y
p
ar
a
m
eter
s
as
r
ed
u
cts
f
r
o
m
th
e
d
ata
s
et.
T
h
e
lo
s
s
o
f
th
e
s
e
p
ar
a
m
e
ter
s
d
o
es
n
o
t
a
f
f
ec
t
t
h
e
o
r
ig
in
al
i
n
f
o
r
m
atio
n
o
f
th
e
u
s
ed
d
ata
s
et.
So
So
f
t
s
et
t
h
eo
r
y
is
also
u
s
ed
i
n
d
i
m
e
n
s
io
n
alit
y
r
ed
u
ctio
n
an
d
g
en
er
all
y
u
s
ed
to
p
r
o
v
id
e
b
etter
an
d
q
u
ick
d
ec
is
io
n
m
a
k
i
n
g
in
co
m
p
ar
e
o
f
p
r
ev
io
u
s
th
eo
r
ies.
RE
F
E
R
E
NC
E
S
[1
]
D.
A
sh
o
k
Ku
m
a
r,
R.
Re
n
g
a
sa
m
y
,
”
P
a
ra
m
e
teriz
a
ti
o
n
Re
d
u
c
ti
o
n
Us
in
g
S
o
f
t
S
e
t
T
h
e
o
r
y
f
o
r
Be
tt
e
r
De
c
isio
n
M
a
k
in
g
”
,
P
ro
c
e
e
d
in
g
s
o
f
th
e
2
0
1
3
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Pa
tt
e
rn
Rec
o
g
n
it
i
o
n
,
I
n
fo
rm
a
ti
c
s
a
n
d
M
o
b
il
e
En
g
i
n
e
e
rin
g
,
F
e
b
r
u
a
ry
2
1
-
22.
[2
]
D.
M
o
l
o
d
ts
o
v
,
“
S
o
f
t
S
e
t
t
h
e
o
ry
-
f
i
rst
re
su
lt
s”
,
Co
mp
u
ter
a
n
d
M
a
th
e
ma
ti
c
s wit
h
Ap
p
li
c
a
ti
o
n
s
.
1
9
9
9
,
3
7
(4
/5
)
,
1
9
-
3
1
.
[3
]
Ya
o
,
Y.Y.
“
Re
latio
n
a
l
i
n
terp
re
tatio
n
s
o
f
n
e
ig
h
b
o
r
h
o
o
d
o
p
e
ra
t
o
rs
a
n
d
r
o
u
g
h
se
t
a
p
p
ro
x
im
a
ti
o
n
o
p
e
ra
to
rs”
,
In
f
o
rm
a
ti
o
n
S
c
ien
c
e
s,
1
9
9
8
,
1
1
1
,
2
3
9
–
25
9
.
[4
]
T
u
tu
t
He
ra
wa
n
,
Ro
z
a
id
a
G
h
a
z
a
li
,
M
u
sta
f
a
M
a
t
De
ris,
”
S
o
f
t
S
e
t
T
h
e
o
re
ti
c
A
p
p
ro
a
c
h
f
o
r
Dim
e
n
sio
n
a
li
ty
Re
d
u
c
ti
o
n
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
D
a
ta
b
a
se
T
h
e
o
ry
a
n
d
Ap
p
li
c
a
ti
o
n
.
2
0
1
0
,
Vo
l.
3
,
N
o
.
2
.
[5
]
P
.
K.
M
a
ji
,
A
.
R.
Ro
y
a
n
d
R.
Bisw
a
s,
“
A
n
a
p
p
li
c
a
ti
o
n
o
f
so
f
t
se
t
s
in
a
d
e
c
isio
n
m
a
k
in
g
p
ro
b
lem
”
.
Co
mp
u
ter
a
n
d
M
a
th
e
ma
ti
c
s wit
h
A
p
p
li
c
a
ti
o
n
,
2
0
0
2
,
4
4
(8
/
9
),
1
0
7
7
-
1
0
8
3
.
[6
]
P
.
K.
M
a
ji
,
A
.
R.
Ro
y
a
n
d
R.
Bisw
a
s,
“
S
o
f
t
S
e
t
T
h
e
o
r
y
”
.
Co
mp
u
ter
a
n
d
M
a
th
e
m
a
ti
c
s
wit
h
Ap
p
li
c
a
ti
o
n
,
2
0
0
3
;
(4
5
)
,
555
-
5
6
2
,
[7
]
Ch
e
n
,
D.
"
T
h
e
p
a
ra
m
e
teriz
a
ti
o
n
re
d
u
c
ti
o
n
o
f
so
f
t
se
ts
a
n
d
it
s
a
p
p
li
c
a
ti
o
n
s"
,
Co
mp
u
ter
s
a
n
M
a
th
e
ma
ti
c
s
wit
h
Ap
p
li
c
a
ti
o
n
s
,
2
0
0
5
,
0
4
/0
5
.
[8
]
T
u
tu
t
He
ra
w
a
n
.
"
S
o
f
t
De
c
isio
n
M
a
k
in
g
f
o
r
P
a
ti
e
n
ts
S
u
sp
e
c
ted
I
n
f
lu
e
n
z
a
"
,
L
e
c
tu
re
No
tes
in
Co
mp
u
ter
S
c
ien
c
e
,
2
0
1
0
.
[9
]
M
a
n
m
a
th
Ku
m
a
r
Bh
u
y
a
n
,
Du
rg
a
P
ra
sa
d
M
o
h
a
p
a
tra,
S
rin
iv
a
s
S
e
th
i,
”
S
o
f
tw
a
re
Re
li
a
b
il
it
y
P
re
d
icti
o
n
u
si
n
g
F
u
z
z
y
M
in
-
M
a
x
A
lg
o
rit
h
m
a
n
d
Re
c
u
rre
n
t
Ne
u
ra
l
Ne
tw
o
rk
A
p
p
ro
a
c
h
”
,
I
n
e
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
c
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
2
0
1
6
,
0
4
/0
6
.
[1
0
]
No
o
r
Ch
o
li
s
Ba
sja
ru
d
d
i
n
,
Ku
s
p
riy
a
n
to
Ku
sp
riy
a
n
to
,
Did
in
S
a
e
f
u
d
in
,
Il
h
a
m
Kh
risn
a
Nu
g
ra
h
a
,
“
De
v
e
lo
p
in
g
A
d
a
p
ti
v
e
Cru
ise
Co
n
tro
l
Ba
se
d
o
n
F
u
z
z
y
L
o
g
ic
Us
in
g
H
a
rd
w
a
r
e
S
im
u
latio
n
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
c
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
2
0
1
4
,
0
4
/
0
6
.
[1
1
]
Ja
n
m
e
ja
y
P
a
n
t,
Am
it
Ju
y
a
l,
S
h
iv
a
n
i
Ba
h
u
g
u
n
a
,
“
S
o
f
t
se
t,
a
s
o
f
t
Co
m
p
u
ti
n
g
A
p
p
ro
a
c
h
f
o
r
Dim
e
n
sio
n
a
li
ty
Re
d
u
c
ti
o
n
,
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
In
n
o
v
a
ti
v
e
S
c
ien
c
e
,
E
n
g
i
n
e
e
rin
g
&
T
e
c
h
n
o
l
o
g
y
(
IJ
IS
ET
)
,
2
0
1
5
,
0
4
/0
2
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
He
is
w
o
rk
in
g
a
s
a
n
A
s
st.
P
r
o
f
e
ss
o
r
in
C
S
E
a
n
d
A
p
p
li
c
a
ti
o
n
s
d
e
p
a
rtm
e
n
t
o
f
G
ra
p
h
ic
Era
Hill
Un
iv
e
rsit
y
;
Bh
im
tal
Ca
m
p
u
s.
He
c
o
m
p
lete
d
h
is
M
.
T
e
c
h
in
In
f
o
rm
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
f
ro
m
G
EU
De
h
ra
d
u
n
.
He
h
a
s
a
n
e
x
p
e
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c
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o
f
a
ro
u
n
d
0
7
y
e
a
rs
o
f
tea
c
h
in
g
.
His
a
re
a
s
o
f
in
tere
st
a
re
M
a
c
h
in
e
L
e
a
rn
in
g
,
S
o
f
t
Co
m
u
p
ti
n
g
a
n
d
d
a
ta
M
i
n
in
g
.
He
h
a
s
tau
g
h
t
se
v
e
ra
l
c
o
re
su
b
jec
ts
li
k
e
C,
JA
V
A
,
DBMS
.
OS
e
tc.
a
s w
e
ll
a
s ad
v
a
n
c
e
d
s
u
b
jec
ts
li
k
e
S
o
f
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Co
m
p
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ti
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Da
ta M
in
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g
e
tc.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
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Vo
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7
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No
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1
,
Feb
r
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ar
y
2
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1
7
:
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–
329
329
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e
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.
T
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o
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e
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d
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ro
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r
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p
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Era
Un
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e
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tere
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s p
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De
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