TELKOM
NIKA
, Vol.12, No
.4, Dece
mbe
r
2014, pp. 10
64~107
2
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i4.787
1064
Re
cei
v
ed Se
ptem
ber 18, 2014; Revi
se
d Octob
e
r 30,
2014; Accept
ed No
vem
b
e
r
17, 2014
Dynamic DEMATEL Group Decision Approa
ch Based
on Intuitionistic Fuzzy Number
Hui Xie*, Wa
nchun Duan,
Yonghe Sun
,
Yuan
w
e
i
Du
F
a
cult
y
of Man
agem
ent an
d Econom
ics, Kun
m
ing U
n
iv
ers
i
ty of Scie
nce a
nd T
e
chnol
og
y, Kunming,
650
09
3, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zhubi
ng
811
1
09@
126.com
A
b
st
r
a
ct
W
i
th respect t
o
the pr
obl
e
m
s of aggr
eg
ati
on
a
b
o
u
t grou
p exp
e
rts
’
info
rmati
on
and
d
y
na
mic
decisi
on in
DE
MAT
E
L
(decis
i
on mak
i
ng
tri
a
l and eval
uat
i
on
lab
o
ratory), a d
y
na
mic DEMA
T
E
L grou
p ex
p
e
rt
decisi
on-
makin
g
metho
d
o
n
i
n
tuitio
nistic fu
zz
y
nu
mb
er
(IF
N
) is pr
ese
n
te
d. F
i
rstly usin
g IF
N inste
a
d
o
f
origi
n
a
l
po
int
estimates to r
e
flect the ex
p
e
rts
’
pr
efer
enc
e, the gro
up
e
x
perts
’
inf
o
rma
tion ar
e inte
gr
ated
hori
z
o
n
tal
l
y at each p
e
rio
d
. T
hen the
aggr
eg
ation i
n
for
m
at
i
on at differe
nt peri
ods
are ag
greg
ated
vertic
all
y
aga
in by dyn
a
m
ic i
n
tuitio
nisti
c
fu
zz
y w
e
i
ght
ed aver
agi
ng (
D
IF
W
A
) operator so as to ob
tain the dyn
a
m
ic
intuiti
onistic
fu
zz
y
DEMATEL
total re
latio
n
matrix.
T
h
irdly,
throug
h th
e
ana
lysis
of ce
nter an
d re
as
on
degr
ee, the p
o
s
itions of the v
a
rio
u
s fa
ctors in the system
a
r
e clear a
nd d
e
finite, a
nd the
inner structur
e
of
system h
a
s b
een rev
eal
ed.
Finally, the fe
asibi
lity an
d p
r
acticab
ility of the prop
ose
d
meth
od is sh
o
w
n
throug
h an i
llus
t
rative exa
m
p
l
e
of a process o
f
course selecti
on in a sch
oo
l.
Ke
y
w
ords
:
D
E
MAT
E
L, intui
t
ionistic fu
zz
y
nu
mbers, dy
na
mic i
n
tuitio
n
i
stic fu
zz
y
w
e
ighte
d
aver
agi
ng
oper
ator
1. Introduc
tion
A kind of co
mplex syste
m
factor an
a
l
ysis metho
d
, called
De
cision Maki
ng T
r
ial an
d
Evaluation L
aboratory m
e
thod (DEM
ATEL) was
first conceived by Ge
orge Washingt
on
university ce
nter in Gen
e
va Battelle associatio
n in
19
73 [1]. This ki
nd of method
is a tool based
on gra
ph the
o
ry and matrix to analyze the impor
ta
nce of the factors
of syst
em. The method
con
s
tru
c
t
s
th
e dire
ct influ
ence matrix(DIM) th
rou
g
h
the expe
rts’
qualit
ative j
udgme
n
t of the
logical rel
a
tio
n
shi
p
an
d infl
uen
ce b
e
twe
en ea
ch
othe
r in the
co
mp
lex system fa
ctors a
nalysi
s
.
Then
it ca
n cal
c
ulate
the
deg
ree
of reason and cent
er,
so
as
to reveal
the
intrin
sic cau
s
al
relation
shi
p
and find out
the key factors of t
he
system. Be
cause of its pra
c
tica
bility and
conve
n
ien
c
e
the method it
self, DEMAT
E
L receive
hi
gh attention
by sch
olars b
o
th at home
and
abro
ad, an
d i
t
has b
een
wi
dely appli
ed i
n
many field [
2
]-[3]. Ho
wev
e
r, thro
ugh
a
lot of pra
c
tical
appli
c
ation,
many schola
r
s have fo
un
d experts’ ju
dgment is
subje
c
tive an
d arbitrary in
the
pro
c
e
s
s of
deci
s
io
n-m
a
ki
ng. The
r
efo
r
e t
he
im
pro
v
ement
of DEMATEL method be
comes
resea
r
ch hot
spot in
re
ce
n
t
years. Seve
ral liter
ature
s
re
spe
c
tively prop
ose u
s
in
g grey numb
e
r,
triangul
ar fuzzy numbe
r in DIM con
s
t
r
uctio
n
in
order to ma
ke
the experts’
judgment m
o
re
obje
c
tive and
sci
entific
su
ch as Tseng
(2009
),
Don&
Hshiun
g (2
01
2) a
nd
Wu
(2
011) [4]-[6]. But
these m
e
thod
s above
are
still failed to solve t
he
sci
ence problem
of experts’ j
udgme
n
t buil
d
in
g
mech
ani
sm.
We
have p
u
t forward u
s
ing
intuition
i
stic fu
zzy n
u
mbe
r
to ex
pre
s
s expe
rt
s’
prefe
r
en
ce in
formation in
DEMATEL d
e
ci
sion
-ma
k
in
g, whi
c
h is
b
a
se
d on the
system intuiti
o
n
thinkin
g
of academi
c
ian
Wang Zho
ngtu
o
[7], and fu
lly consi
deri
n
g
the expert information
su
ch
as co
gnitive ability,
perso
nal
p
r
efe
r
en
ces and
situ
ational ch
ara
c
te
ristics.
T
he e
x
tended
m
e
th
od
results by int
u
itionisti
c
fuzzy numb
e
rs, i
m
pr
ove th
e
DEMATEL e
v
aluation mo
del. Ho
weve
r, the
vast maj
o
rity
literatures of
DEMATEL
d
e
ci
sion
-ma
k
in
g a
r
e
only fo
cu
sed
on
the
judgm
ent
of
the
relation
shi
p
betwe
en sy
stem factors
by one
si
ngl
e expert at
the sam
e
perio
d. But the
relation
shi
p
b
e
twee
n the factors is
co
mplicate
d
an
d diverse at different pe
ri
ods, al
so an
d the
experts’
kno
w
led
ge a
nd i
ndividual
exp
e
rien
ce
ha
s
certai
n limitat
ion in m
any
situation
s
. It is
necessa
ry to
develop
so
me ap
pro
a
ch
es to
deal
wi
th these
issu
es. At this
po
int of view, when
the complexi
ty of system
increa
se
s,
the sc
ien
t
ific d
e
c
i
s
i
o
n
ma
k
i
ng
pr
oc
ess
o
fte
n n
eed
s
evaluation
of multi-pe
rson
and multi
-ro
und
s. In th
is pape
r, we
shall take time dimen
s
io
n
into
deci
s
io
n making pro
c
e
s
s, and ag
gre
gat
e experts’ inf
o
rmatio
n of different peri
o
ds effectively
.
It
can reflect th
e DEMATEL
method mo
re
scie
n
tifically and preci
s
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Dynam
ic DE
MATEL Gro
u
p
De
cisi
on Appro
a
ch Based
on Intuitio
nistic F
u
zzy Num
ber (Hui
Xie)
1065
Curre
n
tly dynamic
deci
s
i
on-m
a
ki
ng problem
s hav
e been m
o
re
widely used
in multi-
crite
r
ia d
e
ci
si
on-m
a
ki
ng, b
u
t there
not
ex
isting re
search about
dy
nami
cs DEMATEL
gro
up
deci
s
io
n-m
a
ki
ng p
r
op
osed
by schol
ars.
The
r
efor
e,
based
on a
p
p
lying the i
n
tuitionisti
c
fu
zzy
numbe
rs (IF
N
) to exp
r
e
s
s expe
rts’ p
r
eferen
ce
s , th
is p
ape
r co
nstru
c
t
s
the
i
n
itial intuitionistic
fuzzy
relation
matrix to imp
l
ement the p
a
i
rwi
s
e
com
p
a
r
iso
n
jud
g
me
nt betwe
en t
w
o fa
ctors .T
hen
the expe
rts’
j
udgem
ent inf
o
rmatio
n at
th
e same
pe
ri
o
d
is integ
r
ate
d
ho
ri
zontally
. Next th
e g
r
oup
experts’
info
rmation
at
different p
e
ri
ods ar
e ve
rtically integ
r
ated throug
h the
dyna
mic
intuitionisti
c
f
u
zzy weight
ed ave
r
ag
e(DIFWA
)
op
er
a
t
o
r
s
in
th
e fo
llo
w
i
n
g
pa
r
t, r
e
s
u
lting in
dynamic intuit
ionisti
c
fuzzy DEMATEL total -re
l
a
tion m
a
trix. Finally the ne
w DEM
A
TEL deci
s
io
n-
making m
e
thod i
s
proposed and
an ex
ample
was
a
pplied to illustrate the
presented m
e
thod to
be pra
c
ticality and feasi
b
ility.
2. The traditi
onal DEMAT
E
L method
The traditio
n
a
l
DEMATEL method spe
c
i
f
ic step
s are as follo
ws[8]
：
Step1:
Suppo
se the
system
contai
ns a set of elements
1,
2
,
i
G
g
in
.
Step2:
Dra
w
di
re
cte
d
grap
h abo
u
t
all links bet
wee
n
the influen
cing fa
cto
r
s. With the a
rro
w from
i
g
to
j
g
mean
s t
hat
i
g
ha
s direct impa
ct to
j
g
, and the n
u
m
bers o
n
th
e arro
ws
illustrate the
direct influence
strength betw
een factors. And
rate
on a
scale of
0 to 4
whe
r
e, 0: no effect, 1: low effect, 2:medi
um
effec
t, 3: high effec
t, 4: very high effec
t.
Step3:
Con
s
tru
c
t the
initial dire
ct-relation matrix
. Based on th
e pair-wi
se
compa
r
ison
s in term
s
of influence
and di
re
ction
s
by expert
s
,
a matrix
ij
nn
a
A
is
obtaine
d, whi
c
h is
an
nn
matrix. Here
ij
i
j
a
(1
,
2
,
,
;
1
,
2
,
,
;
)
in
j
n
i
j
is d
enoted
a
s
the
deg
re
e
to which the factor
i
g
affec
t
s
the fac
t
or
j
g
,i.e.
If there is
no relations
h
ip between
i
g
and
j
g
,
0
ij
a
12
1
21
2
12
0
0
0
n
n
nn
aa
aa
A
aa
(1)
Step4:
Nor
m
ali
z
e
th
e initial dire
ct-relation m
a
trix. Norm
alize the mat
r
ix
A
and form a
norm
a
lized m
a
trix
ij
nn
b
B
，
whe
r
e
/m
a
x
1
ij
ij
ij
b
aa
i
n
.
Step5: C
alc
u
late the total-relation matr
ix. The total relation matrix
T
is defin
ed as
1
()
[
]
ij
n
n
TB
I
B
t
, where
I
is de
noted a
s
the identity matrix.
Step6:
The
sum of
rows an
d colu
mns,
within th
e total relatio
n
matrix T i
s
sep
a
rately d
e
noted a
s
i
f
and
i
e
, using th
e formulate:
1
n
ii
j
j
f
t
,
1
n
j
i
j
i
t
e
, Where
i
f
and
i
e
denote the
sum
of ro
ws and
colum
n
s respe
c
tively. Now
i
f
sum
m
ari
z
e
s
both
dire
ct an
d i
ndire
ct
effects given
by
i
g
to the o
t
her fa
ctors.
So
i
e
sh
ow
s b
o
t
h
dir
e
ct
a
n
d
indi
re
ct
ef
f
e
ct
s
given by
j
g
fro
m
the other
factors. The
sum of
ii
i
rf
e
indi
cate
s the de
gree
of
importa
nce fo
r facto
r
i
g
in the entire
s
y
s
t
em. On the contrary ,the differenc
e
ii
i
uf
e
rep
r
e
s
ent
s th
e net
effect
that facto
r
i
g
contri
bute
s
t
o
sy
stem. S
pecifi
c
ally, if
i
u
is
positive , factor
i
g
is a net ca
use, while factor
i
g
is a net re
ceiver if
i
u
is negative.
Step7:
Set up a thre
shol
d value to obtain dig
r
a
ph. Since m
a
trix
T
provide
s
informatio
n o
n
ho
w
one facto
r
affects a
nothe
r,
it is nece
ssary for a de
cision m
a
ker t
o
set up a th
reshold
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 106
3 – 1072
1066
value to filter out som
e
ne
gligible effe
ct
s.
In doin
g
so, only the ef
fects g
r
eate
r
than the
threshold val
ue wo
uld be
cho
s
e
n
and
shown in digra
ph.
3. Preliminaries
3.1 Defini
tion of intuition
i
stic fu
zzy
Set (IFS)
Bulgari
an
sch
o
lars Atan
assov expan
ds Z
adeh’
s fu
zzy
theory
who
s
e
ba
sic compo
nent i
s
only a members
h
ip fuc
t
ion. The intuitionis
t
ic
fuzzy s
e
ts is char
ac
ter
i
z
e
d by a members
h
ip
fuction and a non- mem
b
ershi
p
fuction [
9
]. Since
intuitionistic fuzzy sets
adds new parameters
into the fuzzy sets, an
d thus IFS ca
n d
e
scrib
e
“n
eith
er this n
o
r th
at” vague
co
nce
p
t, theref
ore
the theo
ry h
a
ve be
en a
very suita
b
le
tool to
b
e
u
s
ed
to de
scri
be the i
m
pre
c
ise o
r
u
n
certain
deci
s
io
n information. In ma
ny compl
e
x d
e
ci
sion m
a
ki
n
g
field, a lot o
f
sch
olars u
s
ed intuitioni
stic
fuzzy
set
s
an
d have
achie
v
ed fruitful re
sults [10]
-[11
]. Dome
stic
schol
ar P
r
ofe
s
sor Xu Z
e
sh
ui
gives rel
e
van
t
concepts of
intuitionisti
c
fuzzy judgme
n
t matrix.
Defini
tion1:
Let a set
X
be a
universe of discourse. An
A-IFS is an o
b
ject havin
g the form:
,(
)
,
(
)
AA
A
x
xv
x
x
X
(2)
Whe
r
e the
function
:[
0
,
1
]
A
X
defines th
e degree o
f
membershi
p
and
:[
0
,
1
]
A
vX
define
s
the
deg
ree
of
non-memb
ership i
n
of t
he ele
m
ent
x
X
to
A
,resp
e
ctively, and for eve
r
y
x
X
,
0(
)
(
)
1
AA
xv
x
(3)
For any A-IFS
A
and
x
X
,
()
1
(
)
(
)
AA
A
x
xv
x
is called th
e
deg
ree
of
indetermina
cy or hesitan
cy of
x
to
A
.
For conveni
ence
of
co
mputation, we call
(,
,
)
an intuitionistic fuzzy
numbe
r(IF
N
),
where
[0
,
1
]
,
[0
,1
]
,
v
1,
v
1.
v
Defini
tion2
: Let a set of
12
,,
,
n
Yy
y
y
be
n
alternative
s
whi
c
h are compa
r
ed
p
a
re-wi
s
e by
deci
s
io
n ma
kers, th
en th
e intuitioni
sti
c
fu
zzy
pref
eren
ce
matri
x
is d
e
fined
as
()
,
nn
ij
B
b
(,
,
)
,
ij
ij
i
j
i
j
bv
,1
,
2
,
,
,
ij
n
whe
r
e
ij
indicate
s
the int
ensity deg
re
e to whi
c
h
i
y
is
prefe
rre
d to
j
y
,
ij
v
indi
cate
s t
he inte
nsity
degree to
which
i
y
is n
o
t
prefe
rre
d to
j
y
,
ij
indicates th
e
intensity de
gree
of un
ce
rtainty,
and
all of them
sho
u
ld
satisf
y the co
ndition:
1,
ij
ij
v
,
ij
i
j
v
0.
5
,
ij
i
j
v
1,
ij
ij
ij
v
,1
,
2
,
,
.
ij
n
We
call
B
the
intuitionisti
c
fuzzy judgme
n
t matrix.
3.2 Des
c
ripti
on of d
y
namic DEMATEL
group decis
i
on problem
The dyn
a
mic
intuitionisti
c
fuzzy DEMAT
E
L gro
up
de
cision
problem
whi
c
h
ha
s
n
fac
t
ors
at
p
different period
s
(
(1
,
2
,
,
)
k
tk
p
) ca
n be define
d
as:
()
()
12
1
()
(
)
()
21
2
()
(
)
12
0
0
0
kk
kk
k
kk
tt
n
tt
t
n
tt
nn
aa
aa
A
aa
(4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Dynam
ic DE
MATEL Gro
u
p
De
cisi
on Appro
a
ch Based
on Intuitio
nistic F
u
zzy Num
ber (Hui
Xie)
1067
12
()
(
(
)
,
(
)
,
,
(
)
)
p
tt
t
t
(5
)
In Eq (4)&(
5
)
,
()
k
t
A
is the initial
intuitionistic
fuz
z
y
relation matrix at
(1
,
2
,
,
)
k
tk
p
.
And we use IFN
(,
,
)
k
tt
t
kk
k
ij
ij
ij
t
ij
aa
a
a
to express expert
s
’ pre
f
eren
ce.
ij
indicate
s
the intensity
degree the e
x
pert gives
whi
c
h
i
is preferred to
j
at
k
t
perio
d.
ij
v
indicate
s
the i
n
tensity
degree th
e e
x
pert give
s
which
i
is not
p
r
eferred
to
j
at
k
t
peri
od.
ij
ind
i
cate
s the i
n
tensity
degree of un
certai
nty. They
meet the
conditio
n
s:
[0
,
1
]
,
t
k
ij
[0
,
1
]
,
t
k
ij
1,
t
kt
k
ij
ij
1,
tt
kk
t
k
ij
ij
ij
(,
1
,
2
,
,
)
.
ij
n
()
k
t
is the weig
ht vector of
k
t
,
()
0
,
k
t
1
()
1
;
p
k
k
t
Therefore, f
o
r a
n
intui
t
ionistic fu
zzy varia
b
le
(,
,
)
k
tt
t
kk
k
ij
ij
ij
t
ij
aa
a
a
, if
12
,,
,
p
tt
t
t
, then
12
,,
,
,
p
t
tt
ij
ij
ij
aa
a
indicat
e
p
IFNs colle
cted at
p
different period
s
.
Dynami
c
i
n
tuitionisti
c
fu
zzy
DEMAT
E
L
group
d
e
ci
sion
ma
ki
ng p
r
o
b
lem
ca
n
be
expre
s
sed
as sim
p
ly: Accordin
g to
the initial intuitionistic fuzzy
d
i
rect
rel
a
tion
matrix which
i
s
given by ea
ch expe
rt at different time
s, the ne
w
m
e
th
od
integ
r
ate
s
these matrix hori
z
ontally
a
n
d
vertically, so
that we can
sort
the
syst
em facto
r
s, d
e
termin
e the
importa
nce a
nd rel
e
van
c
e
of
compl
e
x
sy
st
em.
3.3 Trans
f
or
mation of th
e intuitionistic fuzz
y
function
Each
pa
rticip
ating d
e
ci
sio
n
ma
king
expe
rt ha
s
his o
w
n ri
sk p
r
efe
r
e
n
ce,
and
diffe
rent
risk
prefe
r
en
ce
will lead to different d
e
ci
sio
n
re
sults.
Th
e most
striki
ng feature of
IFS reflects
the
fuzzi
ne
ss a
n
d
uncertainty
of experts i
n
realit
y thro
ugh the com
p
reh
e
n
s
ive d
e
scriptio
n of the
degree
of
m
e
mbe
r
ship, non-memb
ership and he
si
tan
c
y. The
deg
ree
of hesita
n
cy
sh
ows
experts’
un
certainty abo
u
t
the deci
s
io
n maki
ng
p
r
oblem
s, whil
e the pe
rso
n
wh
o tend
to
adventure thi
n
k m
o
st
of the de
ci
sion
make
rs
who hesitate wo
ul
d
suppo
rt
ri
sk a
ppetite, a
nd
peopl
e
who d
i
slikes ri
sk co
nsid
er
m
o
st of
the
de
ci
sio
n
ma
kers
wh
o he
sitate
wo
uld ag
ain
s
t th
e
risk. Peo
p
le
who i
s
risk
n
eutral
believe
the he
sitatin
g
de
cisi
on m
a
ke
rs who
su
pport
or
agai
nst
are half and h
a
lf. Therefore
we introdu
ce
the coefficie
n
t of risk preferen
ce
[0
,
1
]
which is the
prop
ortio
n
of
he
sitant p
e
rson
choo
se
to supp
ort, so
1
is th
e p
r
op
o
r
tion of
he
sitant pe
rson
c
h
oose to agains
t. If
0.5
, we
con
s
id
er the
expert i
s
ri
sk appetite,
an
d the
greater
is
, the
stren
g
th of
ri
sk preferen
ce
is g
r
e
a
ter. If
0.
5
, we thin
k th
e
expert i
s
risk avoidan
ce,
a
nd the
smaller
is , the stre
ngth
of risk pr
efe
r
en
ce i
s
sm
a
ller. Wh
en
0.5
,
the expert i
s
risk
neutral. In
thi
s
p
ape
r, we
l
e
t 1 de
note t
he mem
b
e
r
ship, and
let -1 den
ote the
non-memb
ership,
so the
weig
ht vector of h
e
s
itation i
s
(1
)
2
1
. At last we get the intuitionistic fuzzy
function
ba
sed on
the
coefficient of
risk p
r
efe
r
en
ce a
s
follo
ws:
(2
1
)
,
ij
i
j
ij
i
j
r
[0
,1
]
.
3.4
D
y
namic
intuitionisti
c
fuzz
y
w
e
i
g
hted av
eraging (DIF
WA)
opera
tor
Information
a
ggre
gation
is
an e
s
sential
pro
c
e
s
s an
d i
s
al
so
an i
m
p
o
rtant
re
sea
r
ch to
pic
in the field o
f
information
fusion. If time is ta
ken
into acco
unt, for exampl
e
, the argu
m
ent
informatio
n
may be
colle
cted at diffe
rent pe
ri
od
s,
then the a
g
g
r
egatio
n op
erators and
th
eir
asso
ciated
weights
sho
u
ld
not be kept consta
nt.
Defini
tion3
: Let
t
be
a ti
me vari
able,
and
let
12
()
()
(
)
,,
,
p
t
tt
aa
a
be
a
colle
ction
of IFNs
colle
cted at
different pe
ri
ods
(1
,
2
,
,
)
k
tk
p
, and
12
()
(
(
)
,
(
)
,
,
(
)
)
p
tt
t
t
be the
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 106
3 – 1072
1068
weig
ht vector of the
period
s
(1
,
2
,
,
)
k
tk
p
, and
()
0
(
1
,
2
,
,
)
,
k
tk
p
1
()
1
p
k
k
t
, then we call a dyna
mic intuitioni
stic fuzzy weighted ave
r
aging
(DIF
WA
)
operator.
4. D
y
namic
DEMATE
L gr
oup decisio
n
approa
ch based on in
tuitionistic fu
zzy
number
Based
on th
e above th
eo
ry, this sectio
n sh
ows a
d
y
namic
DEM
A
TEL gro
up
deci
s
io
n
method ba
se
d on IFN. Firstly, the exte
nded meth
od
gives the initial intuitionistic fuzzy dire
ct-
relation mat
r
i
x
by each expert at differe
nt perio
d
s
, then we ag
gre
gate the grou
p experts’ init
ial
intuitionisti
c
fuzzy dire
ct-re
l
ati
on matrix hori
z
ontally a
t
each pe
riod
by certain
wa
y. On that basis,
the ag
gregati
on m
a
trix of i
n
tuitionisti
c
f
u
zzy di
re
ct-re
l
ation at
diffe
rent
peri
o
d
s
are
ag
gre
gat
ed
vertically ag
ain by DIF
W
A ope
rato
r when th
e time vector i
s
already kn
ow. We
get
the
intuitionisti
c
fuzzy total-rel
a
tion matrix. Finally,
we ca
n cal
c
ulate th
e degree of center an
d re
a
s
on
and fin
d
the
key influ
e
n
c
e
facto
r
s of
system. Th
e
sp
ecific flow an
d ste
p
s of th
e meth
od
are
a
s
follows
.
Figure 1. The
flow cha
r
t of dynamic
DE
MATEL grou
p deci
s
io
n-m
a
kin
g
method
Step1
：
Supp
ose a
set of system factors
1,
2
,
i
G
g
in
.
Step2
：
Co
nst
r
uct the
dire
cted g
r
ap
h b
y
the exper
ts wh
o give their ju
dgme
n
t
between th
e
fac
t
ors
.
If
i
g
has dire
ct imp
a
ct
to
j
g
, we
ma
rk
an a
r
row f
r
o
m
the fo
rme
r
to the latter.
And so o
n
,
dire
ct gra
ph a
m
ong all fact
ors i
s
given o
u
t.
Step3
：
Co
nst
r
uct
the i
n
itial
intuitioni
stic f
u
zzy di
re
ct-re
l
ation m
a
trix
by sin
g
le
exp
e
rt at
p
different
perio
ds. S
u
p
pose the
r
e
are
m
expert
s
in
the d
e
ci
sion
makin
g
tea
m
, whi
c
h
are re
pre
s
ente
d
a
s
the set:
12
,,
,
m
F
ff
f
. Let the expert
f
give his judge
ment betwe
e
n
any two factors
(,
)
(
,
1
,
2
,
,
)
,
ij
g
gi
j
n
i
j
. The result can be
expressed:
()
()
(
)
()
(,
,
)
kk
k
k
tt
t
t
ij
ij
i
j
i
j
r
.
()
k
t
ij
indicates th
at the expe
rt
f
think
i
g
is m
o
re
i
m
porta
nt tha
n
j
g
and the va
lue give
s the
degree of importan
c
e
whe
n
he com
pares them at
k
t
period.
()
k
t
ij
v
indicat
e
s that
j
g
is prefere
d
to
i
g
and
()
k
t
ij
reflects the exp
e
rt’s he
sitan
c
y.
()
()
()
,,
kk
k
tt
t
ij
ij
ij
satisfy the con
d
ition
of
2
t
k
t
1
t
pe
rio
d
s
12
,,
,
m
f
ff
e
xpe
rts
init
ia
l int
u
it
io
nist
ic
fuz
z
y
dire
c
t
-re
la
tio
n m
a
trix
12
,,
,
m
f
ff
12
,,
,
m
f
ff
11
1
1(
)
2
(
)
(
)
,,
,
tt
m
t
R
RR
22
2
1
(
)
2
()
()
,,
,
tt
m
t
R
RR
1(
)
2
(
)
(
)
,,
,
kk
k
tt
m
t
R
RR
Grou
p int
u
it
io
nis
tic
fuz
z
y
dire
c
t
-
re
la
tion m
a
trix
inte
gra
t
e
d
i
n
t
u
iti
on
i
s
tic
fuz
z
y
re
la
tion ma
trix
R
Real
n
u
m
b
er
tota
l-
re
la
tion
ma
trix
T
Cal
c
u
l
at
e t
h
e
de
gre
e
of c
e
n
te
r
a
nd re
a
s
on
inf
o
rm
a
tion
norm
a
liz
a
tion
DI
F
W
A
ope
ra
to
r
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Dynam
ic DE
MATEL Gro
u
p
De
cisi
on Appro
a
ch Based
on Intuitio
nistic F
u
zzy Num
ber (Hui
Xie)
1069
Definition
1. Then
we
can
obtain
the initial
intuitionisti
c
fuzzy dire
ct-relation m
a
trix
()
()
()
kk
tt
ij
n
n
Rr
by expert
f
at
(1
,
2
,
,
)
k
tk
p
perio
d.
()
()
()
()
()
()
11
1
1
11
1
1
1
()
()
()
()
()
()
()
21
2
1
21
2
2
2
()
()
()
()
()
()
11
1
(,
,
)
(,
,
)
(,
,
)
(,
,
)
(,
,
)
(,
,
)
kk
k
k
k
k
kk
k
k
k
k
k
kk
k
k
k
k
tt
t
t
t
t
nn
n
tt
t
t
t
t
t
nn
n
tt
t
t
t
t
nn
n
n
n
n
n
n
n
vv
vv
R
vv
Step4
：
Aggregate i
n
tuitio
nistic fuzzy di
rect
-re
l
a
tion
matrix of
sing
le expe
rt at
(1
,
2
,
,
)
k
tk
p
perio
d. The weig
ht vector of every expert is
, and
12
,,
,
m
is the set of all the
experts’
wei
ght vector.
The set of experts i
s
1,
2
,
,
f
m
. So the aggreg
ation of
intuitionisti
c
fuzzy
dire
ct-relation matrix is
()
(
)
1
()
()
m
tt
ij
n
n
kk
k
t
RR
r
. And
()
1
(,
,
)
,
,
1
,
2
,
,
,
,
kk
k
k
k
k
m
tt
t
t
t
t
i
j
i
j
ij
ij
ij
ij
ri
j
n
()
()
11
,
.,
1
,
2
,
,
.
kk
k
k
mm
tt
t
t
ij
ij
ij
i
j
ij
n
Step5:
We a
ggre
gate the aggregatio
n of intu
itionistic fuzzy relati
on matrix
()
()
()
t
ij
n
n
kk
t
Rr
into
integrate
d
intuitionisti
c
fuzzy relation m
a
trix
()
ij
n
n
Rr
at
p
different perio
ds
by the DIFWA
operator:
12
()
(
)
()
()
()
()
()
(
)
(
)
()
()
(
)
()
1
11
1
1
(,
,
,
)
(
)
(
1
(
1
)
,
,
(
1
)
)
p
kk
k
k
k
tt
t
t
kk
k
k
pp
p
p
p
t
tt
t
t
t
tt
tk
aa
a
a
k
kk
k
k
DIFWA
a
a
a
t
a
(,
,
)
i
j
ij
ij
ij
r
r
r
r
,
()
()
1
1(
1
)
k
t
k
ij
ij
p
t
r
r
k
，
()
()
1
k
t
k
ij
ij
p
t
r
r
k
，
()
()
()
(
)
11
(1
)
kk
tt
kk
ij
ij
i
j
pp
tt
r
rr
kk
，
(,
1
,
2
,
,
)
ij
n
.
Step6:
Conv
ert the integ
r
ated intuitioni
stic fu
zzy re
lation matrix.
It is
very important to conver
t
the matrix
which
is const
i
tuted by IFNs fro
m
fu
zzy
numb
e
r into
real
nu
mbe
r
. We ta
ke
ri
sk
prefe
r
en
ce coefficient
into the pro
c
e
s
s of conversi
on, wh
o
s
e v
a
lue is in
se
ction3.3. After
conve
r
si
on t
he re
al nu
mber m
a
trix
is ge
nerated:
()
,
ij
n
n
r
R
(2
1
)
,
i
j
ij
i
j
ij
r
[0
,1
]
.
ij
r
mean
s det
ermin
a
te de
gree
of exp
e
rts’
p
r
e
f
er
en
c
e
w
h
ic
h
is
co
n
v
er
te
d fr
om
hesita
n
cy.
Step7:
Cal
c
ulate total-rel
a
tion matrix. Acco
rding t
o
the formul
a
1
()
[
]
ij
n
n
TB
I
B
t
, we
measure the
com
b
ine
d
i
m
pact
of eve
r
y facto
r
whi
c
h i
s
effe
cte
d
by othe
r fa
ctors di
re
ctly and
indirec
t
ly. And we get the total relation matrix
T
, where
I
is the
identity matrix. It is the
norm
a
lized di
rect
-rel
a
tion
matrix
ij
nn
b
B
, where
/m
a
x
1
i
j
ij
ij
b
rr
i
n
.
Step8:
Calcu
l
ate the de
gree of center
and rea
s
on.
We a
dd the f
a
ctors of
ro
ws re
sp
ectivel
y
to
get the
deg
ree of
ce
ntre
:
1
n
ii
j
j
f
t
. In the
same
way, we get th
e d
egre
e
of
re
a
s
on:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 106
3 – 1072
1070
1
n
j
i
j
i
t
e
.Thus it is infered th
e deg
ree
of centre about
i
g
in all factors:
,(
1
,
2
,
,
)
ii
i
rf
e
i
n
, as
well a
s
the deg
ree
o
f
rea
s
on
abo
ut
i
g
whi
c
h
ca
n indi
cate th
e
internal
stru
ct
ure of it :
,(
1
,
2
,
,
)
ii
i
uf
e
i
n
.
Step9:
Dete
rmine the key
influence fa
ctors. We ra
n
k
all the factors based on their impo
rtan
ce
by the de
gre
e
of cente
r
i
r
.
We
need
to
cho
o
se the
key influe
nce
factors
accordin
g to th
e
pra
c
tical e
n
vironm
ent and
reso
urce
co
ndition
s.
In addition, we
can also put forward relate
d
manag
eme
n
t sug
g
e
s
tion
s to the key fact
ors by the de
gree of rea
s
o
n
i
u
.
5. Applicatio
n example
In this se
ctio
n, we will
offer an exam
ple to illust
ra
te our p
r
o
c
e
dure
and
prove the
feasibility of the method.
The po
stgrad
uate abo
ut econ
omics mu
st
compl
e
te two professio
nal
elective course in third g
r
ade a
c
cordi
n
g to the
training plan in M university. The teach
e
r wh
o is
in ch
arg
e
of the course
arrangem
ent sh
ould give
o
u
t the co
urse
scheduli
ng at th
e end
of gra
d
e
two. In orde
r to arran
ge t
he co
urse re
aso
nably, we
choo
se th
re
e postg
ra
dua
tes to be th
e
deci
s
io
n ma
kers who
gives their
ch
oice
about th
re
e
course
s that
can be
offered
in the
begi
nn
ing
of the gra
d
e
two an
d at the end of t
he seme
ster respe
c
tively. T
he three
course
s a
r
e:
1
a
,
w
e
s
t
e
r
n
ec
ono
mics
;
2
a
, game theory;
3
a
, financi
a
l engin
e
e
ring.
Firs
t determine the s
e
t of sys
tem fac
t
ors
12
3
,,
Ga
a
a
. Three p
o
st
grad
uate
s
12
3
,,
f
ff
(
w
hose weight vec
t
or
is
1
：
0.3
，
2
：
0.3
，
3
：
0.4)
comp
are
the thre
e co
urses by u
s
in
g IFN a
t
two times
1
t
，
2
t
(
w
ho
se w
e
igh
t
v
e
ct
or is
1
t
：
0.3
，
2
t
：
0.7). The po
stgra
d
u
a
tes
(1
,
2
,
3
)
k
f
k
provide
their i
n
itial intuiti
onisti
c
f
u
zzy di
rect
relat
i
on m
a
trix
()
()
33
(
)
(
1
,2
,
3
;
1
,2
)
kk
tt
ij
Rr
k
respec
tively,
as
lis
ted below:
1
2
1(
)
1(
)
(
0
.
5
,0
.
5
,0
)
(
0
.
4
,
0
.
6
,
0
)
(
0
.
5
,
0
.
4
,0
.
1
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
2
,0
.
8
,0
)
(
0
.
9
,
0
.
1
,
0
)
(
0
.
6
,0
.
4
,0
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
3
,0
.
4
,0
.
3
)
,
(
0
.
8
,0
.
2
,0
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
3
,0
.
5
,0
.
2
)
(
0
.
4
,0
.
5
,0
.
1
)
(
0
.
4
,
0
.
3
,
0
.
3
)
(
0
.
5
,0
.
5
,0
)
t
t
RR
1
2
2(
)
2(
)
(
0
.
1
,0
.
9
,0
)
(
0
.
5
,
0
.
3
,
0
.
2
)
(
0
.
5
,0
.
5
,0
)
(
0
.
5
,0
.
5
,0
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
2
,0
.
6
,0
.
2
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
3
,0
.
7
,0
)
(
(
0
.
5
,0
.
5
,0
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
3
,0
.
4
,0
.
3
)
,
(
0
.
6
,0
.
2
,0
.
6
)
(
0
.
4
,
0
.
3
,
0
.
3
)
(
0
.
5
,0
.
5
,0
)
t
t
RR
1
3(
)
0.1
,
0.8
,
0
.
1
)
(
0
.
7
,0
.
3
,0
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
5
,0
.
5
,0
)
(
0
.
8
,0
.
1
,0
.
1
)
(
0
.
5
,
0
.
5
,
0
)
(
0
.
5
,0
.
5
,0
)
(
0
.
5
,0
.
5
,0
)
(
0
.
3
,
0
.
5
,
0
.
2
)
(
0
.
3
,0
.
7
,0
)
(
0
.5
,
0
.3
,
0
.2)
(
0.
5
,
0.
5
,
0)
(
0
.1
,
0
.9
,
0
)
(
0
.
7
,0
.
3
,0
)
(
0
.
9
,
0
.
1
,
0
)
(
0
.
5
,0
.
5
,0
)
t
R
2
3(
)
(
0
.
5
,0
.
5
,0
)
(
0
.
4
,
0
.
5
,
0
.
1
)
(
0
.
6
,0
.
3
,0
.
1
)
,
(
0.5
,
0.4
,
0.1
)
(
0
.5
,
0
.5
,
0
)
(
0
.
4
,
0
.
4
,
0.2
)
(
0
.
3
,0
.
6
,0
.
1
)
(
0
.
4
,
0
.
4
,
0
.
2
)
(
0
.
5
,0
.
5
,0
)
t
R
Then
we u
s
e
step 4 to a
g
g
reg
a
te the
matrix
11
1
1(
)
2
(
)
3
(
)
,,
tt
t
R
RR
and
22
2
1(
)
2
(
)
3
(
)
,,
tt
t
RR
R
hori
z
ontally
into matrix
()
33
()
()
t
ij
kk
t
Rr
:
1
2
()
()
(
0
.
5
,
0
.
5
,
0
)
(
0.
3
9
,
0
.
5
3
,
0.
08
)
(
0.
33
,
0
.58
,
0
.
09)
(
0
.
5
,
0
.
5
,
0
)
(
0.
31
,
0
.
6
5
,
0.
04
)
(
0.
54
,
0
.
3
9
,
0.
07
)
(
0
.5
3
,
0
.
3
9
,
0
.0
8
)
(0
.5
,
0
.5
,
0
)
(
0
.
2
2
,
0
.6
,
0
.1
8
)
,
(
0
.
6
5
,
0
(
0
.
5
8
,
0.
33
,
0
.
09)
(
0
.
6
,
0
.
2
2
,
0.
18
)
(
0.
5
,
0.
5
,
0)
t
t
RR
.
3
1
,
0.
04)
(
0
.
5
,
0
.
5
,
0
)
(
0.
4
,
0.
46
,
0
.
14)
(
0
.
3
9
,
0.
54
,
0
.
0
7
)
(
0
.46
,
0.
4
,
0.
14)
(
0
.
5
,
0
.
5
,
0
)
By DIFWA ,
we fuse the
12
()
(
)
,
tt
RR
again into int
egrate
d
intuitionisti
c
fuzzy relation matrix
R
:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Dynam
ic DE
MATEL Gro
u
p
De
cisi
on Appro
a
ch Based
on Intuitio
nistic F
u
zzy Num
ber (Hui
Xie)
1071
(
0
.
5
,
0
.
5
,
0
)
(
0
.
34
,
0
.
6
1
,
0.
0
5
)
(
0.
49
,
0
.
4
4
,
0.
07
)
(
0
.
6
2
,
0
.
33
,
0
.
0
5
)
(
0
.
5
,
0
.5
,
0
)
(
0.
3
5
,
0
.
5
6
,
0.
09)
(
0
.
4
5
,
0
.
47,
0.
08
)
(
0
.
51
,
0
.
3
3
,
0.
1
6
)
(
0.
5
,
0
.
5
,
0)
R
Next we
utilize step
6 to convert matrix
R
into real
nu
mber m
a
trix
R
. Her
e
w
e
let
0.
5
, s
o
the
real nu
mb
er matrix
R
is:
0
0
.2
7
0
.0
5
0.
29
0
0
.
2
1
0.
02
0.
18
0
R
In the s
a
me way
，
a
c
cordi
ng to the step 7&8, we calc
ul
ate the cente
r
and reason deg
re
e as
sho
w
n in tabl
e 1.
Table1. Th
e rank info
rmati
on of every optional curriculum
curriculu
m
i
f
i
e
ii
f
e
ii
f
e
rank
1
a
-0.37
0.3
-0.07
-0.67
2
nd
2
a
-0.38
-0.65
-1.03
0.27
3
rd
3
a
0.37
-0.03
0.34 0.4 1
st
From the
co
mpari
s
o
n
of data in Tabl
e
1 clea
rly
,
we can
sele
ct
t
he cu
rri
culu
m as t
h
e
seq
uen
ce of
31
2
aa
a
in the process of acad
emi
c
cu
rri
cu
lu
m arrang
ement.
That is to say,
the deci
s
io
n make
rs wh
o is re
sp
on
sible
for the co
urse arrang
eme
n
t shoul
d opt
to the alterna
t
ive
in acco
rda
n
ce with the
ab
ove ord
e
r
wh
en the o
p
tion
is limited. Th
roug
h the
ab
ove analy
s
is,
the
dynamic
DE
MATEL deci
s
ion app
roa
c
h
that this pap
er
present fully consi
der
t
he limitations of
expert co
gnit
i
on. As the appli
c
ation o
f
IFN, t
he
method al
so
completely
expre
ss exp
e
rts’
judgme
n
t on
deci
s
ion ma
king p
r
obl
em
s integ
r
ally. At the same
time, by th
e mean
s of the
judgme
n
t of
multi-pe
rson
and multi
-ro
u
nds, a
nd u
s
in
g DIF
W
A ope
rator to i
n
teg
r
ate the de
ci
si
on-
make
rs’ ju
dg
ment of
different mom
ent,
the ap
pro
a
ch
is
more
coin
cide
nt with
th
e a
c
tual
de
ci
sion
situation. Th
rough th
e pra
c
tical
appli
c
at
ion of th
is in
stan
ce, it ca
n
be seen tha
t
the pre
s
ent
ed
method ha
s the appli
c
atio
n feasibility fo
r the obje
c
tive actual
situa
t
ion.
6. Conclusio
n
s
Since DEMA
TEL wa
s introdu
ced, it ha
s bee
n appl
i
e
d in many areas, such as
in so
cial
life, econ
omi
c
ma
nage
me
nt, and ma
ny other fiel
ds
by its strong
pra
c
ti
cality a
nd conveni
en
ce.
Ho
wever, i
n
the ap
plica
t
ion of DEM
A
TEL me
tho
d
, pre
s
e
n
t literature al
ways ign
o
res the
influen
ce of
subj
ective fa
ctors of d
e
ci
sion m
a
kers.
And the va
st majo
rity of sch
ola
r
s ta
ke
accou
n
t into
only on
e
sin
g
le exp
e
rt’s j
udgme
n
t
ab
o
u
t the fa
ctors relatio
n
ship
of the
com
p
lex
system at a
single pe
rio
d
, who i
gno
re th
e com
p
lexi
ty of the de
cisio
n
-ma
k
in
g pro
c
e
ss. Th
erefo
r
e,
this pap
er p
r
opo
se
s a method called dy
namic
DEMA
TEL grou
p de
cisi
on metho
d
based on I
F
N.
The m
e
thod
has two
follo
wing
adva
n
ta
ges.
Firstly,
usin
g IF
Ns in
stead
of th
e
traditional
poi
nt
estimate
s, can reflect th
e expe
rts’ o
v
erall pe
rcep
tion of co
mp
lex deci
s
io
n
probl
em
s mo
re
obje
c
tively an
d accu
rately.
It is also mo
re deli
c
at
ely p
o
rtray the
fuzzine
s
s an
d u
n
ce
rtainty of the
compl
e
x syst
em in re
al world. Secondl
y, through
m
any expert
s
in multiple ro
und
s of scien
t
ific
deci
s
io
n ma
king, b
r
ingi
n
g
the time
dimen
s
i
on i
n
to DEMATE
L in dynami
c
de
ci
sion,
and
integratin
g g
r
oup i
n
form
ation effe
ctively, will
be m
o
re
in lin
e
with t
he
com
p
lex i
s
sue
of p
r
a
c
tical
deci
s
io
n ma
ki
ng
situation
s
. Finally, an
e
x
ample of ve
rif
i
cat
i
on
re
su
lt
s s
h
o
w
s t
h
a
t
t
h
is ap
pr
oa
ch
is feasi
b
le, which
can effe
ctively solve dynamic
DE
MATEL grou
p deci
s
io
n problem in p
r
a
c
tice.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 106
3 – 1072
1072
Referen
ces
[1]
Shie
h JI, W
u
HH, Huan
g KK. A DEMAT
E
L met
hod i
n
identif
yi
ng ke
y
success factors of hospita
l
service q
ual
it
y
.
Know
ledg
e-Ba
sed Syste
m
s
. 201
0; 23(9): 27
7–2
82.
[2]
Barua
h
S,
Raj
S, Sh
abb
irud
din,
Ra
y
A,
Ch
akravort
y S.
A
nal
ysis
of
infl
u
enci
ng f
a
ctors
for costs o
n
substatio
n
sitin
g
base
d
on DE
MAT
E
L method.
Procedi
a En
gin
eeri
n
g
. 20
1
2
; 38(1): 25
64-
257
1.
[3]
W
en-Hsie
n T
,
W
e
i H. A n
o
vel
h
y
bri
d
mo
del
base
d
o
n
DEM
A
T
E
L and ANP
for selecti
ng c
o
st of qu
ali
t
y
mode
l deve
l
o
p
m
ent.
T
o
tal Quality Man
age
ment & Busin
e
ss
Excelle
nce
. 20
10; 21(4): 4
39-
456.
[4]
T
s
eng M L. A causa
l
an
d ef
fect decisi
on
makin
g
mod
e
l
of service
qua
l
i
t
y
e
x
pectati
on
usin
g gre
y
-
fuzz
y
DEMAT
E
L appr
oac
h.
Expert Systems
w
i
th Applicati
o
ns.
2009; 3
6
(4)
:
7738-7
7
4
8
.
[5]
Don J, G
w
o
-
Hs
hiu
ng, T
.
Socia
l
infl
ue
nce
on t
he us
e of c
lin
ic
al d
e
cisi
on s
u
p
port s
y
stem :R
evisitin
g th
e
unifi
ed th
eor
y
of accept
ance
and
use
of te
chno
log
y
b
y
fu
zz
y
D
E
MAT
E
L techni
qu
e.
Co
mp
uters &
Industria
l Engi
neer
ing
. 2
012;
62(3):8
19-8
28.
[6]
Wu WW. Segmenting critical factors for succe
ssful kno
w
l
edg
e man
age
ment impl
eme
n
tation us
in
g
the fuzz
y
DEM
A
T
E
L method.
Appl
ied S
o
ft Computi
n
g
. 20
1
1
; 12(6): 52
7-5
35.
[7]
Xi
e H,
Du
an
W
C
, Sun YH.
Group
DEM
A
T
E
L decisio
n
ap
proac
h b
a
s
ed
on
intuiti
onistic f
u
zz
y
prefere
n
ce.
Co
mp
uter Eng
i
n
e
e
rin
g
and A
ppl
i
c
ations
. 20
14;
50(1
1
): 33-3
8
.
[8]
W
e
i PL,
Hua
n
g
H, T
z
eng
GH, W
u
SI. Ca
u
s
al m
ode
lin
g
o
f
w
e
b-
advertis
i
ng
effects b
y
i
m
provin
g SEM
base
d
on DEM
A
T
E
L
techniq
u
e
.
Internatio
nal
Journa
l of Informatio
n
T
e
ch
nol
ogy & Deci
sion Mak
i
ng
.
201
0; 9(5): 799
–82
9.
[9]
Atanassov K,
Pasi G, Yager
RR. Intuitio
nist
ic fuzz
y
interpr
e
tations
of mul
t
i-criteria mu
lti-
perso
n an
d
multi-meas
ure
m
ent too
l
decis
ion
maki
ng.
Int
e
rnati
ona
l J
our
nal
of Syste
m
s
Scie
nce
. 200
5
;
36(1
4
-1
5):
859-
868.
[10]
Li DF
. Mu
ltiattribute
dec
isio
n
makin
g
mo
del
s an
d meth
ods
usin
g i
n
tuiti
o
n
i
stic fuzz
y sets
.
Jo
u
r
na
l
of
Co
mp
uter and
System Sci
enc
es
. 2005; 7
0
(1)
:
73-85.
[11]
Panko
w
s
k
a A, W
y
gral
ak M.
Genera
l
IF
-sets
w
i
th
tria
ng
ul
ar norms an
d their ap
plic
atio
ns to grou
p
decisi
on mak
i
n
g
.
Informati
on Scienc
es
. 200
6; 176(1
8
): 271
3-27
54.
[12]
Xu
ZS. Com
p
atibil
it
y a
nal
ys
i
s
of int
u
itio
nist
ic fuzz
y pr
efer
ence
rel
a
tio
n
s
in gro
up deci
s
ion
m
a
ki
ng.
Group Dec
i
sio
n
and N
e
g
o
tiati
o
n
. 201
3; 22(3)
: 463-48
2.
[13]
Xu
Z
S
. Intuiti
o
nistic
prefere
n
c
e re
latio
n
s
an
d the
i
r
app
licat
ion
in
gr
oup
d
e
cisio
n
m
a
kin
g
.
Information
Scienc
es
. 200
7; 177(1
1
): 236
3-23
79.
[14]
Xu
Z
S
, Ro
nal
d
R. Yag
e
r. D
y
n
a
mic i
n
tuiti
onis
t
ic fuzz
y multi-
attribute
decis
i
on m
a
kin
g
.
Sci
ence
Dir
ect
.
200
8; 48: 246-
262.
Evaluation Warning : The document was created with Spire.PDF for Python.