Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 5
,
O
c
tob
e
r
201
6, p
p
. 2
462
~246
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
5.1
094
6
2
462
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Multicriteria Group Deci
sion Making Using Fuzzy
Approach for Evaluating
Criteria of Electrician
Wiwien Hadi
kurniaw
ati
1
, Khabib Mus
t
of
a
2
1
Faculty
of
Info
rmation Techno
log
y
, Un
iversitas Stikubank,
Semarang, Indonesia
2
Department of
Computer Scien
ce and Electron
ics,
Universitas Ga
djah Mad
a
, Y
o
g
y
ak
arta, Indon
esia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 20, 2016
Rev
i
sed
Ju
l 19
,
20
16
Accepte
d
J
u
l 30, 2016
This paper presents an approach
of
fuzzy
m
u
lticr
i
teri
a group decis
i
on m
a
king
in det
e
rm
ining a
ltern
ativ
es to so
lve th
e sel
ect
ion
problem
of the
ele
c
tri
c
i
a
n
through a competency
test. Fuzzy
approa
ch is used to determine the highest
priority
of altern
ativ
e electrician who ha
s kno
wledge and ability
that best fits
the given p
a
ram
e
ters.
Linguistic variable
s are pr
esented b
y
tr
ian
gular fu
zzy
num
bers
. The
y
a
r
e us
ed to repres
ent a s
ubjec
tive
as
s
e
s
s
m
ent of the decis
i
on-
makers so that uncertainty
and impreci
sion in the selection pro
cess can b
e
minimized. Fuzzy
appro
ach r
e
quire transfor
ming crisp data to f
u
zzy
numbers. Output of the best alternat
ives is generated b
y
r
a
nking method.
Ranking has been made base on eight
cri
t
er
ia
which m
a
ke the
evalua
tion
basis of each
alternative. Rank
in
g of th
e results is determined
using differ
e
nt
value of optimism index (
).
The fuzz
y m
u
lt
i crite
ria de
cis
i
on m
a
king
(FMCDM) calculation
is using the best
alt
e
rn
ativ
e us
ing thre
e valu
e o
f
optim
ism
index. The result of c
a
lcu
l
at
ion shows that the sam
e
altern
ativ
e
reach
ed from
different
index of
optim
is
m
.
This
alte
rnat
ive is
t
h
e highes
t
priority
of d
ecision making pro
c
ess.
Keyword:
Electrician
F
u
z
z
y
ap
pro
a
ch
Gr
ou
p deci
si
o
n
m
a
ki
ng
Mu
lticriteria
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
W
i
wien
Ha
dik
u
r
n
iawati,
Facu
lty of Inform
at
io
n
Techno
log
y
,
Un
i
v
ersitas Stik
ub
an
k,
Tri
l
o
m
b
a Jua
n
g
1
Sem
a
rang.
Em
a
il: wiwien
@edu
.un
i
sb
ank
.
ac.i
d
1.
INTRODUCTION
In
frast
ruct
ure
devel
opm
ent
i
n
In
d
onesi
a
i
s
ra
pi
dl
y
g
r
owi
n
g
.
T
h
e e
ffect
o
f
t
h
i
s
de
vel
o
pm
ent
need
s
m
o
re ele
m
ents
of infra
structure de
velopm
ent such as
hum
a
n res
o
urces
.
Worker as a
human res
o
urces is
one
of t
h
e im
port
a
nt elem
ents that affects
the survi
v
al
an
d t
h
e
i
m
pl
ement
a
t
i
on
o
f
c
onst
r
uct
i
o
n
p
r
oject
s
.
Im
provi
ng t
h
e
quality of
human resources
is very im
portant because t
h
e c
onst
r
uction industry nee
d
s e
x
perts
in
a hu
g
e
n
u
m
b
ers. Hu
m
a
n
resou
r
ces co
m
p
eten
cies
are a prereq
u
i
site fo
r
q
u
a
lity wo
rk
ers.
Qu
ality
co
m
p
eten
ce sho
w
s th
e ab
ility o
r
co
m
p
eten
cy of work
er as ex
p
ected
.
The g
o
v
er
nm
ent
of I
n
do
nesi
a
has reco
g
n
i
z
e
d
t
h
e i
m
portance of the hum
a
n res
o
urces c
o
m
p
etency in
th
e electr
i
city en
terp
r
i
se so th
at th
e law
o
f
electr
i
city ar
e m
a
d
e
in
1985
.
A
s
th
e im
p
l
e
m
en
tatio
n
of th
e
l
e
gi
sl
at
i
on m
e
nt
i
one
d a
b
o
v
e,
t
h
e g
ove
r
n
m
e
nt
has
de
vel
o
p
e
d a G
o
ver
n
m
e
nt
R
e
g
u
l
a
t
i
o
n
No
. 3/
20
0
5
a
s
an
am
endm
ent
t
o
Go
ve
rnm
e
nt
R
e
gul
at
i
o
n N
o
.
10/
19
8
9
ab
o
u
t
t
h
e Pr
o
v
i
s
i
on a
nd
Use
of El
ec
t
r
i
c
Po
wer.
It
s
t
at
es
that "Each engi
neer on t
h
e ele
c
tricity busin
es
s m
u
st have a
c
e
rtificate of com
p
etence".
To
get a c
e
rtificate of c
o
mpetence, a
n
e
xpe
rt
on electrical constructi
o
n
shou
ld
do
th
e
sev
e
r
a
l
co
m
p
eten
cy tests. Co
m
p
eten
cy test co
n
s
ist o
f
kn
ow
ledg
e, sk
ills and
attitu
d
e
tests.
Kno
w
led
g
e
, sk
ill, and
attitu
d
e
tests
o
b
t
ain
e
d fro
m
sev
e
ral
p
a
rts, bo
th written
an
d
o
r
al tests as
well as
practice o
f
sk
ill. Each
com
pone
nt
ha
s m
a
ny
cri
t
e
ri
a. C
o
m
p
et
enc
y
t
e
st
i
n
v
o
l
v
e
s
a
num
ber
o
f
asses
s
o
r
s.
T
o
e
q
u
a
t
e
asse
ssor
s
’s
o
p
i
n
i
on
s of com
p
eten
cy co
mp
on
en
ts tests u
s
ed
a fu
zzy app
r
o
a
ch
. Mu
lticriteria d
ecisio
n
m
a
k
i
n
g
refers to
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mu
lticriteria
Gro
u
p
Decision
Ma
king
Using
Fu
zzy
App
r
oa
ch
for Eva
l
ua
ting
.... (Wiwien
Had
i
kurn
i
a
wa
t
i
)
2
463
pre
f
ere
n
ces of decision-m
aking,
suc
h
as e
v
al
uat
i
on,
p
r
i
o
ri
t
i
zat
i
on an
d se
l
ec
tion of avail
a
ble alternatives [1].
Multi criteria decision m
a
king (MC
D
A) focuses on
the
o
retical
m
e
thodol
ogical de
ve
lopm
ent
and practical
appl
i
cat
i
o
ns
of
deci
si
o
n
t
e
c
h
n
i
ques
t
o
Deci
si
on Make
r’s
evaluate alternati
v
es
[2].
Deci
si
o
n
m
a
ker m
a
y
consi
s
t
m
o
re t
h
an
on
e
pers
o
n
or e
x
pe
rt
.
Di
ffe
re
nt
b
ackg
r
ou
n
d
of e
ach
deci
si
o
n
maker suc
h
as socio-culture, expe
rience
and inte
llige
n
ce som
e
t
i
m
es
m
a
ke each decision m
a
ke
r gives
diffe
re
nce pre
f
erence
.
T
h
e
r
e can be differe
n
t pre
f
ere
n
ces of
each criteri
on a
nd prefe
r
e
n
ces m
a
tch rate each
alternative on
each criteria.
Decision m
a
ker’s
opi
nion m
u
st be unif
ied e
m
ploying a unification proce
ss [3].
Mu
lticriteria Decisio
n
m
a
k
i
n
g
in
g
r
oup
s d
eci
sio
n
m
a
k
e
rs can
g
e
n
e
rate b
e
tt
er so
lu
tion
s
to
co
m
p
lex
p
r
o
b
l
e
m
s
i
n
v
o
l
v
i
n
g
t
h
e
use
of
opi
ni
o
n
o
f
s
o
m
e
expe
rt
s.
Deci
si
o
n
p
r
o
b
l
e
m
occur
r
e
d i
n
m
a
ny
or
gani
zat
i
o
ns.
S
o
m
e
of
th
ese p
r
ob
lem
s
select a set
o
f
altern
ativ
es b
y
co
n
s
i
d
er
ing
mu
ltip
le criteria. Ch
o
[4
] stated
th
at th
e p
u
r
pose of
m
u
lticriteria decision m
a
king is
reach
i
n
g a
decision
by c
h
oosi
ng the
be
st
alternative
from
several
potential
can
d
i
d
a
tes,
p
u
t
tin
g
th
e
subj
ect to
so
m
e
criteria or attrib
utes. The criteria
or attri
bute ca
n be the
one c
a
uses
som
e
benefi
t
s
or
t
h
e
one that
causes c
o
st.
Fu
[5
] stated
,
in
o
r
d
e
r to ach
i
e
v
e
satisf
action
in so
lv
ing
pro
b
l
em
s in
a
g
r
o
u
p
d
ecision
m
a
k
i
ng
,
gr
oup
deci
si
o
n
-m
aki
ng m
e
t
h
o
d
s an
d m
odel
,
t
h
e
p
r
oces
s o
f
t
h
at
usu
a
l
l
y
consi
s
t
s
of
t
w
o p
r
o
c
e
sses, t
h
e a
g
ree
m
ent
and the
selection process.
Sudarm
a
et.al
[6
] in
h
i
s study d
i
scu
s
ses m
u
lti-criteria
o
f
d
ecision
m
a
k
i
n
g
th
at
h
a
s an
altern
ativ
e i
n
th
e form
o
f
adv
i
ce for stud
ents who
will cho
o
s
e a cou
r
se
o
f
st
u
d
y
b
a
sed o
n
acad
e
m
i
c
ab
ility o
f
stu
d
en
ts to
p
u
rsu
e
h
i
gh
er
ed
u
cation
.
Th
is stud
y u
s
es El
i
m
in
atio
n
et Ch
o
i
x
Trandu
it
La Realite (ELECTRE) m
e
th
o
d
.
C
h
ri
st
i
n
a [
7
]
pr
o
pose
d
t
h
e
desi
g
n
o
f
deci
si
on
-m
aki
ng i
n
u
n
cert
a
i
n
t
y
assessm
ent
appr
oac
h
usi
n
g
Analytical Hie
r
arc
h
y Proces
s
(AHP).
T
h
e c
a
se study foc
u
sed
on a
discre
te
decision.
The prefe
r
ence
s i
n
this
case use a ke
y
perf
orm
a
nce i
ndi
cat
or
. Thi
s
pr
ocess ca
n sol
v
e t
h
e
pr
o
b
l
em
of conse
n
sus-
base
d de
ci
si
on
-
mak
i
n
g
gr
oup
t
o
ch
oo
se on
e
of
two
op
tio
n
s
.
Lo
w and Li
n
[
1
]
i
n
t
h
ei
r research p
r
op
ose
d
a com
m
on fuzzy
m
u
l
t
i
cri
t
e
ria deci
si
on m
a
ki
ng m
odel
,
a
co
n
c
ep
t
fu
zzy
ti
m
e
weig
h
t
ed
sch
e
m
e
. It ad
op
ted fo
r con
s
id
ering
in th
e m
o
d
e
l to
bu
ild
a
fu
zzy
m
u
l
tip
le
criteria d
ecisio
n
m
a
k
i
n
g
wi
th
ti
m
e
weig
ht (FMCDMTW). Th
at m
o
d
e
l can
tak
e
in
to
accoun
t th
e ti
m
e
d
e
p
e
nd
en
cies of th
e ev
al
u
a
tion
criteria and
prov
id
e relativ
ity lo
w-co
st
way
.
Dal
j
ooi
a
nd
E
s
ka
nda
ri
[
8
]
p
r
o
p
o
sed m
odel
ext
r
act
s re
gi
o
n
al
co
nt
ext
s
a
nd
vi
s
u
al
t
opi
cs fr
om
t
h
e
im
age usi
n
g
m
u
lt
i
cri
t
e
ri
a deci
si
o
n
m
a
ki
ng
ap
pr
oac
h
base
d o
n
Tec
hni
que
f
o
r
O
r
der
o
f
P
r
efe
r
e
n
ce
by
Si
m
ilarit
y
to
Id
eal So
l
u
tion
(TOPSIS) m
o
del. Mian
ab
ad
i
and A
f
sha
r
[3]
in
their res
earc
h
stated that de
cision
m
a
kers
opi
ni
o
n
s
were t
r
ans
f
orm
e
d i
n
t
o
f
u
z
z
y
pre
f
ere
n
ce
r
e
l
a
t
i
on an
d a
g
gre
g
at
ed
usi
n
g
O
W
A
o
p
erat
o
r
. T
h
i
s
fuzzy
gr
o
u
p
de
ci
si
on m
a
ki
ng
al
go
ri
t
h
m
was appl
i
e
d
f
o
r
a
gr
ou
n
d
wat
e
r
dev
e
l
opm
ent
pr
o
b
l
e
m
.
Hegazy
[
9
]
ex
pl
ai
ned
ho
w t
o
sol
v
e t
h
e pr
obl
em
of
u
n
c
ertain
ty in
th
e med
i
cal wo
rld, esp
ecially
mental health issues using a fuzzy
set approach. The unc
e
rtainties incl
u
d
e ass
u
m
p
t
i
ons of t
h
e e
x
pert
s an
d
d
a
ta. Th
ey are at risk
d
u
e
t
o
u
n
c
ertain
tie
s
a
ssociated with me
dical condition. C
h
e
n
et.al
[1
0]
an
d
Do
n
g
ji
ng
[11] stated that the decisi
on
-
m
aki
ng i
s
a research
gr
ou
p d
e
vel
o
ped
ove
r t
h
e l
a
st
t
w
ent
y
y
ears, whi
l
e
r
e
searc
h
on the
the
o
ry
and m
e
thod
of group
decision-m
aking ha
s
always recei
ve
d
attention from
researchers
in
the
wo
rl
d
.
Gr
o
up
deci
si
o
n
-m
aki
ng i
s
oft
e
n di
f
f
i
c
ul
t
t
o
det
e
r
m
i
n
e t
h
e appr
oval
o
r
ag
ree
m
ent
of t
h
e expe
rt
s i
n
giving
prefe
r
ence beca
use
of differe
nces i
n
kn
owledge or judgm
ent
of
eac
h decision
m
a
kers.
Tava
na
et.al
[1
2]
ha
ve
bee
n
d
o
i
n
g researc
h
o
n
A hy
b
r
i
d
f
u
z
z
y
gr
o
u
p
deci
si
on
s
u
p
p
o
rt
fra
m
e
wor
k
f
o
r
assesm
ent at N
A
SA. T
h
e com
p
licated structure
of the
as
sesm
ent criteria and altern
ative
are represe
n
ted a
nd
evaluate
d with Analytical Network
Process
(ANP). The
Alternative a
r
e
ran
k
ed usi
n
g fuzzy
Tec
hni
q
u
e
f
o
r
Ord
e
r of Preferen
ce
b
y
Sim
ila
rity to
Id
eal Solu
tio
n
(TOPSIS).
W
i
b
o
w
o
[
13]
use
d
a fuzzy
m
u
lt
i
c
riteria approach to
t
h
e
group
decision m
a
king t
o
i
n
crease
the
con
f
i
d
e
n
ce l
e
v
e
l
of t
h
e
deci
si
on m
a
ker
or t
h
e deci
si
o
n
m
a
ker i
n
s
o
l
v
i
ng t
h
e pr
o
b
l
e
m
of sel
ect
i
on o
f
s
u
p
p
l
i
e
rs.
Fuzzy
l
i
n
gui
st
i
c
vari
a
b
l
e
s a
r
e
use
d
t
o
re
prese
n
t
su
b
j
ec
tive a
ssessm
ent decision m
a
kers
so
th
at
th
e un
cert
a
in
ty
can be
m
i
nim
i
zed.
Zhai
et.al
[14] stated t
h
at in
com
p
lex system
, are ofte
n
faced
with
a d
e
cisio
n
prob
lem
th
at
in
clud
es
m
a
ny
at
t
r
i
but
es or m
a
ny
cri
t
e
ri
a and
req
u
i
r
e
s
ju
d
g
m
e
nt
or deci
si
o
n
-m
aki
ng
by
som
e
of t
h
e exp
e
rt
s i
n
a
gr
ou
p.
It req
u
i
res co
nsid
eration
o
f
th
e ex
p
e
rts’ judg
m
e
n
t
s to
resolv
e th
e
un
certain
ty. Mu
lticriteria d
ecision
mak
i
ng
m
e
thod ca
n s
o
lve com
p
lex
de
cision m
a
ki
ng
problem
s
, because: (a
) the e
x
istence of a va
riety decision
m
a
ker
opi
ni
o
n
s,
(
b
)
t
h
e
prese
n
ce
o
f
unce
r
t
a
i
n
t
y
an
d i
m
preci
si
on
,
and
(c
) t
h
e
dec
i
si
on m
a
ki
ng
p
r
oces
s i
s
base
d
o
n
t
h
e
conce
p
t
o
f
nat
u
ral
desi
re. T
h
e unce
r
t
a
i
n
t
y
and i
m
preci
si
on
i
nhere
nt
i
n
t
h
e
pr
obl
em
of gr
ou
p deci
si
on
m
a
ki
ng
fo
r s
p
ecific alternatives
m
u
st be c
hose
n
fr
om
several
altern
ativ
es av
ail
a
b
l
e, often
con
f
lict of criteria th
at
in
vo
lv
e rep
e
titiv
e d
ecision
mak
e
rs. Acco
rd
in
g
to
Tav
a
n
a
et.al
[1
2]
, u
n
c
e
rt
ai
nt
y
and i
m
preci
si
on can m
a
ke
decision m
a
kers feel ba
d t
o
give their subj
ec
tive asse
ssm
ent because
their
positions
a
r
e
not fully confident i
n
their asses
s
m
e
nts.
In t
h
i
s
pa
pe
r,
sel
ect
i
on o
f
t
h
e best
al
t
e
rnat
i
v
e fr
om
gro
u
p
deci
si
on m
a
kers i
s
obt
ai
ne
d
usi
n
g fuzzy
m
u
lt
i
att
r
i
but
e
deci
si
on m
a
ki
n
g
m
e
t
hods.
The p
r
o
p
o
se
d m
e
t
hod use
an ap
pr
oac
h
of t
r
i
a
n
g
u
l
a
r
fuzzy
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. 5
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24
69
2
464
m
u
lt
i
c
ri
t
e
ri
a gr
ou
p
deci
si
o
n
-
m
a
ki
ng
t
o
s
o
l
v
e
deci
si
o
n
makers
’s
subjective assessm
ent. T
h
eir
judgm
e
nts are
rep
r
ese
n
t
e
d by
t
r
i
a
ng
ul
ar f
u
zz
y
num
b
e
rs
sp
ecified
in lin
gu
i
s
tic form
.
Selectio
n
of t
h
e b
e
st altern
ativ
e ap
p
lied
in th
e group
d
e
cisio
n
-
m
a
k
i
ng p
r
o
b
l
em
to
determin
e th
e
com
p
etency test criteria for
a qualified ele
c
trician. T
h
e
r
e
st
of t
h
e
pape
r i
s
o
r
g
a
ni
se
d
as fol
l
ows
.
Se
ct
i
on
2
decri
b
es relate
d work
of our researc
h
. Sec
tion
3 ex
plains about
fuzzy
m
u
lticr
iteria approach. Sect
ion
4
discuss
e
s a ca
s
e
study, a
n
alysis and re
sult
our re
s
earc
h
.
Our conclusi
ons
are presente
d in
Section
5.
2.
FUZ
Z
Y
MUL
T
ICRITE
RI
A
APP
R
O
A
CH
W
i
bo
wo
[
1
3
]
stated
th
at th
e selectio
n
of
an
ap
pro
p
r
i
ate alter
n
ativ
e
gr
oup d
ecision
-
m
ak
in
g
i
n
clud
es
sev
e
ral step
s (a) d
e
term
in
atio
n
of altern
ativ
es, (b
) t
h
e
d
e
termin
atio
n
of the selectio
n
crit
eria, (c) pro
v
i
sio
n
of
rat
i
ng t
h
e al
t
e
rnat
i
v
es
pe
rf
or
m
a
nce and
w
e
i
ght
s
of c
r
i
t
e
ri
a, (
d
) a
g
gre
g
at
i
on
o
f
pe
rf
orm
a
nce rat
i
n
g a
n
d
weigh
t
ed
criteria to
g
e
n
e
rat
e
th
e ov
erall
p
e
rform
a
n
ce
in
d
e
x
for all th
e altern
ativ
es an
d
criteria,
an
d
(e)
ch
oo
si
n
g
th
e
best altern
ativ
e.
A m
a
jor adva
ntage of fuzzy logic is can be use
d
as com
p
e
n
satory and non com
p
ensatory in a s
i
ngle
m
o
d
e
l in
d
i
f
f
e
r
e
n
t
co
n
t
ex
ts,
b
y
u
s
i
n
g
i
n
f
e
ren
ces thr
ough
j
udg
m
e
n
t
s p
r
ov
id
ed
b
y
t
h
e
D
ecision
Maker
(D
M)
[1
2]
.
To
reso
l
v
e t
h
e un
certain
ty and
im
p
r
ecisio
n
in
fu
zzy m
u
lti
cr
iter
i
a gr
oup
d
ecision
-
m
ak
in
g pr
ob
lem
s
,
th
e lin
gu
istic fo
rm
s are used to
facilitate th
e assessm
e
n
t
o
f
th
e
d
ecision
m
a
k
e
rs. Th
e lin
gu
istic form
s are
rep
r
ese
n
t
e
d
by
t
r
i
a
ng
ul
ar
f
u
zz
y
num
bers a
s
t
h
ei
r a
p
pr
oxi
m
a
t
e
val
u
e.
Fuzzy
num
ber is expresse
d
as a fuzzy set a fuzzy in
t
e
r
v
al
i
n
real
n
u
m
ber. The
bo
un
da
ry
o
f
t
h
i
s
in
terv
al is a
m
b
i
g
u
o
u
s; th
e in
terv
al is also
a fu
zzy se
t. Generally a fu
zzy
in
terv
al is represen
ted
b
y
two
end
poi
nt
s a
1
and
a
2
and a pea
k
poi
nt
a
2
as [a
1
, a
2
, a
3
]
Tri
a
ngul
a
r
Fuzzy
N
u
m
b
ers (TF
N
)
i
s
a fuzzy
nu
m
b
er
rep
r
ese
n
t
e
d
by
t
h
ree
val
u
es
,
n
a
m
e
l
y
A = (a,
b, c
)
.
It
ca
n
be
defi
ned
as s
h
o
w
n
i
n
e
q
uat
i
o
n
(
1
).
0,
,
,
1,
(
1
)
Th
is
p
r
esen
tatio
n is ex
pressed as m
e
m
b
ersh
i
p
fu
nct
i
o
ns as
sho
w
n i
n
t
h
e
F
i
gu
re
1.
Fi
gu
re
1.T
r
i
a
n
gul
a
r
F
u
zzy
N
u
m
b
er A
= (a
,
b, c
)
The e
v
aluation and selection
process
start from
each d
ecisi
on m
a
ker Dk
(k =
1,
2, ..., k) give
s the
per
f
o
r
m
a
nce assessm
ent
(rat
i
ng
) f
o
r eac
h d
eci
si
on al
t
e
rna
t
i
v
e Ai
(i
= 1,2, ..
., m
)
whi
c
h i
s
form
ed fr
om
n
com
p
letion criteria Cj (j = 1, 2, ...,
n). T
h
e result is a decision m
a
trix th
at contains the
prefe
r
e
n
ces of each
decision-m
aker
on any c
r
iteri
a expres
sed as
equation
(2):
⋮
…
⋮…
⋮
…
(2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8-8
7
0
8
Mu
lticriteria
Gro
u
p
Decision
Ma
king
Using
Fu
zzy
App
r
oa
ch
for Eva
l
ua
ting
.... (Wiwien
Had
i
kurn
i
a
wa
t
i
)
2
465
The weight ve
ctor Wj
s
h
ows
the
influe
nce of
eac
h cri
t
e
ri
a i
n
deci
si
o
n
m
a
ki
ng i
s
ex
pre
sse
d as:
w =
[w
1
w
2
...
w
n
] (
3
)
Let w
ij
= (a
ij
, b
ij
, c
ij
), w
jk
R
,
j = 1
,
2
,
..
, n
,
k
= 1,
2, .
.
k i
s
t
h
e wei
g
ht
gi
ve
n
by
t
h
e deci
si
o
n
-m
akers
D
k
of
the
c
r
iteria Cj. Avera
g
e weights w'
j
= (a,
b, c
)
of
t
h
e
cri
t
eri
a
C
j
i
s
gi
ven
by
t
h
e
deci
si
o
n
-m
akers
k
(D
k)
can
be calculate
d
by
w’
j
= (1
/k)
(w
j1
w
j2
.
..
w
jk
) (
4
)
and
are t
h
e op
erat
o
r
of mu
ltip
licatio
n
and
ad
d
ition
o
n
fu
zzy nu
m
b
ers.
These
wei
g
ht
s
(4
) ca
n
be t
r
a
n
sfo
r
m
e
d by
t
h
e
eq
uat
i
o
n
(
5
):
w’
j
=
∑
(5
)
Fuzzy num
b
ers of evaluations that
have
been carried
out it is
n
ecessary to return the process
defuzzyfication. It is change
fuzzy
num
b
ers
into crisp num
bers. Num
b
ers cr
i
s
p
be a si
ngl
e val
u
e. T
h
i
s
i
s
t
h
e
fi
nal
val
u
e o
b
t
a
i
n
ed by
wei
g
ht
cal
cul
a
t
i
o
n al
t
e
rnat
i
v
es pr
ovi
ded
by
eac
h deci
si
o
n
m
a
ker
.
T
h
e fi
nal
val
u
e
i
s
th
e su
m
o
f
th
e
m
u
l
tip
licatio
n
b
e
tween
weight an
d fitn
ess
i
n
dex
.
T
h
e
fi
nal
val
u
e ca
n
be
f
o
rm
ul
at
ed as f
o
l
l
o
ws:
′
1
(6)
a, b an
d c are
vari
a
b
l
e
s of t
r
i
a
ng
ul
ar
fuzzy
num
ber an
d
is an
in
d
e
x
of
o
p
tim
is
m th
at
represen
ts op
timis
m
l
e
vel
deci
si
o
n
m
a
kers. T
h
e d
e
gree
of
o
p
t
i
m
i
sm
i
s
i
n
t
h
e range
of
0
1.
If t
h
e va
l
u
e of
i
s
hi
gh
, i
t
i
ndi
cat
es t
h
at
d
eci
si
on m
a
kers
have
hi
g
h
o
p
t
i
m
i
s
m
.
To de
term
in
e th
e ran
k
o
f
altern
ativ
e, th
is form
u
l
a c
a
n
be
use
d
:
∑
′
(
7
)
Ran
k
i
n
g
o
f
th
e altern
ativ
es is d
e
term
in
ed
fro
m
th
e v
a
lu
e of S
i
. The
great
er value is the
highest ra
nk
(m
ore rec
o
m
m
ende
d
by
t
h
e
d
eci
si
on m
a
ker)
.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
We
use
a
fuzz
y approach, t
h
e problem
of
determinin
g the
com
p
etency t
e
st criteria to
evaluate a
n
d
select a qualifi
e
d electrician.
The
purp
o
s
e
of prob
lem
so
lv
in
g
is to
d
e
termin
e su
itab
l
e criteria. Con
s
tru
c
tion
Services Agency is im
ple
m
e
n
ting c
o
m
p
et
ency
test for e
x
perts in the
field
of electrical
const
r
uction.
In this
com
p
etency test certificatio
n involves
thre
e assess
ors a
s
decision
m
a
kers.
Pr
obl
em
s t
o
be
sol
v
ed
i
s
t
h
e
d
e
term
in
atio
n
o
f
t
h
e lev
e
l
o
f
i
m
p
o
r
tan
c
e of th
e criteria
u
s
ed
in
t
h
e co
m
p
eten
cy test.
Determ
in
atio
n
o
f
t
h
e
i
m
p
o
r
tan
ce
o
f
th
is criterio
n
will b
e
u
s
ed
as th
e b
a
sis for a d
ecisio
n
o
r
ju
dg
m
e
n
t
o
f
a co
m
p
eten
t elec
trician
.
There
are
thre
e alternative
c
o
m
pone
nts
of
com
p
etence,
S
1
(knowle
dge
),
S
2
(skill)
a
n
d
S
3
(attitude
).
Eac
h
altern
ativ
e is awak
en
ed
fro
m
8
criteria,
C
1
(written
test 1),
C2
(written
test
2
)
, C
3
(written
test 3
)
, C4
(written
test 4
)
, C5
(written
test 5
)
, C
6
(oral test), C7
(test
o
f
th
e th
eory o
f
k
nowled
g
e
) and
C8
(practice k
n
o
w
led
g
e
test). T
h
ere
are
three
assess
ors as
deci
si
o
n
m
a
ker
D
1
,
D
2
a
n
d
D3
.
Li
ng
ui
st
i
c
val
u
e ex
pre
ssed
by
t
r
i
a
ng
ul
ar
fuzzy
n
u
m
b
er is used to
re
prese
n
t the prefere
n
ces of
decision m
a
kers so t
h
at the
unce
r
tainty and im
preci
sion
in the selection process ca
n be m
i
nimized. The
linguistic val
u
e of relative i
m
portance level or wei
ght
of each criteria
are give
n
by
the res
p
ective
decision
mak
e
rs. Th
ere
are 5
ling
u
i
stic fo
rm
s o
f
relativ
e im
p
o
r
ta
nce
level, VL (
V
e
r
y
Low)
, L (L
o
w
), M
(M
e
d
iu
m
)
, H
(Hi
g
h),
VH (Very Hi
gh).
Eac
h
of them
are
represe
n
ted by t
r
iangular fuzzy
num
b
ers.
V
L
= (0
, 0.
1,
0
.
3
)
L
=
(0.1,
0.
3, 0.5)
M =
(
0
.
3
,
0.
5, 0.7)
H
=
(0
.
5
,
0.
7,
0.
9
)
VH
=
(0.7,
0.
9, 1)
The weight of each
c
r
iteria
for
eac
h deci
sion m
a
ker can
be
shown in Ta
ble 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
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20
16
:
246
2
–
24
69
2
466
Table
1. T
h
e
weight
of each c
r
iteria
for each Decision
Make
r
Criteria
Decision M
a
ker
D1 D2
D3
C1 M
L
M
C2
L
L
M
C3
L
L
L
C4
L
L
M
C5 M
L
M
C6 H
H
VH
C7 H
H
VH
C8 H
H
VH
Th
e
qu
alitativ
e assessm
en
t g
i
v
e
n each
d
ecisio
n
-m
ak
er to
each
altern
ativ
e rating
o
f
th
e co
m
p
eten
cy
t
e
st
com
ponent
rep
r
ese
n
t
e
d
b
y
l
i
ngui
st
i
c
f
o
r
m
s. They
are VP
(Ve
r
y
P
o
o
r
), P
(P
o
o
r
)
, F
(
F
ai
r),
G
(G
o
o
d
)
,
V
G
(Ve
r
y
G
o
od
).
They
are
re
pr
e
s
ented
by
triang
u
l
ar fu
zzy
n
u
m
b
er as fo
llo
ws:
VP
=
(0,0,3)
P =
(0,3,5)
F =
(2,5,8)
G
=
(5,7,10)
VG
=
(7
,1
0,
1
0
)
The rate
of eac
h alternative
on each c
r
iteria
for ev
e
r
y decis
i
on m
a
ker is based
on linguistic form
s as
sho
w
n i
n
Ta
bl
e 2.
Table
2. Rating eac
h alternative
on
each crit
eria by
decision-m
aker
Criteria
Alternative
Decision M
a
ker
D1 D2
D3
C1
S1 G
F
G
S2 F
F
F
S3 G
F
F
C2
S1 G
F
G
S2 F
F
F
S3 G
F
F
C3
S1 F
P
P
S2 F
P
P
S3 G
F
F
C4
S1 F
P
P
S2 F
P
P
S3 G
F
F
C5
S1 F
F
F
S2 F
F
F
S3 G
F
G
C6
S1 G
G
G
S2 G
G
G
S3 VG
G
G
C7
S1 G
G
VG
S2 G
G
VG
S3 VG
G
VG
C8
S1 G
G
VG
S2 VG
G
VG
S3 VG
G
VG
The a
v
era
g
e
weight for the
fi
rst criteria (C
1) can be
cal
cul
a
t
e
d by
usi
n
g e
quat
i
o
n
(5
).
Th
e wei
g
ht
of
cri
t
e
ri
a 1
(C
1)
by
d
eci
si
on
m
a
ker
1
(
D
M
1
)
i
s
M
(M
e
d
i
u
m
)
,
DM
2 i
s
L
(
L
o
w
)
an
d
DM
3 i
s
M
e
di
um
(
M
).
I
n
accorda
n
ce wit
h
the
qualitative assesm
ents
of t
h
e decision
m
a
ker, for M = (0
.3, 0.5, 0.7) and L =
(0.1, 0.3,
0.5), the
ave
r
a
g
e
of criteria C
1
as
follows:
′
0
.
3
0
.
10
.
3
3
0
.2333
′
0
.
50
.
3
0
.
5
3
0
.4333
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mu
lticriteria
Gro
u
p
Decision
Ma
king
Using
Fu
zzy
App
r
oa
ch
for Eva
l
ua
ting
.... (Wiwien
Had
i
kurn
i
a
wa
t
i
)
2
467
′
0.7
0.5
0.7
3
0
.6333
The
t
r
i
a
ng
ul
ar fuzzy
num
ber fo
r
wei
g
ht
of
C
1
i
s
(
0
.
2
3
3
3
,
0.
43
3
3
, 0.
6
3
3
3
)
.
W
e
use si
m
i
l
a
r
way
t
o
calcu
late th
e weig
h
t
of ano
t
h
e
r criteria (fro
m
C2
u
n
til C8
).
Th
e resu
lts o
f
av
erag
e wei
g
h
t
fo
r each
criteria is
sho
w
n i
n
Ta
bl
e 3.
Table 3. Avera
g
e weight
of
ea
ch
c
r
iteria
Criteria
Decision M
a
ker
Average Weight
(
w
j
)
D1 D2
D3
C1
M
L
M
(
0
.
2333,
0.
433
3,
0.
6333)
C2
L
L
M
(
0
.
1666,
0.
366
6,
0.
5666)
C3
L
L
L
(
0
.
1
,
0.
3,
0.
5)
C4
L
L
M
(
0
.
1666,
0.
366
6,
0.
5666)
C5
M
L
M
(
0
,
2333,
0.
433
3,
0.
6333)
C6
H
H
VH
(
0
.
5666,
0.
766
6,
0.
9333)
C7
H
H
VH
(
0
.
5666,
0.
766
6,
0.
9333)
C8
H
H
VH
(
0
.
6333,
0.
833
3,
0.
9666)
The ne
xt step i
s
calculating of avera
g
e wei
g
ht of
each c
r
iteria based
on dec
i
sion m
a
kers prefe
r
ences
.
C
r
i
t
e
ri
a 1 (C
1)
gi
ves i
n
fl
uenc
e t
o
al
t
e
rnat
i
v
e 1 (S1
)
, S
2
an
d
S3. The
pre
f
er
ences o
f
deci
si
on m
a
ker (DM
)
1 i
s
G (
G
oo
d
)
,
D
M
2 i
s
F
(Fai
r
)
an
d
DM
3 i
s
G
(G
o
o
d
)
.
G
= (
3
,
7,
1
0
)
d
a
n F
= (
2
,
5
,
8)
. T
h
e cal
cul
a
t
i
on
of
avera
g
e
weight
of Criteria
1 t
o
wa
rd eac
h alterna
tive
(S
1,
S
2
,
S3
)
by
eac
h
decision m
a
ker are:
′
5
2
5
3
4
′
7
5
7
3
6.3333
′
10
8
10
3
9.3333
Results of the
avera
g
e
rating
of each alterna
tive for ea
ch criteria are s
h
own in Ta
ble 4.
Table 4. Avera
g
e rating
of
ea
ch
alternative
for each criteria
Criteria
Alternative
Decision M
a
ker
Average Weight
(x
ij
)
D1 D2
D3
C1
S1
G
F
G
(
4
,
6.
3333,
9.
3333)
S2
F
F
F
(2, 5, 8)
S3
G
F
F
(
3
,
5.
6666,
8.
6666)
C2
S1
G
F
G
(
4
,
6.
3333,
9.
3333)
S2
F
F
F
(2, 5, 8)
S3
G
F
F
(
3
,
5.
6666,
8.
6666)
C3
S1
F
P
P
(
0
.
6666,
3.
666
6,
6)
S2
F
P
P
(
0
.
6666,
3.
666
6,
6)
S3
G
F
F
(
3
,
5.
6666,
8.
6666)
C4
S1
F
P
P
(
0
.
6666,
3.
666
6,
6)
S2
F
P
P
(
0
.
6666,
3.
666
6,
6)
S3
G
F
F
(
3
,
5.
6666,
8.
6666)
C5
S1
F
F
F
(2, 5, 8)
S2
F
F
F
(2, 2, 8)
S3
G
F
G
(
4
,
6.
3333,
9.
3333)
C6
S1
G
G
G
(
5
,
7,
3.
3333)
S2
G
G
G
(5, 7, 10)
S3
VG
G
G
(
5
.
6666,
8,
10)
C7
S1
G
G
VG
(
5
.
6666,
8,
10)
S2
G
G
VG
(
5
.
6666,
8,
10)
S3
VG
G
VG
(
6
.
3333,
9,
10)
C8
S1
G
G
VG
(
5
.
6666,
8,
6.
6666)
S2
VG
G
VG
(
6
.
3333,
9,
10)
S3
VG
G
VG
(
6
.
3333,
9,
10)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
246
2
–
24
69
2
468
Rating weighted for
eac
h
alt
e
rnativ
e
can
be calculated a
s
follows
.
Fo
r altern
ativ
e
1
(S1
)
, criteria 1
(C1
)
.
= (w
S1
.
w
c1
) /
(
Ʃ
w
S
.
Ʃ
w
DM1
)
(8
)
=
weigh
t
ed
rating
criteria
(C
1
)
for
altern
ativ
e S1
b
y
DM1
=
w
e
igh
t
ed
av
er
ag
e
r
a
tin
g of
alt
e
r
n
ativ
e (
S
1)
by D
M
1
=
weigh
t
ed
av
erag
e
ratin
g criteria (C1) for altern
ativ
e (S1)
b
y
DM1
Ʃ
w
S
=
t
h
e am
ount
of
avera
g
e
wei
g
ht
f
o
r al
l
al
t
e
r
n
at
i
v
es
by
DM
1
Ʃ
w
DM1
=
t
h
e am
ount
of
avera
g
e
wei
g
ht
f
o
r al
l
c
r
i
t
e
ri
a
by
DM
1
Calcu
l
atio
n
o
f
a weigh
t
ed rati
n
g
fo
r all altern
ativ
es sho
w
n
in
Tab
l
e 5.
Tab
l
e 5
.
Weigh
t
ed
rating
for all
altern
ativ
es
Alternative
Criteria
r
D1
r
D2
r
D3
1 0.
0062
61
0.
0378
37
0.
2463
16
2 0.
0031
3
0.
0298
72
0.
2111
29
3 0.
0046
96
0.
0338
54
0.
2287
21
S1 4
0.
0044
71
0.
0320
13
0.
2203
74
5 0.
0022
35
0.
0252
73
0.
1888
93
6 0.
0033
53
0.
0286
43
0.
2046
32
7 0.
0005
63
0.
0198
33
0.
2596
59
8 0.
0005
63
0.
0198
33
0.
2596
59
1 0.
0025
32
0.
0306
52
0.
3750
6
2 0.
0009
37
0.
0242
36
0.
2942
46
3 0.
0009
37
0.
0242
36
0.
2942
46
S2 4
0.
0042
18
0.
0374
56
0.
4250
18
5 0.
0032
13
0.
0380
86
0.
2375
2
6 0.
0032
13
0.
0152
35
0.
2375
2
7 0.
0064
25
0.
0482
42
0.
2771
06
8 0.
0211
78
0.
0571
73
0.
0744
75
1 0.
0211
78
0.
0571
73
0.
2234
28
2 0.
0240
02
0.
0653
41
0.
1396
35
3
0.
0186
68
0.
0575
0.
1981
35
S3
4
0.
0186
68
0.
0575
0.
1981
35
5 0.
0208
64
0.
0646
87
0.
1981
35
6 0.
0234
74
0.
0600
99
0.
1318
27
7 0.
0262
36
0.
0676
11
0.
1977
42
8 0.
0262
36
0.
0676
11
0.
1977
42
Th
e
n
e
x
t
step is p
r
i
o
ritizin
g an
altern
ativ
e d
eci
sion
s
b
a
sed
on
t
h
e resu
lts o
f
agg
r
egatio
n
.
Th
is
p
r
i
o
rity is n
ecessary to
rank th
e d
ecisio
n
altern
ativ
es
. The resu
lts o
f
the ag
greg
ation
represen
ted
b
y
u
s
in
g
t
r
i
a
ng
ul
ar
f
u
zz
y
num
bers.
T
h
e fi
nal
val
u
e i
s
det
e
rm
i
n
ed
by
usi
n
g
eq
uat
i
o
n
(6
).
Thi
s
de
f
u
zzy
m
e
t
hod i
s
use
d
t
o
det
e
rm
i
n
e ranks
of al
t
e
r
n
at
i
v
es, s
h
o
w
n by
equat
i
o
n
8. T
h
e i
nde
x o
f
o
p
t
i
m
i
s
m
(
) is u
s
ed
to
so
lv
e th
is case
is
= 0,
=
0.
5 a
nd =
1
.
The i
n
de
x
of
opt
i
m
i
s
m
(
= 1)
sh
o
w
s n
o
t
opt
i
m
i
s
ti
c and
=
0 s
h
o
w
s very
o
p
tim
ist
i
c. Th
e resu
lt of calcu
l
atio
n
use in
d
e
x
o
f
o
p
timis
m
(
= 0.5)
as fi
nal
val
u
e of al
t
e
r
n
at
i
v
e S1
(k
n
o
wl
e
dge
) s
h
o
w
n i
n
Ta
bl
e
6.
Tab
l
e 6
.
Fin
a
l Valu
e of Altern
ativ
e
S1
r’
1
r’
2
r’
3
r’
4
r’
5
r’
6
r’
7
r’
8
0.
0820
63
0.
0722
18
0.
0749
72
0.
0859
14
0.
0792
26
0.
0525
0.
0829
5
0.
0688
75
To
d
e
term
in
e th
e
rank
o
f
p
a
rameter o
n
alternativ
e S1 using
eq
u
a
tion
(7
) as fo
llo
ws:
1
∑
0
.
0
820
63
+0
.0
72
218
+0.074
972
+0.085
914
+0.0
792
26
+0
.0
525
+0.082
951
+0.0
688
75
=
0.
598718
In
th
e sam
e
form
u
l
a, it can
b
e
calcu
lated
for altern
ativ
e S2
(sk
ill) and
S3
(attitu
d
e
). Th
e resu
lts o
f
co
m
p
lete calcu
latio
n
s
for all deg
r
ee of
o
p
tim
i
s
m
(
= 0,
α
=
0.
5 a
n
d
α
=
1
)
as show
n in
Tab
l
e 7.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mu
lticriteria
Gro
u
p
Decision
Ma
king
Using
Fu
zzy
App
r
oa
ch
for Eva
l
ua
ting
.... (Wiwien
Had
i
kurn
i
a
wa
t
i
)
2
469
Tab
l
e
7
.
Alternativ
e Pri
o
rity fo
r Variou
s
Val
u
e
α
Alternatives
α
= 0
α
= 0.
5
α
= 1
S1 0.
2.
2771
0.
5987
18
0.
9946
66
S2 0.
1864
47
0.
6200
95
1.
0537
43
S3 0.
2344
07
0.
7228
38
1.
2112
69
Table 7 shows
that alternative 3
(S3)
has the highes
t in
tegral to
tal v
a
lu
e
for each
d
i
fferen
t
ind
e
x
of
o
p
tim
is
m
(
= 0,
=
0.
5 a
n
d
=
1).
T
h
e se
l
ect
i
on re
sul
t
s
are
obt
ai
ne
d i
n
t
h
e
fo
rm
of
ra
nki
ng
t
h
e
fi
nal
val
u
e
o
f
criteria.
Finally, th
e alternativ
e S3 is th
e
h
i
gh
est
p
r
iority.
4.
CO
NCL
USI
O
N
The pr
ocess o
f
eval
uat
i
n
g
a
nd det
e
rm
i
n
i
ng
cri
t
e
ri
a
in the c
o
m
p
etency test electricians is
very
co
m
p
lex
an
d
i
n
vo
lv
es a gr
oup
of
d
ecisi
on-makers. T
h
ere
are m
a
ny crite
ria and uncerta
inty and im
precision
en
v
i
ron
m
en
t o
f
d
ecision
m
a
k
i
ng
pro
cess.
Our research
d
e
v
e
l
o
ps an
ap
pro
ach
fu
zzy
m
u
lticriteria
g
r
ou
p
d
ecision
-m
ak
in
g to
so
l
v
e th
e p
r
ob
lem
o
f
d
e
termin
in
g
t
h
e
c
o
m
p
etency test criteria. T
h
e c
a
se study shows that
th
e fu
zzy ap
pro
a
ch
is u
s
ed to
so
lv
e the p
r
o
b
l
em
s an
d
th
e ev
al
u
a
tio
n
criteria u
s
ed
in
d
e
term
i
n
ing
th
e
com
p
etency test expe
rt electrical co
nstructio
n
field
.
From
th
e resu
lts
with
th
e t
r
iang
u
l
ar fu
zzy app
r
o
a
ch
attitu
d
e
is th
e
su
prem
e criteri
a. Th
is criteria
m
u
st b
e
co
n
s
id
ered
b
y
th
e assessor in
d
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a
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a
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