TELKOM
NIKA
, Vol.9, No.1, April 2011,
pp. 37~4
6
ISSN: 1693-6
930
accredited by D
G
HE (DIKTI
), Decree No: 51/Dikti/Kep/2010
¢
37
Re
cei
v
ed No
vem
ber
2
8
th
, 2010; Revi
se
d March 12
th
, 2011; Accept
ed April 4
th
, 2011
A Fuzzy
Topsis Multiple-Attribute Decision Making for
Scholarship Selection
Shof
w
a
tul ‘Uy
un*
1
, Imam
Riadi
2
1
Informatics De
partment, State Islamic Un
ive
r
sit
y
of Sun
an
Kalij
ag
a
Jl. Marsda Adi
s
ucipto N
o
. 1 Yog
y
ak
arta 55
2
81, T
e
lp. (0274
) 5197
39, F
a
x (027
4) 54
097
1
2
Information S
ystem Departm
ent, Univers
i
t
y
of Ahmad Da
hl
an
Jl, Prof.Dr.Soepmomo, Jantur
an, Yog
y
ak
arta
,
T
e
lp (0274) 5
635
15, F
a
x (
0
2
74) 56
46
04
e-mail: sh
of
w
a
t
u
l.u
y
u
n
@u
in-s
uka.ac.id
*
1
, imam_ria
di@
u
a
d
.ac.id
2
A
b
st
r
a
k
Biaya
pe
nd
idik
an s
e
maki
n
maha
l, ba
nyak
ma
has
isw
a
meng
ajuk
an
be
a
s
isw
a
. Ratusa
n b
ahka
n
ribu
an for
m
ul
ir pen
gaj
ua
n be
a
s
isw
a
harus di
seleksi
ole
h
sp
onsor. Per
m
as
ala
han ters
ebu
t bertujua
n
unt
u
k
me
mili
h be
ber
apa
altern
atif terba
i
k ber
das
a
r
kan b
eber
ap
a
atribut (kriteri
a
)
yang
dig
u
n
a
k
an. Da
la
m ra
n
g
ka
pen
ga
mb
il
an k
eputus
an
pa
da
per
masal
a
h
a
n
yan
g
bersifat f
u
zz
y
d
a
p
a
t di
g
unak
an
F
u
zz
y
Multipl
e
Attrib
u
t
e
Decisi
on
Mak
i
ng (F
MADM).
Pada
p
ene
liti
an i
n
i
dil
a
kuk
a
n pe
mod
e
la
n
me
ng
gun
aka
n
Unifie
d Mo
de
lli
ng
Lan
gu
age (UM
L
) pad
a F
M
ADM deng
an
met
ode T
O
PSIS dan W
e
ig
hted P
r
oduct unt
uk me
nye
l
eksi ca
l
o
n
pen
eri
m
a
be
as
isw
a
akad
e
m
ik
dan
non
aka
d
e
mik di
Univ
er
sitas Isla
m Ne
geri S
una
n Ka
l
ijag
a
. Data y
a
ng
dig
unak
an
ad
ala
h
d
a
ta fu
zz
y
da
n cris
p. Hasi
l p
e
n
e
liti
an
menu
nj
ukk
an
bahw
a M
e
tode T
O
PSIS da
n
W
e
ighte
d
Pr
oduct pa
da
F
M
ADM dapat d
i
gu
nak
an u
n
tuk se
leksi b
easisw
a
. Hasil s
e
l
e
ksi
mer
e
ko
mend
a
s
ikan ma
hasis
w
a
yang me
mi
liki
tin
g
ka
t
kelay
a
kan
pal
ing tin
g
g
i
unt
uk mend
ap
atka
n
beas
isw
a
berd
a
sarka
n
nil
a
i pr
eferens
i yan
g
di
mil
i
ki.
Ka
ta
k
unc
i
: F
u
zz
y
Multi
p
l
e
Attribute D
e
cisi
on
Ma
king, T
O
PSIS, W
e
ighted Product, Schol
ar
ship
A
b
st
r
a
ct
As the e
duc
ation fe
es ar
e b
e
co
mi
ng
mor
e
expe
nsiv
e, more stud
ents
app
ly for sch
o
l
arshi
p
s
.
Cons
equ
ently, hun
dreds and even
tho
u
sa
nd
s
of
applic
ati
o
n
s
need to b
e
h
and
led
by the spons
or. T
o
solve
the pr
obl
e
m
s,
some a
l
tern
ativ
es bas
ed
on
se
veral
attri
butes
(criteria)
ne
ed
to be s
e
l
e
cted.
In ord
e
r to
mak
e
a
de
ci
sio
n
on
su
ch
fu
z
z
y
p
r
ob
l
e
m
s
, Fu
z
z
y
Mu
l
t
i
p
le
Attri
bute
D
e
ci
si
on
Maki
n
g
(FMD
AM) ca
n be
a
p
p
l
i
e
d
.
In
this study, Un
ified M
ode
lin
g
Lan
gu
age (
U
ML) in F
M
AD
M w
i
th T
O
PSIS and W
e
ig
hted Pro
duct (
W
P)
meth
ods
is
ap
plie
d to s
e
l
e
ct
the ca
ndi
dates
for ac
a
d
e
m
ic
and
no
n-ac
ade
mic
scho
l
arsh
i
p
s at U
n
ivers
i
tas
Islam
Neg
e
ri S
una
n Kal
ija
ga.
Data us
ed w
e
r
e
a crisp
an
d fu
zz
y
data. T
h
e
result
s show
that T
O
PSIS an
d
W
e
ighte
d
Pro
d
u
ct F
M
ADM methods c
an
be
used t
o
se
l
e
c
t
the most suit
abl
e ca
ndi
date
s
to receiv
e th
e
schol
arshi
p
s si
nce the
prefer
ence v
a
lu
es a
ppli
ed
in
this
meth
od c
an s
how
app
lica
n
ts
w
i
th the hig
h
e
st
elig
ib
ility.
Ke
y
w
ord:
F
u
z
z
y
Multi
p
l
e
Attribute Dec
i
sio
n
Makin
g
, T
O
PSIS, W
e
ighted Pr
oduct, Schol
ar
ship
1. Introduc
tion
The nation
a
l edu
cation
system defines e
ducat
ion a
s
conscio
u
s an
d
plans
some
efforts
to create
a g
ood l
earning
atmosp
he
re
and l
earning
pro
c
e
ss. The
r
efore,
stu
d
e
n
ts can
a
c
tively
develop thei
r potentials
so they w
ill have strong reli
gious faith,
sel
f
-cont
rol, st
rong personality,
intellectu
a
l, e
t
hics
and
skil
ls for the
m
se
lves, so
ci
ety, and
cou
n
try. In line with t
hose pu
rpo
s
es
are fou
r
edu
cation visi
on
s by UNES
C
O (United
Nation on Edu
c
ation, Sci
e
n
t
ific and Cult
ural
Orga
nization
) in 21
st
centu
r
y. Those a
r
e
(1) l
earning
how to
l
earn, (2) l
earning
how to
do, (3
)
learni
ng
ho
w to be,
and
(4) lea
r
nin
g
how to liv
e t
ogethe
r. In
o
r
de
r to
su
pp
ort the
proce
ss,
Ministry of Religiou
s
Affairs ha
s be
en o
fferi
ng sch
o
la
rshi
ps fo
r stu
dents at
UIN
Sunan Kalija
ga
in a
re
gula
r
b
a
si
s, in
cludi
n
g
sch
o
larshi
p
s
fo
r
stude
nts with
high
a
c
ademi
c
a
c
hi
e
v
ements. So
me
resea
r
ch on appli
c
ation of
multi-attribut
e deci
s
ion m
a
kin
g
(MADM
)
has be
en wi
dely cond
uct
ed.
In its
develo
p
ment, resea
r
ch
o
n
MA
DM is al
so fo
cus
on
ho
w t
he d
e
ci
sio
n
make
rs give
their
prefe
r
en
ce
s
on
certai
n alt
e
rnative
s
a
n
d
crite
r
ia
[1]. T
y
pically, the d
e
ci
sion
ma
ke
rs
gave
nume
r
ic
weig
hting pre
f
eren
ce
s to make the co
mputation
ea
sier. Howeve
r, current ling
u
istic p
r
efere
n
ce
s
are
also a
ppli
ed to
simplify
the de
ci
sion
make
rs
in
giving thei
r o
p
ini
ons. F
o
r exa
m
ple, the val
u
e
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 9, No. 1, April 2011
: 37 – 46
38
of alternative
A1 is "very good" in the criterion C1
, while altern
ative A1 is "mod
erate" in crite
r
ion
C2. Th
e imp
o
r
tance level
o
f
C1 i
s
"very
high", while
criterio
n C2 h
a
s
a
“lo
w
” leve
l of impo
rtan
ce
,
and so on.
If the
preferen
ce
is given
li
n
guisti
c
a
lly, then fu
zzy lo
gi
c
can
be
use
d
to hel
p
solv
in
g
the probl
em. Fuzzy logic i
s
very effecti
v
e to so
lve the MADM p
r
oblem whe
r
e
the given da
ta is
ambigu
ou
s o
r
pre
s
e
n
ted li
n
guisti
c
ally [2]. In fac
t, the
r
e
are
a
lot of
d
e
ci
sion
s
creat
ed in
the fu
zzy
environ
ment [3].
The
MA
DM method
i
s
used
to solve
a ca
se whi
c
h
h
a
s seve
ral alternative
s
a
n
d
prio
rity
for variou
s attributes. MA
DM tech
niqu
e is a popul
ar tech
niqu
e and ha
s wid
e
ly been use
d
in
several field
s
, includi
ng: e
ngine
erin
g, e
c
on
omic
s, m
anag
ement
s, tran
spo
r
tatio
n
plan
ning, e
t
c.
Several app
roache
s
that h
a
ve
be
en dev
elope
d
a
r
e
calcul
ating th
e
wei
ghts of M
A
DM p
r
o
b
le
ms,
su
ch a
s
th
e
eigenve
c
to
r method
an
d ELECT
R
E.
The
pape
r
descri
bed
th
e formul
ation
o
f
weig
hting in
MADM case with fuzzy de
cisi
on matrix
wa
s gen
erat
ed by two pe
ople [4]. Fuzzy
multi attribute
de
cisi
on
ma
king
(F
MADM) h
a
s b
een
use
d
to
sele
ct future
lectu
r
er
at Depa
rt
ment
of Comp
uter Scien
c
e, Fa
culty of Indu
strial T
e
chno
logy, Islamic University o
f
Indone
sia (UII)
usin
g ge
netic algo
rithm to
find the val
ue of a
ttri
but
e wei
ghts.
T
he value
is searche
d
thro
ugh
subj
ective ap
proa
ch. After the weight of ever
y alternative ha
s b
een foun
d, the gra
d
e
s
were
pro
c
e
s
sed to
determi
ne o
p
t
imal altern
atives; th
o
s
e a
r
e the a
ppli
c
a
n
ts
who
have
been
a
c
cept
ed
as
the future
lec
t
urer
at Department of Comput
er Sc
ienc
e
UII. In additi
on, the FMADM has
also
been u
s
e
d
to determin
e
the best lo
catio
n
for a wa
reh
ouse (from
several alte
rn
ative location
s),
usin
g gen
etic algorithm
s in
finding the value of attribu
t
e weight
s [5], [6].
Fuzzy mo
del
is al
so
u
s
ed
to sel
e
ct
a p
r
oje
c
t
for re
search and de
velopment (R
&
D)
with m
u
lti-cri
t
eria d
e
ci
sio
n
ma
king.
The
proj
ect
sel
e
ctio
n u
s
ed
several
qualitative
and
quantitative criteria. The
criteria
in
clu
de co
st
an
d
som
e
of the
obtai
ned
advanta
g
e
s if th
e p
r
oj
e
c
t
was implemented. Howev
e
r, mode
ls
produced
by Ramadan [7] st
ill
can
not be
used in group.In
orde
r to anticipate a g
r
o
up asse
ssme
nt, Zhou et
al. [8] implemented fuzzy
logic in de
ci
sion
sup
port
syste
m
to asse
ss
proje
c
t p
r
od
u
c
ed
by
stu
d
e
n
ts. The
proj
ect is rate
d b
y
more th
an
one
person
with
several fuzzy
criteri
a
. The
best proj
e
c
t is a project
with the high
est memb
ership
value. Another metho
d
for the deci
s
io
n sup
port
sy
stem is an
alytical hierarch
y proce
s
s (A
HP
)
fuzzy. AHP fuzzy can
hel
p use
r
s to m
a
ke d
e
ci
sio
n
s
on b
o
t
h
st
r
u
ct
ur
ed
a
nd semi stru
ctured
probl
em
s [9]. In addition,
[10] fuzzy an
alytical
hie
r
archy process
is al
so u
s
ed
to help ma
ke
deci
s
io
ns
on
the process of multicrite
ria robot
sel
e
ction. Re
se
arche
r
s
[1
1] have
de
scri
b
e
d
several p
r
o
c
e
dure
s
on
a m
odified te
chni
que fo
r o
r
de
r prefe
r
e
n
ce b
y
simila
rity to ideal
sol
u
tio
n
(TOPSIS) me
thod so that t
he TOPSIS can al
so b
e
u
s
ed for
a case
of deci
s
io
n m
ade in
group
or
multi-criteri
a
grou
p de
cisi
on maki
ng (MCG
DM).
In
this study, TOPSIS algorithm is u
s
e
d
in
FMADM to asse
s the eligibi
lity of scholarship
reci
pient
s and h
e
lping
the deci
s
ion
make
r to make
a quick, accu
rate and o
b
je
ctive deci
s
io
n
.
TOPSIS algorithm is u
s
ed
to evaluate the re
sult
s of prod
uctio
n
proce
s
se
s relat
ed to
environ
ment. Data u
s
ed in
the algorith
m
is a cris
p
dat
a so that the output
is a qu
antitative data.
The outp
u
t data will be e
v
aluated an
d
used
as
a
n
input for the
next pro
c
ess [12]. TOPSIS
method i
s
sui
t
able to
solve
the p
r
obl
em
de
cisi
on
m
a
king
by intro
duci
ng
qua
ntity multiplicati
on
operation of triang
ula
r
fuzzy numb
e
r.
A case stu
d
y indicate
s th
at the metho
d
can
be ap
plied
effectively wi
th less information
and
the q
uantit
ati
v
e re
sult i
s
obje
c
tive an
d
re
asona
ble
[13].
Linea
r p
r
og
ramming
mod
e
l for m
u
lti
attribute g
r
o
up de
ci
sion
makin
g
(MAGDM
) h
a
s
b
een
introdu
ce
d by
Xu [14]. T
he
given p
r
efe
r
e
n
ce
inform
ati
on
can
be
pre
s
ente
d
in
the
s
e th
ree
di
sti
n
ct
uncertain preference st
ructures:
interval utility values; interval
fuzzy preference rel
a
tions; and
interval multi
p
licative p
r
ef
eren
ce
rel
a
tions. T
he
fo
rmat of preference info
rma
t
ion attribute
s
in
MAGDM is
not uniform. Initially, data g
a
thered fr
om
the deci
s
ion
make
rs with
variou
s form
ats.
For th
at Xu [15] propo
se
a metho
d
tha
t
can
accom
m
odate
all of
deci
s
io
n ma
kers’
pro
p
o
s
a
l
s.
Therefore,
a
re
sea
r
ch to
develop
an
unified
mod
e
ling la
ngu
a
g
e
(
U
M
L)
for Fuzz
y TOPSIS
multiple attrib
ute de
cisi
on
makin
g
(FMA
DM) i
s
need
ed to a
s
se
ss the eligibility
of schol
arsh
ip
reci
pient
s an
d helpin
g
the deci
s
io
n maker to make a quick, accu
ra
te and obje
c
ti
ve deci
s
ion.
2. Res
earc
h
Method
Req
u
ire
m
ent
gatheri
ng a
nd mod
e
ling
activities are the step
s whe
r
e the
neede
d
material
s a
r
e
colle
cted. A
n
alysis
of a
c
tivity diagr
am
result
s in
som
e
potential
a
c
tors to
be
co
me
the use
r
of th
e system
und
er devel
opme
n
t. In
general
, the method
s which a
r
e u
s
ed for multipl
e
attribute de
ci
sion ma
kin
g
in this study can be sho
w
n
in Figure 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
¢
A
Fuzz
y To
ps
is Mult
iple
-A
t
t
r
ibut
e D
e
ci
sio
n
Makin
g
for Schola
r
ship Selection (Sh
o
fwatul
‘
U
yu
n
)
39
Figure 1
.
The
multiple attribute de
cisi
on
making
The
Req
u
ire
m
ent an
alysi
s
a
c
tivity is t
he process
of analysi
n
g
system re
q
u
irem
ent
based o
n
the
list of nee
ds colle
cted i
n
previou
s
a
c
ti
vities. The m
e
thod
whi
c
h i
s
u
s
ed to
asse
s
the suita
b
le
can
d
idate
s
f
o
r FMA
D
M
ca
se
s a
r
e T
O
PSIS dan
Weig
hted Produ
ct. The b
a
si
c
con
c
e
p
t of T
O
PSIS method is th
at the
best alte
rn
ative not only h
a
s the
sh
orte
st dista
n
ce from
positive i
deal
sol
u
tion, b
u
t also h
a
s the
long
est
dista
n
ce
with
neg
ative ideal
so
lution. Weight
ed
prod
uct (WP) is a stan
da
rd form of F
M
ADM. That
con
c
ept h
a
s been u
s
e
d
widely in
several
MADM mod
e
l
to solve a problem p
r
a
c
tically [16].
2.1.
FMADM
In Gene
ral, the fuzzy multip
le attribute de
cisi
on ma
king
procedu
re fol
l
ows these st
eps:
Step 1
:
Set a numbe
r of alternative
s
and
some attrib
utes or
crite
r
ia.
Decisi
on-makers determine some
alternatives
that will
be
selected
following several
attributes or
criteria.
For ex
ample S
= {S
1, S2
, ..., Sm} is the
s
e
t
of
alternative;
K =
{K1
,
K2, ..., Kn} is
the set of at
tribute or
c
r
it
eria
, and A
= {aij | i=1,2,...
,m; j=
1,2,...,n
} is
the
matrix deci
s
io
n whe
r
e aij is
the nume
r
ical
value of alternative i for attribute j.
Step 2:
Evaluation of Fuzzy Set
There are two activities at this step:
a)
Cho
o
si
ng a
set of rating for the
weight
of criteri
a
a
nd the de
gre
e
s
of suitabili
ty for
each altern
ative with the cri
t
eria.
b)
Evaluating the weig
ht of cr
iteria and d
e
g
r
ee of suita
b
il
ity for each al
ternative with
th
e
criteria.
2.2. TOPSIS
Method
In general, the TOPSIS method proc
ed
ure follo
ws th
ese
step
s:
Step 1: The Normali
z
ed f
u
zzy deci
s
io
n
matrix
In TOPSIS, the perfo
rma
n
c
e of ea
ch alt
e
r
native ne
ed
s to be grade
d with equ
ation 1.
∑
=
=
m
i
ij
ij
ij
x
x
r
1
2
; with x= deci
s
ion mat
r
ix; i=1,2, … ,m; and j=1,2, … ,n.
(1)
Step 2: The weig
hted no
rmalize
d
fuzzy deci
s
ion mat
r
ix
Positive ideal
solution
+
A
and
negative ide
a
l solutio
n
−
A
ca
n be determin
ed ba
sed o
n
the weig
hted
norm
a
lized ra
ting (
ij
y
) a
s
:
;
ij
i
ij
r
w
y
=
with i=1,2,…,
m; and j=1,2,
…,n.
(2)
Step 3: Determining po
sitive and ne
gative ideal solutio
n
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40
Positive ideal
solution mat
r
ix is calculate
d
with equ
ation 3, whe
r
ea
s the neg
ative ideal
solutio
n
matri
x
based o
n
e
quation 4.
);
,...,
,
(
2
1
+
+
+
+
=
n
y
y
y
A
(
3
)
);
,...,
,
(
2
1
−
−
−
−
=
n
y
y
y
A
(
4
)
Step 4: The distan
ce of ea
ch candi
date
fr
om po
sitive and ne
gative ideal solution
The dista
n
ce betwe
en alternative
i
A
with positive ideal
solution can b
e
formulate
d
with
equatio
n 5:
∑
=
+
+
−
=
n
j
ij
i
i
y
y
D
1
2
)
(
;
i=1,2,…,m.
(5)
The dista
n
ce betwe
en alternative
i
A
with negative ideal
solutio
n
ca
n be formul
ated
with
equatio
n 6:
∑
=
−
−
−
=
n
j
i
ij
i
y
y
D
1
2
)
(
;
i=1,2,…,m.
(6)
Step 5: Determinin
g the value of
prefe
r
ence for ea
ch
alternative
The prefere
n
c
e value for e
a
ch alte
rnativ
e (
i
V
) is given a
s
:
+
−
−
+
=
i
i
i
i
D
D
D
V
;
i
=
1
,
2
,
…
,
m
.
(
7
)
2.3. WP
Meth
od
In general, the FMADM we
ighted produ
ct proce
d
u
r
e follows the
s
e
step
s:
Step 1: The Normali
z
ed f
u
zzy deci
s
io
n
matrix
The WP method uses
multiply to relate attri
bute rating,
in which ea
ch of it has to be
powere
d
with
its associ
ate
d
weig
ht.
Step 2: In WP, the performance of each alternative
i
A
need
s to be g
r
adin
g
with e
quation 8.
j
w
ij
n
j
i
x
S
1
=
∏
=
;
with
i=
1,2,…,m.
(8)
whe
r
e
∑
j
w
= 1.
j
w
is the powe
r
wi
th positive value for advant
age attribute,
and with
negative valu
e for co
st attribute.
Step 3: The relative prefe
r
ence fo
r ea
ch
alternative is given as:
∏
∏
=
=
=
n
j
w
j
n
j
w
ij
i
j
j
x
x
V
1
*
1
)
(
; with i=
1, 2,…,m.
(9)
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A
Fuzz
y To
ps
is Mult
iple
-A
t
t
r
ibut
e D
e
ci
sio
n
Makin
g
for Schola
r
ship Selection (Sh
o
fwatul
‘
U
yu
n
)
41
3. Resul
t
s
and
Analy
s
is
The sch
o
larships
com
e
from governm
ent
agen
cie
s
, State Ente
rpri
se
s an
d
several
private fou
n
d
a
tions that
concern
with
t
he a
d
van
c
em
ent of e
d
u
c
at
ion. Annu
ally, the Mi
nistry
of
Religio
us Affairs offe
rs a
c
ademi
c
and n
on ac
ademi
c
schola
r
ship
s for stud
ents at
UIN.
3.1.
Requir
e
ment Gathe
r
ing a
nd Modelling
3.1.1 Requir
e
ment G
a
th
e
r
ing
Req
u
ire
m
ent
s
gath
e
rin
g
activities were
aimed
to analyze
the schola
r
ship selectio
n
pro
c
e
s
s at th
e Fa
culty of
Scien
c
e
and
Tech
nolo
g
y.
The
pro
c
e
s
s
wa
s d
e
scribe
d
in
the
activ
i
ty
diagram sho
w
n in Figu
re
2.
Figure 2. Activity Diagram for Asse
ssi
ng
the Feasibility of Scholarshi
p
Figure 3. Use
case diag
ra
m for sup
e
r a
d
min
use
r
Figure 4. Use
case diag
ra
m for use
r
ad
min
3.1.2 Actor a
nd Use
Cas
e
The use ca
se
diagra
m
for each acto
r was:
a)
Super Admi
n User
Super-ad
m
in
use
r
wa
s
a use
r
with
an authorit
y to i
nput an
d up
-date data
on
the sy
stem.
Super
admin
input data
a
bout the type
, criteri
a
an
d
rating d
e
ci
si
on sch
o
larshi
ps that
were
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42
use
d
for sch
o
larship
sele
ction.
Use
case
dia
g
ra
m
for
a
supe
r admin
u
s
e
r
is
sh
own in
Figure 3.
b) Admin
User
Admin u
s
e
r
i
s
a
user
wh
o
s
e ta
sk is to
sele
ct
studen
ts who
we
re
applying fo
r
a sch
o
larshi
p
.
Admin can in
put stud
ent d
a
ta and
the t
y
pe of
sch
o
l
a
rship
and it
s criteri
a
. Th
e syste
m
will
displ
a
y the re
sults of the schol
arship
se
lect
ion u
s
ing
TOPSIS method. Use ca
se diagram for
an admin u
s
e
r
is shown in Figure 4.
3.1.2 Sequen
ce Diagr
a
m
A sequ
en
ce
diagram in
Unified M
o
d
e
ling La
ngu
a
ge (UML
) is a kin
d
of intera
ction
diagram that
sho
w
s h
o
w pro
c
e
s
ses
work a
nd in
what order.
The se
que
nce di
agram
for
schola
r
ship selectio
n is sh
own in Fig
u
re
5.
Figure 5. Sequen
ce dia
g
ra
m
3.2.
Requir
e
ment Analy
s
is for Fuzzy
Multiple Attribute Decision Making
The propo
se
d method wh
ich is ap
plie
d to solve this pro
b
lem a
nd the com
p
utational
pro
c
ed
ure we
re su
mma
rize
d as follo
ws:
Step 1: Set a
numbe
r of alternative
s
and
some attrib
utes or
crite
r
ia.
There we
re 3
crite
r
ia u
s
ed
as a b
a
si
s for
deci
s
ion m
a
king in
acade
mic sch
o
larship. The
criteria include:
C1 =
cumul
a
tive grade p
o
i
n
t;
C2 = in
com
e
/ economi
c
p
a
rent
s;
C3 = number
of family members
As for the
prefe
r
en
ce,
aca
demi
c
scholarshi
p
wa
s give
n to
students with
a g
o
o
d
aca
demi
c
a
c
hievement, a
nd comin
g
from a lo
w
cla
s
s with
a big
family memb
er. On
the
other h
and,
there
we
re 9
crite
r
ia u
s
e
d
to sele
ct the candid
a
te
s for n
on a
c
ademi
c
schola
r
ship. These criteria
are co
nsi
s
te
d of:
C1 =
cumul
a
tive grade p
o
i
n
t;
C2 = in
com
e
/ economi
c
p
a
rent
s;
C3 = number
of family members;
C4 =
religio
u
s
and mo
ral a
s
pe
cts of Pan
c
a
s
ila;
C5 = a
s
p
e
ct
s of reasoning
and ide
a
lism;
C6 = a
s
p
e
ct
s of leadership
and loyalty;
C7 =
as
pec
t
s of interes
t
s
,
talents
and sk
ills
;
C8 = a
s
p
e
ct
s of profession
al activities / intern
ship
s;
C9 = a
s
p
e
ct
s of communit
y
service;
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¢
A
Fuzz
y To
ps
is Mult
iple
-A
t
t
r
ibut
e D
e
ci
sio
n
Makin
g
for Schola
r
ship Selection (Sh
o
fwatul
‘
U
yu
n
)
43
The preferen
ce for n
o
n
-
a
c
ademi
c
sch
o
larship
reci
pie
n
ts wa
s
stud
ents who ha
d
cre
a
tive
achi
evement
s and j
o
ined
in extracurricular a
c
tivities. The admini
s
trative re
qui
reme
nts
for stu
dent
s to get a
schol
arship
we
re:
Indone
sia
n
ci
tizen, a
c
tive
stude
nt; passed the
Sosiali
s
a
s
i Pembelaj
ara
n
(intro
du
ctory
aca
demi
c
) prog
ram at
UIN
Sun
an Kalijaga;
passe
d u
s
e
r
edu
cation
wit
h
a valu
e b
e
t
ween
60
-74;
cum
u
lative
grad
e p
o
int
≥
3,0; at
least the
3rd
seme
ste
r
stu
dent; not receiving
a
schol
arship from a
nother spon
sor at the
moment an
d
encl
o
sed a
certificate of g
ood
cond
uct.
The pu
rp
ose
of this de
cisi
on was
to find the best thre
e ca
n
d
idate
s
for th
e sc
hola
r
ship
base
d
on sp
ecific
crite
r
ia.
There
were 15
peo
ple (alte
r
nat
e
)
wh
o pa
sse
d
the admi
n
i
s
tration
and
surpa
s
sed th
e pa
ssi
ng
grad
e given i
n
ce
rtain co
n
d
ition: MH01,
MH02, MH0
3
, MH04, M
H
05, MH06,
MH07,
MH08, M
H
09
, MH10, MH1
1
, MH12, MH13, MH14 d
a
n
MH15.
Step 2: Evaluation of Fuzzy Set
The
cho
o
si
ng
oaf a
set of
rating
s for cri
t
er
ia weig
hts and
d
e
g
r
ee
s of
suitability of
each
alternative i
s
based the
cri
t
eria. Top of f
o
rm
ling
u
isti
c variable
s
re
pre
s
ente
d
th
e weig
ht
of deci
s
ion fo
r ea
ch attrib
ute (criteri
on).
The
de
ci
sion
for schol
arshi
p
crite
r
ia
wa
s grad
ed
as it sho
w
n i
n
Table 1. Th
e deci
s
ion fo
r non aca
dem
ic schola
r
ship
criteri
a
wa
s grad
ed
as it sho
w
n in
Table 2.
Table 1. Ling
uistic vari
able
s
for the
impo
rtance wei
ght
of each criterion
Criteria
Linguistic Variable
Fuzz
y
Numbe
r
C1
Ver
y
High
(VH)
(0.75, 1.00
, 1.00)
C2
High (H)
(0.50, 0.75
, 1.00)
C3
Medium (M)
(0.25, 0.50
, 0.75)
Table 2. lingu
istic varia
b
le
s for the
importance
weig
ht of each
crite
r
i
o
n
Criteria
Linguistic Variable
Fuzz
y
Numbe
r
C1
Medium (M)
(0.25, 0.50
, 0.75)
C2
Ver
y
Lo
w (VL
)
(0.00, 0.25
, 0.50)
C3
Ver
y
Lo
w (VL
)
(0.00, 0.25
, 0.50)
C4
Ver
y
High
(VH)
(0.75, 1.00
, 1.00)
C5
Ver
y
High
(VH)
(0.75, 1.00
, 1.00)
C6
Ver
y
High
(VH)
(0.75, 1.00
, 1.00)
C7
High (H)
(0.50, 0.75
, 1.00)
C8
Ver
y
High
(VH)
(0.75, 1.00
, 1.00)
C9
High (H)
(0.50, 0.75
, 1.00)
All
crite
r
ia
u
s
ed fuzzy data
except for the firs
t and third criteri
on. Cumulative gra
de point
and numb
e
r of
family
me
mbers used crisp
data. Crit
eria of
in
com
e
/
e
c
on
omic pare
n
ts (C2) had
comp
atibility degree
with
some alte
rnati
v
es de
ci
si
on:
T (Comp
a
tibi
lity) = {S, F,
B}. Membe
r
ship
function
for e
a
ch
elem
ent
wa
s
rep
r
e
s
en
ted u
s
ing
tria
ngula
r
fu
zzy
numbe
rs
with
S = small
wi
th
fuzzy n
u
mb
ers (0.10, 0.10,
0.50); F
= F
a
ir
with
fuzzy
numb
e
rs (0.00, 0.50, 0.9
0
) a
nd B
= B
i
g
with fuzzy nu
mber (0.50, 0
.
90, 0.90).
On the
othe
r
hand, th
e
crit
eria
of C4, C5, C6,
C7,
C8 an
d
C9
have compatibilit
y degree
with som
e
alt
e
rnatives decision: T (Com
patibility)
= {VP, P, F, G,
VG}. }. Membership functi
on
for each ele
m
ent is rep
r
e
s
ente
d
usin
g triangul
ar
fuzzy numbe
rs
with VP = Very Poor with fuzzy
numbe
rs of (0.00, 0.00, 0.25); P = Poo
r
with fu
zzy numbe
rs (0.0
0, 0.25, 0.50) ; F = Fair with
fuzzy num
bers at (0.25, 0.50,
0.75); G = Goo
d
with fuzzy numbe
rs (0.50, 0.75,
1.00) and VG =
Very Good
with fuzzy n
u
mbe
r
s
(0.75
,
1.00, 1.
00).
Weight
s for the criteria
and de
gre
e
s
of
suitability of each
alternative were
evaluated with the
criteria. De
ci
sion criteri
a
gi
ven by decisi
on
makers were graded to
assess the
eligi
b
ility of schol
arship
reci
pients. The degree of suitability
crite
r
ia an
d d
e
ci
sion alte
rn
atives we
re shown in Tabl
e 3.
3.3. TOPSIS
Method
Data o
n
Tabl
e 3 were fi
rst
norm
a
lized
usin
g eq
uatio
n 1 in o
r
de
r t
o
obtain
normalize
d
matrices fo
r both acade
m
i
c and
non
-a
cad
e
mic
sc
h
o
larship
s
. A norm
a
lized
weig
ht of fuzzy
deci
s
io
n wa
s then cal
c
ula
t
ed based on
equation 2 f
o
llowin
g
the
previou
s
step
. Positive ideal
solut
i
o
n
(
+
A
)
i
s
cal
c
ulate
d
by
equ
ation 3. While
ne
gative
ide
a
l soluti
on (
−
A
) wa
s
cal
c
ulat
e
d
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44
usin
g equatio
n 4 for each type of schol
arship. The re
sult of acad
emis sch
o
larship i
s
sho
w
n in
Table 4, whil
e the re
sult of non academi
c
schol
arship
is sh
own in Table 5.
Table 3. The
final aggregat
ed re
sults o
b
tained fro
m
grading the n
u
m
eri
c
al exam
ple pre
s
e
n
ted
in
this pap
er by deci
s
io
n makers
Alternative
C1
C2
C3 C4 C5 C6 C7 C8
C9
MH1 3,22
S
7
VP
VP
VG
G
VG
F
MH2 3,34
F
3
VP
VP
VG
G
VG
F
MH3 3,51
F
3
F
VP
VG
G
VG
F
MH4 3,48
B
2
F
P
P
G
P
VG
MH5 3,77
B
2
P
P
VP
F
P
VG
MH6
3,80
B
3
G
F VP
F VP
VG
MH7
3,50
F
4
G
F F F
VP
VG
MH8 3,00
F
5
VG
VG
F
VP
G
B
MH9
3,12
S
4
F VG F
VP
G
B
MH10
3,90
S
3
VP G
VG
VP G
B
MH11
3,58
B
2
P
G
G
VG
G
B
MH12
3,72
B
2
G G G
VG
VP
VP
MH13
3,12
B
1
VG
VP
VP
G
VG
P
MH14
3,01
S
3
F
P
P
G
VG
P
MH15
3,92
F
4
F
F
VP
VP
VG
F
Table 4. positive and
negative ide
a
l solutio
n
s fo
r aca
demi
c
schol
arship
1
y
2
y
3
y
Solusi Ideal posit
if
)
(
+
n
y
0,291
0,363
0,258
Solusi Ideal negatif
)
(
−
n
y
0,223
0,040
0,037
Table 5. po
sitive and neg
ative ideal solut
i
ons for n
on a
c
ad
emic
scho
larship
1
y
2
y
3
y
4
y
5
y
6
y
7
y
8
y
9
y
Solusi Ideal posit
if
)
(
+
n
y
0,450
0,091
0,000
0,444
0,465
0,408
0,303
0,346
0,276
Solusi Ideal negatif
)
(
−
n
y
0,110
0,010
0,000
0,444
0,000
0,000
0,000
0,000
0,000
Table 6. Re
sult of TOPSIS for aca
demi
c
and non a
c
a
demic
schola
r
shi
p
Alternative
Academic Scholarship
Non Academic Scholarship
positive
D
negative
D
i
V
Rank
positive
D
negative
D
n
V
Rank
MH1
0.395
0.016
0.039
15
0.668
0.593
0.472
10
MH2
0.182
0.219
0.547
8
0.664
0.599
0.474
9
MH3
0.179
0.222
0.552
7
0.541
0.639
0.542
6
MH4
0.049
0.373
0.883
4
0.581
0.464
0.444
13
MH5
0.331
0.162
0.328
15
0.699
0.374
0.348
15
MH6
0.074
0.359
0.829
6
0.613
0.521
0.459
12
MH7
0.198
0.119
0.501
10
0.502
0.555
0.525
7
MH8
0.229
0.177
0.436
11
0.385
0.753
0.661
1
MH9
0.346
0.111
0.243
14
0.450
0.646
0.589
3
MH10
0.039
0.376
0.907
1
0.567
0.632
0.572
5
MH11
0.045
0.374
0.893
3
0.348
0.661
0.632
2
MH12
0.039
0.375
0.904
2
0.482
0.652
0.575
4
MH13
0.059
0.391
0.868
5
0.658
0.616
0.484
8
MH14
0.338
0.147
0.304
13
0.567
0.499
0.468
11
MH15
0.196
0.207
0.514
9
0.619
0.495
0.444
14
The dista
n
ce
betwee
n
alte
rnative
i
A
with their ide
a
l po
sitive and neg
ative solution
are
comp
uted
usi
ng eq
uation
5 and
6 o
n
ce
the ide
a
l so
l
u
tions
are ob
tained. Prefe
r
rential val
ue f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
¢
A
Fuzz
y To
ps
is Mult
iple
-A
t
t
r
ibut
e D
e
ci
sio
n
Makin
g
for Schola
r
ship Selection (Sh
o
fwatul
‘
U
yu
n
)
45
each altern
ative (
i
V
)
is
comp
uted usi
ng eq
uation 7. A larg
e
r
value sh
ows that alternative
i
A
is
prefe
rre
d. Th
e result of TOPSIS comp
utation is
sh
own in Tabl
e
6. Student
with the high
est
value for a
c
a
demic
schola
r
shi
p
is M
H
1
0
while M
H
8
is that of hig
hest value fo
r non
-a
cad
e
m
ic
schola
r
ship a
c
cordi
ng to T
O
PSIS method.
3.4. WP
Meth
od
A fuzzy set fo
r each criterio
n is define
d
. This
set is tra
n
sformed into
its fuzzy nu
mber to
be n
o
rm
alize
d
in
orde
r to
obtain it
s
normal
weight.
T
he p
r
efe
r
en
ce for alte
rnati
v
e
i
A
(
i
S
)
and
the relative preferen
ce fo
r each altern
ative (
i
V
)
are
sho
w
n in Tabl
e 7. Student with the highest
value for a
c
a
demic
schola
r
shi
p
is M
H
1
0
while M
H
8
is that of hig
hest value fo
r non
-a
cad
e
m
ic
schola
r
ship a
c
cordi
ng to weighted p
r
od
u
c
t method.
Table 7. Re
sult of Weighte
d
Produ
ct for
aca
demi
c
an
d non a
c
ad
e
m
ic schol
arsh
ip
A
l
te
r
n
at
i
v
e
A
cad
em
i
c
S
c
hol
a
r
s
h
i
p
N
o
n
A
c
a
d
em
i
c
S
c
h
o
l
a
r
sh
i
p
i
S
i
V
Rank
i
S
i
V
Rank
MH1 0.15
0.07
4
0.00
0.00
4
MH2 0.07
0.03
7
0.00
0.00
5
MH3 0.08
0.04
6
0.00
0.00
6
MH4 0.06
0.03
8
1.19E-12
0.02
2
MH5 0.07
0.03
9
0.00
0.00
7
MH6 0.05
0.02
14
0.00
0.00
8
MH7 0.06
0.03
10
0.00
0.00
9
MH8 0.04
0.02
15
4.99E-11
0.97
1
MH9 0.26
0.13
3
0.00
0.00
11
MH10
0.43
0.22
1
0.00
0.00
12
MH11
0.07
0.03
11
0.00
0.00
15
MH12
0.07
0.03
12
0.00
0.00
13
MH13
0.11
0.05
5
0.00
0.00
14
MH14
0.33
0.17
2
1.73E-13
0.01
3
MH15
0.06
0.03
13
0.00
0.00
15
4. Conclu
sion
It can be
con
c
lud
ed from t
he re
sult
s an
d analysi
s
th
at modelin
g u
s
ing
UML in
FMADM
with TOPSIS and weighted
produ
ct meth
od ca
n be ap
plied for sch
o
larship sele
ction. Some UM
L
element
s were inco
rp
orate
d
within this
study, su
ch
as: activity diagram, use case and
sequ
en
ce
diagram. TO
PSIS and we
ighted p
r
odu
ct can
be u
s
ed for fuzzy
and/or
cri
s
p
data FMADM
.
A
sele
ction b
a
sed on tho
s
e
method
s pro
v
ide simila
r
p
r
odu
ct for its first re
sult. The preferre
ntial
values for b
o
th of those
methods a
r
e neverthel
e
ss different due to the d
i
fferences in
their
matrices
no
rmalizatio
n p
r
oce
s
s. A stu
dent with th
e high
est va
lue is
re
com
m
ende
d for
the
schola
r
ship.
R
e
fe
re
nc
es
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e
rano T
.
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gen
o M.
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u
zz
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heor
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ond
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¢
ISSN: 16
93-6
930
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: 37 – 46
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