Indonesian
Journal
of
Electrical
Engineering
and
Computer
Science
V
ol.
2,
No
.
1,
Apr
il
2016,
pp
.
187
193
DOI:
10.11591/ijeecs
.v2.i1.pp187-193
187
Finding
Kic
king
Rang
e
of
Sepak
T
akra
w
Game:
Fuzzy
Logic
and
Dempster
-Shaf
er
Theor
y
Appr
oac
h
Andino
Maseleno
*
,
Md.
Mahm
ud
Hasan
,
Muhammad
Muslihudin
,
and
T
ri
Susilo
wati
STMIK
Pr
ingse
wu,
Pr
ingse
wu,
Lampung,
Indonesia
F
aculty
of
Inf
or
mation
T
echnology
,
Kazakh
Br
itish
T
echnical
Univ
ersity
,
Kazakhstan
*
corresponding
author
,
e-mail:
andinomaseleno@y
ahoo
.com
Abstract
Sepak
takr
a
w
is
pla
y
ed
b
y
tw
o
regus
,
each
consisting
of
three
pla
y
ers
.
One
of
th
e
three
pla
y
ers
shall
be
at
the
bac
k
and
he
is
called
a
T
ek
ong.
The
other
tw
o
pla
y
ers
shall
be
in
front,
one
on
the
left
and
the
other
on
the
r
ight.
Ha
ving
v
olle
y
kic
k
ed
a
thro
w
from
the
net
b
y
a
team
mate
,
the
ball
m
ust
then
tr
a
v
el
o
v
er
the
net
to
begin
pla
y
.
Dur
ing
the
ser
vice
,
as
soon
as
the
T
ek
ong
kic
ks
the
ball,
all
the
pla
y
ers
are
allo
w
ed
to
mo
v
e
about
freely
in
thei
r
respectiv
e
cour
ts
.
The
no
v
el
approach
is
the
i
nteg
r
ation
within
a
Tsukamoto’
s
Fuzzy
reasoning
and
inf
erences
f
or
e
vidential
reasoning
based
on
Dempster-Shaf
er
theor
y
.
Sepak
takr
a
w
is
a
highly
comple
x
net-barr
ier
kic
king
spor
t
that
in
v
olv
es
dazzling
displa
ys
of
quic
k
refle
x
es
,
acrobat
ic
twists
,
tur
ns
and
s
w
er
v
es
of
the
agile
human
body
mo
v
ement.
Because
of
the
humans
in
v
olv
ement
in
the
game
,
the
Fuzzy
Logic
type
reasoning
are
the
most
appropr
iate
.
The
individual
r
ule
outputs
of
Tsukamoto’
s
Fuzzy
reasoning
scheme
are
cr
isp
n
umbers
,
and
theref
ore
,
the
functional
relationship
betw
een
the
input
v
ector
and
the
system
output
can
be
relativ
ely
easily
identified.
The
result
re
v
eals
that
if
T
ek
ong
is
kic
k
f
ar
and
front
pla
y
er
is
kic
k
near
then
another
regu’
s
pla
y
er
is
kic
k
f
ar
,
if
T
ek
ong
is
kic
k
near
and
front
pla
y
er
is
kic
k
f
ar
then
another
regu’
s
pla
y
er
is
kic
k
near
,
moreo
v
er
possibility
of
kic
king
r
ange
is
another
regu’
s
pla
y
er
is
kic
k
f
ar
in
kic
king
r
ange
.
K
e
yw
or
ds:
fuzzy
logic;
Dempster-Shaf
er
theor
y;
sepak
takr
a
w;
kic
king
r
ange
Cop
yright
c
2016
Institute
of
Ad
v
anced
Engineering
and
Science
1.
Intr
oduction
Mentioned
in
the
Mala
y
histor
ical
te
xt,
Sejar
ah
Mela
yu,
there
is
a
descr
iption
of
an
incident
where
Sultan
Mansur
Shahs
son,
Raja
Muhammad,
w
as
accidentally
hit
with
a
r
attan
ball
b
y
the
son
of
T
un
P
er
ak,
in
a
game
that
w
as
called
sepak
r
aga.
In
Thai
language
,
it
is
called
takr
a
w
,
meaning
twine-kic
k,
as
the
ball
w
as
made
of
r
attan
twines
.
The
game
became
popul
ar
throughout
the
Southeast
Asia
and
in
the
1940s
,
r
ules
w
ere
estab
lished
and
the
game
became
officially
kno
wn
as
sepak
takr
a
w
.
Sepak
takr
a
w
or
kic
k
v
olle
yball
is
a
spor
t
nativ
e
to
Southeast
Asia,
resemb
ling
v
olle
yball,
e
xcept
that
it
uses
a
r
attan
ball
and
only
allo
ws
pla
y
ers
to
use
their
f
eet
and
head
to
touch
the
ball.
A
cross
betw
een
f
ootball
and
v
olle
yball,
it
is
a
popular
spor
t
in
Thailand,
Cambodia,
Mala
ysia,
Laos
,
Philippines
and
Indonesia.
The
str
ategies
in
Sepak
takr
a
w
are
also
v
er
y
similar
to
those
in
v
olle
yball.
The
receiving
team
will
attempt
to
pla
y
the
takr
a
w
ball
to
w
ards
the
f
ront
of
the
net,
making
the
best
use
of
their
three
hits
,
to
set
a
nd
spik
e
the
ball
[1].
In
pre
vious
w
or
k
[2],
w
e
used
Fuzzy
Logic
to
find
kic
king
r
ange
of
sepak
takr
a
w
game
.
The
organization
of
the
paper
is
as
f
ollo
ws:
sectio
n
2
discusses
Fuzzy
Logic
and
Dempster-Shaf
er
theor
y
.
Section
3
discusses
using
Fuzzy
Logic
and
Dempster-Shaf
er
theor
y
in
sepak
takr
a
w
ga
me
.
Conclusion
is
presented
in
section
4.
2.
Fuzzy
Logic
and
Dempster
-Shaf
er
theor
y
Fuzzy
Logic
can
handle
prob
lems
with
imprecise
da
ta
and
giv
e
more
accur
ate
results
.
Prof
essor
L.A.
Zadeh
introduced
the
concept
of
Fuzzy
Logic
[3];
soon
after
,
resea
rchers
used
this
theor
y
f
or
de
v
eloping
ne
w
algor
ithms
and
decision
analysis
.
Fuzzy
sets
,
proposed
b
y
Zadeh
[3]
Receiv
ed
J
an
uar
y
21,
2016;
Re
vised
F
ebr
uar
y
27,
2016;
Accepted
March
12,
2016
Evaluation Warning : The document was created with Spire.PDF for Python.
188
ISSN:
2502-4752
as
a
fr
ame
w
or
k
to
encounter
uncer
tainty
,
v
agueness
and
par
tial
tr
uth,
represents
a
deg
ree
of
membership
f
or
each
member
of
the
univ
erse
of
discourse
to
a
subset
of
it.
Assume
that
the
specific
case
of
composition
based
on
the
Max-Min
oper
ator
,
then
the
special
case
of
the
abo
v
e
gener
al
model
of
Fuzzy
reasoning
can
be
defined
using
equation
1
as
B
0
(
y
)
=
_
x
2
A
((
A
0
(
x
)
^
R
(
x;
y
))
=
max
x
2
A
min
(
A
0
(
x
)
;
R
(
x;
y
)
(1)
The
Dempster-Shaf
er
theor
y
or
iginated
from
the
concept
of
lo
w
er
and
upper
probability
induced
b
y
a
m
ultiv
alued
mapping
b
y
Dempster
[4],
[5].
F
ollo
wing
this
w
or
k
his
student
Glenn
Shaf
er
[6]
fur
ther
e
xtended
the
theor
y
in
his
book
”A
Mathematical
Theor
y
of
Evidence”,
a
more
thorough
e
xplanation
of
belief
functions
.
The
Dempster-Shaf
er
theor
y
[6]
assumes
that
there
is
a
fix
ed
set
of
m
utually
e
xclusiv
e
and
e
xhaustiv
e
elements
called
h
ypotheses
or
propositions
and
symboliz
ed
b
y
the
Greek
letter
,
represented
as
=
f
h
1
;
h
2
;
:::;
h
n
g
,
where
h
i
is
called
a
h
ypothesis
or
proposition.
A
h
ypothesis
can
be
an
y
subset
of
the
fr
ame
,
in
e
xample
,
to
singletons
in
the
fr
ame
or
to
combinations
of
elements
in
the
fr
ame
.
is
also
called
fr
ame
of
discer
nment
[6].
A
basic
probability
assignment
(bpa)
is
represented
b
y
a
mass
function
m
:
2
!
[0
;
1]
[6].
Whe
re
2
is
the
po
w
er
set
of
.
The
sum
of
all
basic
probability
assignment
of
all
subsets
of
the
po
w
er
set
is
1
which
embodies
the
concept
that
total
belief
has
to
be
one
[7].
Y
ager
and
File
v
attempted
to
present
a
Fuzzy
inf
erence
system
based
on
Fuzzy
Dempster-Shaf
er
mathematical
theor
y
of
e
vidence
which
combining
the
probabilistic
inf
or
mation
in
the
output
[8].
The
basic
probability
assignment
is
a
p
r
imitiv
e
of
e
vidence
theor
y
.
Gener
ally
speaking,
the
ter
m
basic
probability
assignment
does
not
ref
er
to
probability
in
t
he
classical
sense
.
The
bpa,
represented
b
y
m,
defines
a
mapping
of
the
po
w
er
set
to
the
inter
v
al
betw
een
0
and
1,
where
the
bpa
of
the
n
ull
set
is
0
and
the
bpas
of
all
the
subsets
of
the
po
w
er
set
is
1.
In
Fuzzy
Logic
,
tw
o-v
alued
logic
often
considers
0
to
be
f
alse
and
1
to
be
tr
ue
.
Fuzzy
Logic
deals
with
tr
uth
v
alues
betw
een
0
and
1,
and
these
v
alues
are
considered
as
the
intensity
or
deg
rees
of
tr
uth.
Dempster-Shaf
er
theor
y
pro
vides
a
met
hod
to
combine
the
pre
vious
measures
of
e
vidence
of
diff
erent
sources
[6].
This
r
ule
assumes
that
these
sources
are
independent.
The
combination:
m
=
m
1
m
2
,
also
called
or
thogonal
sum,
is
defined
according
to
the
Dempster’
s
r
ule
of
combi-
nation
[6],
giv
en
in
equation
2.
It
can
be
applied
repetitiv
ely
when
the
sources
are
more
than
tw
o
.
After
the
combination,
a
decision
can
be
made
among
the
diff
erent
h
ypotheses
according
to
the
decision
r
ule
chosen.
(
m
1
m
2
)(
A
)
=
8
>
>
>
>
>
<
>
>
>
>
>
:
0;
A
=
0
X
B
i
\
B
j
=
A
m
1
(
B
i
)
m
2
(
B
j
)
1
X
B
i
\
B
j
6
=0
m
1
(
B
i
)
m
2
(
B
j
)
;
A
6
=
0
(2)
Where
A
2
2
,
B
i
2
2
and
B
j
2
2
.
T
o
use
Dempster-Shaf
er
mathematical
theor
y
of
e
viden
ce
,
there
m
ust
be
the
f
easib
le
measures
to
deter
mine
basic
probability
assignment.
3.
Using
Fuzzy
Logic
and
Dempster
-Shaf
er
Theor
y
in
Sepak
T
akra
w
Game
When
a
game
begins
b
y
one
ser
v
e
,
a
ball
can
be
touched
b
y
the
attac
k
of
one
time
to
three
times
.
The
pla
y
er
can
use
a
head,
a
bac
k,
legs
,
and
an
ywhere
e
xcept
f
or
the
ar
m
from
the
shoulder
to
the
point
of
the
finger
.
Suppose
w
e
are
giv
en
pla
y
er
position
and
kic
king
r
ange
in
the
beginning
of
sepak
takr
a
w
game
as
sho
wn
in
T
ab
le
1.
IJEECS
V
ol.
2,
No
.
1,
Apr
il
2016
:
187
193
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
189
T
ab
le
1.
Pla
y
er
position
and
kic
king
r
ange
P
osition
Kic
king
Range
(m)
F
ar
Near
T
ek
ong
6.50
4
F
ront
Pla
y
er
7.50
2
Opponent’
s
Pla
y
er
9.50
4.50
W
e
ha
v
e
defined
the
realistic
r
ules
according
to
the
kic
king
r
ange
calculations
,
these
r
ules
will
become
the
kno
wledge
base
of
each
of
the
prob
lems
considered
in
the
sepak
takr
a
w
game
.
It
is
necessar
y
to
sa
y
that
the
whole
kno
wledge
does
not
necessar
ily
ha
v
e
to
be
tr
anslated
in
r
ules
,
sometimes
some
of
the
r
ules
can
be
redundant.
T
ab
le
2
sho
ws
the
r
ule
to
find
kic
king
r
ange
in
sepak
takr
a
w
game
.
T
ab
le
2.
The
Rule
Rule
IF
AND
THEN
T
ek
ong
is
F
ront
pla
y
er
is
Opponent’
s
pla
y
er
Rule
1
Near
F
ar
Near
Rule
2
Near
Near
Near
Rule
3
F
ar
F
ar
F
ar
Rule
4
F
ar
Near
F
ar
[Rule
1]
IF
T
ek
ong
is
near
AND
F
ront
Pla
y
er
is
f
ar
THEN
Opponent’
s
Pla
y
er
is
near
[Rule
2]
IF
T
ek
ong
is
near
AND
F
ront
Pla
y
er
is
near
THEN
Opponent’
s
Pla
y
er
is
near
[Rule
3]
IF
T
ek
ong
is
f
ar
AND
F
ront
Pla
y
er
is
f
ar
THEN
Opponent’
s
Pla
y
er
is
f
ar
[Rule
4]
IF
T
ek
ong
is
f
ar
AND
F
ront
Pla
y
er
is
near
THEN
Opponent’
s
Pla
y
er
is
f
ar
Dur
ing
the
Sepak
takr
a
w
game
,
both
teams
will
mak
e
diff
erent
po
w
erful
mo
v
es
to
kic
k
and
spik
e
the
ball
to
go
to
the
opponent
side
and
f
all
within
the
boundar
y
line
of
the
cour
t,
pla
y
ers
tr
y
to
pla
y
the
ball
to
w
ard
the
front
of
the
net,
making
the
best
use
of
their
three
hits
to
pass
,
set
and
spik
e
.
Suppose
w
e
are
giv
en
5
conditions
kic
king
r
ange
in
which
already
kno
wn
as
sho
wn
in
T
ab
le
3.
T
ab
le
3.
Kic
king
r
ange
of
tek
ong
and
front
pla
y
er
P
osition
Condition
Condition
1
Condition
2
Condition
3
Condition
4
Condition
5
T
ek
ong
6
5.50
5
4.5
4.25
F
ront
Pla
y
er
2.5
3.50
4.50
5.50
6.50
Kic
king
r
ange
of
tek
ong
is
the
r
ange
of
kic
king
the
ball
from
tek
ong
to
front
pla
y
er
.
Kic
king
r
ange
of
front
pla
y
er
is
the
r
ange
of
kic
king
the
ball
from
front
pla
y
er
to
opponents
pla
y
er
.
Figure
1
sho
ws
g
r
aphic
of
kic
king
r
ange
of
tek
ong
and
front
pla
y
er
.
Fuzzy
Logic
and
Dempster-Shaf
er
Theor
y
to
Find
Kic
king
Range
of
Sepak
T
akr
a
w
Game
Evaluation Warning : The document was created with Spire.PDF for Python.
190
ISSN:
2502-4752
Figure
1.
Gr
aphic
of
kic
king
r
ange
of
tek
ong
and
front
pla
y
er
T
ek
ong
(
T
ek
ong
near
[
x
])
=
8
>
<
>
:
1
;
x
4
6
:
5
x
2
;
4
<
x
6
:
5
0
;
x
6
:
5
(3)
(
T
ek
ong
f
ar
[
x
])
=
8
>
<
>
:
0
;
x
4
x
4
2
:
5
;
4
<
x
6
:
5
1
;
x
6
:
5
(4)
Membership
v
alue
(
T
ek
ong
near
[6])
=
6
:
5
6
2
:
5
=
0
:
20
(
T
ek
ong
f
ar
[6])
=
6
4
2
:
5
=
0
:
80
Fr
ont
Pla
y
er
(
F
ront
Pla
y
er
near
[
y
])
=
8
>
<
>
:
1
;
y
5
:
5
7
:
5
y
5
:
5
;
5
:
5
<
y
7
:
5
0
;
y
5
:
5
(5)
(
F
ront
Pla
y
er
f
ar
[
y
])
=
8
>
<
>
:
0
;
y
5
:
5
y
2
5
:
5
;
5
:
5
<
y
7
:
5
1
;
y
7
:
5
(6)
Membership
v
alue
(
F
r
ontP
l
ay
er
near
[2
:
5])
=
7
:
5
2
:
5
5
:
5
=
0
:
9
(
F
r
ontP
l
ay
er
f
ar
[2
:
5])
=
2
:
5
2
5
:
5
=
0
:
09
Opponent
Pla
y
er
(
Opponent
Pla
y
er
near
[
w
])
=
8
>
<
>
:
1
;
w
4
:
5
9
:
5
w
5
;
4
:
5
<
w
9
:
5
0
;
w
9
:
5
(7)
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V
ol.
2,
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.
1,
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il
2016
:
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IJEECS
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191
(
Opponent
Pla
y
er
f
ar
[
w
])
=
8
>
<
>
:
0
;
w
4
:
5
w
4
:
5
5
;
4
:
5
<
w
9
:
5
1
;
w
9
:
5
(8)
w
v
alue
f
or
each
r
ule
with
min
function.
Figure
2
sho
ws
g
r
aphic
of
fuzzy
membership
function.
Figure
2.
Gr
aphic
of
fuzzy
membership
function
1
=
(
T
ek
ong
near
)
\
(
F
ront
Pla
y
er
f
ar
)
;
1
=
min
(
(
T
ek
ong
near
[6]
\
(
F
ront
Pla
y
er
f
ar
[2
:
5])
1
=
min
(0
:
2
;
0
:
09)
;
1
=
0
:
09
F
rom
the
calculation
abo
v
e
,
w
e
ha
v
e
f
our
r
ules
.
ON
is
opponents
pla
y
er
near
in
r
ange
,
OF
is
opponents
pla
y
er
f
ar
in
r
ange
.
With
Dempster-Shaf
er
Theor
y:
1.
Rule
1
m
1
f
O
N
g
=
0
:
09
;
m
1
f
g
=
1
0
:
09
=
0
:
91
2.
Rule
2
m
2
f
O
N
g
=
0
:
2
;
m
2
f
g
=
1
0
:
2
=
0
:
8
The
calculation
of
the
combined
m
1
and
m
2
is
sho
wn
in
T
ab
le
4.
Each
cell
of
the
tab
le
contains
the
intersection
of
the
corresponding
propositions
from
m
1
and
m
2
along
with
the
product
of
their
individual
belief
.
Fuzzy
Logic
and
Dempster-Shaf
er
Theor
y
to
Find
Kic
king
Range
of
Sepak
T
akr
a
w
Game
Evaluation Warning : The document was created with Spire.PDF for Python.
192
ISSN:
2502-4752
T
ab
le
4.
The
first
combination
of
the
r
isk
of
Rule
1
and
Rule
2
f
ON
g
0.2
0.8
f
ON
g
0.09
f
ON
g
0.018
f
ON
g
0.07
0.91
f
ON
g
0.18
0.73
The
first
tw
o
bpas
m
1
and
m
2
are
calculated
to
yield
a
ne
w
bpa
m
3
b
y
a
co
mbination
r
ule
as
f
ollo
ws:
m
3
f
O
N
g
=
0
:
018+0
:
18+0
:
07
1
0
=
0
:
27
;
m
3
f
g
=
0
:
73
1
0
=
0
:
7
3.
Rule
3
m
4
f
O
F
g
=
0
:
09
;
m
4
f
g
=
1
0
:
09
=
0
:
91
The
calculation
of
the
combined
m
3
and
m
4
is
sho
wn
in
T
ab
le
5.
Each
cell
of
the
tab
le
contains
the
intersection
of
the
corresponding
propositions
from
m
3
and
m
4
along
with
the
product
of
their
individual
belief
.
T
ab
le
5.
The
second
combination
of
Rule
1,
Rule
2
and
Rule
3
f
OF
g
0.2
0.8
f
ON
g
0.27
;
0.02
f
ON
g
0.25
0.73
f
OF
g
0.07
0.66
The
second
tw
o
bpas
m
3
and
m
4
are
calculated
to
yield
a
ne
w
bpa
m
5
b
y
a
combination
r
ule
as
f
ollo
ws:
m
5
f
O
F
g
=
0
:
07
1
0
:
02
=
0
:
07
;
m
5
f
O
N
g
=
0
:
25
1
0
:
02
=
0
:
26
;
m
5
f
g
=
0
:
66
1
0
:
02
=
0
:
67
4.
Rule
4
m
6
f
O
F
g
=
0
:
8
;
m
6
f
g
=
1
0
:
8
=
0
:
2
The
calculation
of
the
combined
m
5
and
m
6
is
sho
wn
in
T
ab
le
6.
Each
cell
of
the
tab
le
contains
the
intersection
of
the
corresponding
propositions
from
m
5
and
m
6
along
with
the
product
of
their
individual
belief
.
T
ab
le
6.
The
third
combination
of
Rule
1,
Rule
2,
Rule
3,
and
Rule
4
f
OF
g
0.8
0.2
f
OF
g
0.07
f
OF
g
0.06
f
OF
g
0.01
f
ON
g
0.26
;
0.21
f
ON
g
0.05
0.67
f
OF
g
0.54
0.13
The
third
tw
o
bpas
m
5
and
m
6
are
calculated
to
yield
a
ne
w
bpa
m
7
b
y
a
combination
r
ule
as
f
ollo
ws:
m
7
f
O
F
g
=
0
:
06+0
:
54+0
:
01
1
0
:
21
=
0
:
77
;
m
7
f
O
N
g
=
0
:
05
1
0
:
21
=
0
:
06
;
m
7
f
O
F
g
=
0
:
13
1
0
:
21
=
0
:
16
Finally
,
the
final
r
anking
of
t
he
deg
ree
of
belief
is
0.77
>
0.06
<
0.16.
The
deg
ree
of
belief
is
the
m
7
f
O
F
g
that
is
equal
to
0.77
which
means
the
possibility
of
kic
king
r
ange
is
another
regu’
s
pla
y
er
is
f
ar
in
kic
king
r
ange
as
sho
wn
in
the
figure
3.
IJEECS
V
ol.
2,
No
.
1,
Apr
il
2016
:
187
193
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
193
Figure
3.
Gr
aphic
of
fuzzy
membership
function
4.
Conc
lusion
W
e
ha
v
e
descr
ibed
a
method
to
find
kic
king
r
ange
of
sepak
takr
a
w
game
using
Tsukamoto’
s
Fuzzy
reasoning
and
Dempster-Shaf
er
theor
y
.
The
v
agueness
present
in
the
definition
of
ter
ms
is
consistent
with
the
inf
or
mation
contained
in
the
conditional
r
ules
when
obser
ving
some
com-
ple
x
process
.
Ev
en
though
the
set
of
linguistic
v
ar
iab
les
and
their
meanings
is
compa
tib
le
and
consistent
with
the
set
of
conditional
r
ules
used,
the
o
v
er
all
outcome
of
the
qualitativ
e
process
is
tr
anslated
into
obje
c
t
iv
e
and
quantifiab
le
results
.
Fuzzy
mathematical
tools
and
the
calculus
of
Fuzzy
IF-THEN
r
ules
pro
vide
a
most
useful
par
adigm
f
or
the
automation
and
implementation
of
an
e
xtensiv
e
body
of
human
kno
wledge
heretof
ore
not
embodied
in
the
quantitativ
e
modelling
process
.
These
mathematical
tools
pro
vide
a
means
of
shar
ing,
comm
u
nicating,
and
tr
ansf
err
ing
this
human
subjectiv
e
kno
wledge
of
systems
and
processes
.
The
result
re
v
eals
that
if
tek
ong
is
f
ar
and
front
pla
y
er
is
near
then
another
regu’
s
pla
y
er
is
f
ar
,
if
tek
ong
is
near
and
front
pla
y
er
is
f
ar
then
another
regu’
s
pla
y
er
is
near
,
moreo
v
er
possibility
of
kic
king
r
ange
is
another
regu’
s
pla
y
er
is
f
ar
in
kic
king
r
ange
.
Ref
erences
[1]
Inter
national
Sepak
T
akr
a
w
F
eder
ation.
La
ws
of
the
Game
Sepak
T
akr
a
w
in
The
24th
Kings
Cup
Sepaktakr
a
w
W
or
ld
Championship
2009
Prog
r
am.
Bangk
ok,
Thailand,
J
uly
2-7,
2009.
[2]
Maseleno
A,
Hasan
MM.
Finding
Kic
king
Range
of
Sepak
T
akr
a
w
Game:
A
Fuzzy
Logic
Approach.
TELK
OMNIKA,
V
ol.14,
No
.3,
pp
.
1-8,
2015.
[3]
Zadeh
LA.
Fuzzy
Sets
.
Inf
or
mation
and
Control,
V
ol.8,
pp
.338-353,
1965.
[4]
Dempster
AP
.
Upper
and
lo
w
er
proba
bilities
induced
b
y
a
m
ultiv
alued
mapping.
Ann.
Math.
Stat.
38:
325-339,
1967.
[5]
Dempster
AP
.
A
Gener
alization
of
Ba
y
esian
inf
erence
.
Jour
nal
of
the
Ro
y
al
Statistical
Society
.
30:
205-247,
1968.
[6]
Shaf
er
G.
A
Mathematical
Theor
y
of
Evidence
.
Pr
inceton
Univ
ersity
Press
,
Ne
w
Jerse
y
,
1976.
[7]
Y
ager
RR.
Ar
it
hmetic
and
other
oper
ations
on
Dempster-Shaf
er
str
uctures
.
Inter
national
Jour-
nal
of
Man-Machine
Studies
.
25:
357-366,
1986.
[8]
Y
ager
RR,
File
v
P
.
Including
Probabilistic
Uncer
tainty
in
Fuzzy
Logic
Controller
Modeling
Using
Dempster-Shaf
er
Theor
y
,
IEEE
T
r
ansactions
on
Systems
,
Man,
and
Cyber
netics
.
25:
1221-
1230,
1990.
Fuzzy
Logic
and
Dempster-Shaf
er
Theor
y
to
Find
Kic
king
Range
of
Sepak
T
akr
a
w
Game
Evaluation Warning : The document was created with Spire.PDF for Python.