TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4814 ~ 4
8
2
4
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.554
1
4814
Re
cei
v
ed
De
cem
ber 3
1
, 2013; Re
vi
sed
March 16, 20
14; Accepted
March 29, 20
14
A Dominance Degree for Rough Sets and Its
Application in Ranking Popularity
Jia Zhao*
1
, Jia
n
f
e
n
g
Gu
an
2
, Changqia
o
Xu
2,3
and Hongke Zh
an
g
1
1
Nation
al Eng
i
neer
ing L
a
b
o
ra
tor
y
for Ne
xt Gener
ation Inter
net Intercon
ne
ction Dev
i
ces,
Beiji
ng Ji
aoto
n
g
Univ
ersit
y
, B
e
iji
ng, Ch
ina
2
State Ke
y
La
b
o
rator
y
of Net
w
orkin
g
and S
w
i
t
ching T
e
chno
l
o
g
y
,
Beiji
ng U
n
ivers
i
t
y
of Posts an
d T
e
lecommun
i
catio
n
s, Beiji
n
g
, Chin
a
3
Institute of Sensin
g
T
e
chnolo
g
y
and
Bus
i
n
e
ss,
Beiji
ng U
n
ivers
i
t
y
of Posts an
d T
e
lecommun
i
catio
n
s, W
u
xi,
Jian
gsu, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 1111
10
04@
b
j
tu.edu.cn
A
b
st
r
a
ct
Rou
gh set theory is use
d
i
n
data
min
i
ng
through co
mplex l
earn
i
ng
systems an
d uncerta
i
n
infor
m
ati
on d
e
c
ision fro
m
arti
ficial i
n
tell
ige
n
c
e. F
o
r
multi
p
l
e
attribute d
e
ci
sion
mak
i
ng, r
oug
h sets e
m
p
l
oy
attribute re
duc
tion to g
e
n
e
ra
te decis
ive ru
l
e
s. How
e
ver,
dyna
mic infor
m
ati
on
data
b
a
s
es, w
h
ich rec
o
r
d
attribute va
lu
e
s
chan
gin
g
w
i
th time, raise
q
uestio
n
s
to rou
gh set b
a
se
d mu
ltipl
e
attrib
u
t
e reducti
on. T
h
i
s
pap
er prop
ose
s
a dyna
mic
attribute bas
e
d
do
mi
nanc
e degr
ee for ro
ugh-s
e
t-bas
ed
rankin
g decis
ion
.
Accordi
ng t
o
th
e d
o
m
in
anc
e r
e
lati
ons
betw
e
en tw
o
obj
ects
in
dyna
mic i
n
fo
rmati
o
n
tabl
e,
w
e
prop
ose
thr
e
e
jud
g
m
ents an
d
their
ju
dgi
ng
v
a
lu
es
to get a do
mi
nanc
e de
gree
val
ue,
by
w
h
ich w
e
ca
n
deny
or
ap
prov
e of
the d
o
m
in
anc
e
relati
ons. T
h
e
n
w
e
us
e the
d
o
min
ance-
de
gr
ee-b
a
sed
ro
ug
h set to
make
dyna
mic attrib
ute
reducti
on. W
e
app
lie
d this method i
n
ranki
n
g pop
ular
it
y of netw
o
rk servic
e resourc
e
s. and extract rank
in
g
decisi
on ru
les. Experi
m
ents show
co
mparis
o
n
betw
een the
search
ing e
n
g
i
nes w
i
th and w
i
thout the rank
i
n
g
function a
nd th
e efficiency of r
oug
h set ranki
ng by our pr
op
osed d
o
m
in
anc
e degr
ee va
lue
.
Ke
y
w
ords
:
ro
ugh set, ju
dgi
n
g
valu
e, do
mi
n
ance d
egr
ee, d
y
na
mic attrib
ute, popu
larity ra
nkin
g
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Develo
pment
s in m
a
chine
learni
ng a
nd
data minin
g
e
x
pand the
di
mensi
on of
capability
in pattern re
cognition an
d enlarge the knowl
edge
d
o
m
ain [1]. Diverse features or pattern
s are
mined a
s
well
as so
me jud
g
ing rul
e
s ext
r
acte
d for recogni
zing of n
e
w obj
ect
s
. Learni
ng p
r
o
c
e
s
s
can
be reg
a
rded
a
s
either cla
ssify
ing
or
clu
s
terin
g
p
r
o
c
e
s
s [2]. Sup
e
rvise
d
le
arni
ng
system
s u
s
e
introdu
ction
a
nd
classification mo
del to i
dentify obje
c
ts, while u
n
su
pervised
syst
ems ta
ke
so
me
discrimi
natory
judgment
s to
clu
s
ter obj
ects and ex
p
l
ain their sim
ilarity. Pawla
k
[3] propo
sed
roug
h
set th
eory a
nd
attribute redu
cti
on to
solv
e
multi-attribute
de
cisi
on m
a
king
problem
s in
machi
ne l
earning a
nd a
r
ti
ficial intellig
e
n
ce.
Rou
gh
set, empl
oye
d
as un
su
pe
rvised
lea
r
ni
ng
method, is
su
itable for un
certain info
rm
ation pr
oce
ssing. Rou
gh fu
nction
wa
s al
so p
r
op
ose
d
to
descri
be the
approximatio
n to co
mplex
function
s o
r
pattern
s [4]. The
con
c
ept
and te
chni
qu
es
are
appli
ed
widely in
ma
chin
e lea
r
ni
n
g
an
d a
r
tifici
al intellige
n
t
system
de
sig
n
ing.
Roug
h
set
make full u
s
e
of binary rel
a
tion betwee
n
each two
o
b
ject
s. Origi
n
al roug
h set theory di
scusse
s
the indi
scrimi
nate bin
a
ry relation a
nd u
s
e attrib
ute in
formation ta
bl
e to gro
up o
b
j
ects [5]. Th
e
r
e
are al
so
oth
e
r bin
a
ry rel
a
tions. Slo
w
i
n
ski et al. [6
] propo
se
d similarity relati
on ba
se
d ro
ugh
approximatio
ns. Gre
c
o [7
] propo
sed d
o
minan
ce rel
a
tion based
roug
h set m
e
thod to sol
v
e
multiple attri
b
ute de
ci
sion
probl
em
s. In
appli
c
ation
s
,
roug
h
set
ca
n eithe
r
b
e
u
s
ed
in
de
cisi
on
makin
g
in da
ta mining, or assi
st as pretreat
me
nt system with o
t
her learning
and cla
ssifyi
n
g
method
s su
ch as ne
ural n
e
twork o
r
fuzzy set.
Domin
ance relatio
n
based ro
ugh
set frame
w
o
r
k is
employed i
n
multiple attrib
ute deci
s
io
n
makin
g
w
hen
one de
ci
sive
grou
p is p
r
ef
erred to an
other
one on
an a
ttribute in th
e inform
ation
tables. Dom
i
nan
ce de
gre
e
de
scribe
s
how m
u
ch o
n
e
obje
c
t outp
e
rforms an
othe
r on
e a
bout
an attrib
ut
e [
8
]. As an
efficient
soft
co
mputing
met
hod,
roug
h set ha
s been
widel
y applied in the realm of in
formatio
n science. Li et a
l
. [9] propo
se
d a
Rou
gh sets-b
ase
d
se
arch
engin
e
for g
r
i
d
se
rvice
di
scovery. Roug
h set ba
se
d multiple attrib
ute
deci
s
io
n hav
e be
en
used
in ai
rpo
r
t
se
rvice
quality
ran
k
ing
[10,
11]. Domi
nan
ce
ba
sed
ro
u
gh
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Dom
i
nance
Degree for
Rough Sets a
n
d
Its App
licati
on in Ra
nki
n
g
Popularit
y (Ji
a
Zhao
)
4815
sets
app
roa
c
h has
bee
n a
pplied in
eval
uating the
im
pact of info
rmation techn
o
logy. Kanei
wa et
al. [12] used
roug
h set b
a
s
ed d
e
ci
sio
n
method to mi
ne the se
que
ntial pattern.
Facto
r
s affe
ct
ing
the adoptio
n
of Software
servi
c
e were analyzed
with ro
ugh
set deci
s
ion
method. Rou
gh set
plays its rol
e
to deal with
static inform
ation table
s
.
Ho
wever, th
e
r
e a
r
e
so
m
any dynami
c
databa
se
a
nd dyna
mic i
n
formatio
n ta
bles to
record fre
q
u
ently cha
nge
d and
upd
ated attrib
ute
va
lues
of an
obje
c
t [13]. Traditio
nal
static
informatio
n table
s
do not reflect variati
on of a
value over a perio
d of time. So
me compli
cat
ed
dynamic dat
aba
se
s
can
reco
rd th
e va
riation
se
que
nc
e
s
fo
r a
n
attribute item
of obje
c
ts i
n
a
ran
k
ing
syste
m
[14]. For e
x
ample, we
analyze se
rvice po
pula
r
ity of a campu
s
netwo
rk in o
u
r
experim
ents.
In this examp
l
e, some attri
butes
of a co
ntent item are dynamicall
y
chang
ed ov
e
r
an
o
b
servati
on
time. The
s
e attribute
s
can
be
some
kin
d
of
in
cre
a
sin
g
st
at
ist
i
cs
s
u
c
h
as
c
lic
k
rates o
r
visiti
ng time
s. Ho
w to d
eal
wi
th these dyn
a
mic
attribut
es
and
emb
ody variatio
n
in
deci
s
io
n mechani
sm of popularity be
co
mes a tough
question, be
cau
s
e po
pul
arity has to be
recogni
ze
d a
s
a co
mplex pattern, whi
c
h deserve
s d
e
liberate de
si
gn of ran
k
ing
method.
In this pap
er,
we p
r
op
ose a
domina
n
ce d
egre
e
for rou
gh set
-
ba
se
d popul
arity ran
k
ing to
solve dynami
c
attribute de
cisi
on ma
king
proble
m
and
its appli
c
ation
in a network
servi
c
e ran
k
i
ng
and se
archi
n
g system. We give three domina
n
ce
re
lation ca
se
s and propo
se
judgin
g
value
s
on
each attribut
e in three
ca
se
s: (i) in th
e
basi
c
domi
n
ance judg
me
nt, we judg
e wheth
e
r o
b
je
ct A
outperfo
rm B
in compa
r
ati
v
ely more ob
servatio
n
times; (ii) in the
freque
ntly ch
angin
g
judgm
ent,
we j
udg
e
wh
ether A
an
d
B cha
nge
th
eir d
o
min
ant
relation
fre
q
u
ently in different ob
se
rvation
times; (iii) in t
he greatly ch
angin
g
judg
m
ent, we
ju
dge
wheth
e
r
at some ob
se
rvat
ion time poi
nts
one obj
ect o
u
tperfo
rms
a
nother
one v
e
ry mu
ch to
a larg
e en
ou
gh deg
re
e. With the
s
e t
h
ree
degree value
s
, we can cal
c
ulate the do
minan
ce
de
gree judgin
g
value. If the do
minan
ce de
gre
e
value is gre
a
ter than a thre
shol
d, we jud
ge there is a
domina
n
ce re
lation betwe
e
n
two obje
c
ts.
If
the domi
nan
ce
deg
ree va
lue is le
ss th
an a th
re
shol
d, we
deny t
he do
mina
nce rel
a
tion. After
assign
a dom
inan
ce deg
re
e
value
to ea
ch attri
bute, we obtain
all
domina
n
ce re
lations
bet
we
en
each two o
b
j
e
cts in i
n
form
ation tabl
e. T
hen
we
u
s
e rough
set-ba
sed
attri
bute redu
ction
to
m
a
ke
a multiple attribute de
ci
sio
n
and emplo
y
these
meth
ods to ran
k
the popul
arity
of the campus
netwo
rk
se
rvi
c
e resou
r
ce. Experimental
results
sh
o
w
that the syst
em with o
u
r p
r
opo
se
d ran
k
ing
machi
n
e
r
y can efficiently
react to th
e variati
on i
n
dynamic a
ttribute information table
and
outperfo
rm th
e situation
wi
thout ran
k
in
g
.
The main
contributio
ns
o
f
this pape
r i
n
clu
d
e
s
: 1)
We
recogni
ze
po
pularity a
s
a
compl
e
x patt
e
rn th
at ha
s
multiple attrib
utes a
nd
de
serves ela
borate
learni
ng met
hod; 2) We give three case to de
scribe the varia
t
ion of attributes in dyna
mic
informatio
n table an
d pro
pose thre
e ju
dging valu
e to obtain a d
o
minan
ce d
e
g
r
ee; 3)
We a
pply
this domin
an
ce de
gre
e
in the rou
gh set-based de
ci
sio
n
to extract ru
les for ran
k
in
g popul
arity.
The rem
a
ind
e
r of this pap
er is organi
ze
d as follows: Section II introdu
ce
s som
e
related
theories including learning function and rough se
t. In section III, we prop
ose the three judgi
ng
values an
d t
he d
o
mina
nce de
gre
e
fo
r
roug
h
set. In
additio
n
, we
prove
some
prop
ertie
s
of
the
domina
n
ce d
egre
e
b
a
se
d
on roug
h set. In Secti
on IV,
we
do the
experim
ent ba
sed on
a n
e
twork
servi
c
e retrie
val system. Section V co
nclude
s the pap
er.
2. Res
earc
h
Method
2.1.
Degr
ee Fun
c
t
ion for Dy
n
a
mic Attribu
t
es
Dynami
c
attri
bute data
al
ways exits i
n
in
form
ation pro
c
e
ss.
T
able 1
sho
w
s click rates
of
two
web vid
e
o
s i
n
seven
d
a
ys. Cli
c
k rates
stan
ds
for attribute
of p
opula
r
ity
in some way.
Th
ese
popul
arity val
ues a
r
e va
ria
b
le d
u
rin
g
a
wee
k
.
Co
n
s
id
ering
that m
o
re
popul
ar video i
s
preferred,
we n
eed
to
deci
de
wheth
e
r the
r
e i
s
a
domin
an
ce
relation b
e
twe
en two video
s. New
meth
od
sho
u
ld be introdu
ced to ra
nkin
g de
cisi
o
n
by using a
n
attribute wh
o
s
e value
cha
nge
s frequ
en
tly
over a
n
ob
se
rvation time.
On the
othe
r hand,
al
thou
gh the
r
e i
s
n
o
t an o
b
viou
s g
r
eat
or litt
l
e
nume
r
ical rel
a
tion b
e
twe
e
n
two
dynam
ic attrib
ute
seque
nces,
we can
use a
deg
ree
fun
c
tion
extracted
fro
m
attribute p
e
rformi
ng
sta
t
istics
ov
er
a
time to analy
z
e the
domi
n
ance relation.
Let
A
and
B
are two
obje
c
ts
with
a dyna
mic attribute.
We
ca
n see
pe
rformance
of the
attribute
a
s
two se
que
nces
A
S
and
B
S
, in which
n
a
and
n
b
are
values in time point
n
.
12
{
,
,.
.
.
,.
.
.
}
An
Sa
a
a
(
1
)
12
{
,
,
...
,
.
..}
Bn
Sb
b
b
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4814 – 4
824
4816
E
a
ch
cou
p
le
of
(
n
a
,
n
b
) ha
s a
dominatin
g
or do
minate
d
relation. F
o
r finding
way
to
deci
de the p
r
eferred relation between t
he two whol
e
sequ
en
ce
s, we u
s
e the
s
e
value cou
p
le
s to
figure o
u
t a statistic
re
sul
t. Numeri
cal
relati
on
between a value
cou
p
le
s ca
n be express a
s
a
point in a
co
o
r
dinate
sy
ste
m
wh
ere
dom
inan
ce re
latio
n
mean
s th
e
value coupl
e
point ab
ove the
line
yx
, and dominated rel
a
tio
n
mean
s the value co
uple
point belo
w
the line
yx
.
Table 1. Cli
c
k Rates of We
b Video A an B in Seven Days
ID
Click rates
Day1
Day2
Day3
Day4
Day5
Day6
Day7
A
96
215 299 411 658
872
1305
B
118 187 351 564 643
945
1138
2.2. Dominance Judgin
g
Values
Con
s
id
er th
ree cases:
(i) One
obje
c
t
has
more va
lues
greater
than an
othe
r in the
dynamic
attri
bute sequ
en
ce. (ii) Prefere
n
ce
rela
tio
n
b
e
twee
n two
o
b
ject
s chan
g
e
frequ
ently o
v
e
r
a time. (iii) One obje
c
t has a value much greate
r
tha
n
anothe
r obj
ect in the sa
me positio
n of the
dynamic attri
bute
seq
uen
ce. Fo
cu
sing
on the
thr
ee
ca
se
s, we
propo
se th
re
e j
udgin
g
valu
e
s
to
cal
c
ulate the
domina
n
ce degree valu
e
,
by which
we app
rove o
r
deny the do
minan
ce relat
i
on
betwe
en ea
ch two obje
c
ts.
2.2.1. Basic judging v
a
lu
e
In
Equation
s
(1) and (2), we
expre
s
s
the
dy
namic
attribute a
s
two
seque
nces a
n
d
give
the value
co
uple in
sa
me
positio
n of t
he sequ
en
ce
as
(
n
a
,
n
b
). To
analyze the
domina
n
ce
relation
cou
p
l
e
in coo
r
din
a
t
e system, we use the p
o
i
n
t
(,
)
ii
x
y
to presen
t the value couple in
positio
n
i
of th
e sequ
en
ce.
Length
of
se
quen
ce
can
b
e
defin
ed
as
N
. So there a
r
e
N
points in
the coordinat
e. As
sho
w
n
in Fig
u
re
1,
the poi
nt a
bove the li
n
e
yx
indicate
s t
hat on th
e
dynamic attri
bute
obj
ect
A
has
a value
prefe
rre
d to
obje
c
t
B
in th
e sam
e
po
sit
i
on of the
seq
uen
ce. T
hen we
cal
c
ulate the to
tal number of
points ab
ove
the line
yx
and define this
numbe
r a
s
n
. So the probabilistic value of
A
dominatin
g
B
can be exp
r
esse
d as foll
ow:
b
n
p
N
(
3
)
Con
s
id
erin
g the domi
nan
ce deg
ree i
n
domina
n
ce relation, when
degree valu
e gre
a
ter
than
ze
ro, d
o
m
inan
ce
rel
a
tion exi
s
ts. Ot
herwise, a
d
o
minated
rel
a
tion exi
s
ts.
We
ca
n u
s
e
the
dominance probabilisti
c value to
act as plus or mi
nus
sign
i
n
dominance relation judgment.
Given a th
re
shol
d value
0.5
T
b
p
, we te
mpo
r
arily ap
prove
of the d
o
m
i
nan
ce
relati
on an
d
A
t
t
r
i
b
ut
e
Va
l
u
e
C
oupl
e
A
ttr
i
b
ute
V
a
l
u
e
s
for
A
A
t
tr
i
b
ute V
a
l
u
es
fo
r B
P
i
Figure 1. Basic Domi
nan
ce
Jud
geme
n
t
A
t
t
r
ibut
e V
a
l
u
e
C
ouple
A
t
tr
ibu
t
e
V
a
lu
e
f
o
r
A
A
t
t
r
i
b
u
te
V
a
lu
e
fo
r
B
P
i
P
i+
1
t
1
t
2
Figure 2. Fre
quently ch
an
ging
judgem
ent
A
t
t
r
ib
u
t
e
V
a
lu
e
C
o
u
p
le
Attr
ib
u
t
e
Valu
e for
A
A
ttribute
V
a
l
u
e
for B
P
i
P
j
Figure 3. Gre
a
tly changi
ng
judgem
ent
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TELKOM
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ISSN:
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046
A Dom
i
nance
Degree for
Rough Sets a
n
d
Its App
licati
on in Ra
nki
n
g
Popularit
y (Ji
a
Zhao
)
4817
pre
s
ent
it wit
h
plu
s
deg
re
e
d
on th
e
con
d
ition that
ou
r b
a
si
c j
udgin
g
value
is g
r
e
a
ter th
an
T
b
p
.
Corre
s
p
ondin
g
ly, when
b
p
i
s
l
e
s
s
t
h
a
n
T
b
p
, we
dire
ctly deny
the domi
nan
ce rel
a
tion
and
pre
s
e
n
t
it as min
u
s d
egre
e
d
. The
basi
c
ju
dgin
g
value
b
p
also
contri
bute
s
to
the domi
nan
ce d
e
g
r
ee
value
h
. Bec
a
us
e
h
eve
n
tually decid
es the domi
nan
ce rel
a
tio
n
, basi
c
jud
g
ing value i
s
a
temporary jud
g
ment and th
e first step to
judge a d
o
mi
nan
ce rel
a
tio
n
.
2.2.2. Freque
ntly
Changin
g
Judging Value
Whe
n
on
e obje
c
t sati
sfies the
co
nd
ition
T
bb
p
p
to an
other o
b
je
ct, wheth
e
r a
dominance relation exist
s
i
s
still
a question.
Because there are ot
her situations abou
t
distrib
u
tion
of
attribute
val
ue
cou
p
le
s,
we
ca
nnot
di
rectly j
udg
e
a do
minan
ce
rel
a
tion j
u
st
by
more poi
nts
above the lin
e
yx
. let us introdu
ce anoth
e
r
situation in
whi
c
h we
can
also get a
judgin
g
value
and make it contri
bute to the final domi
nan
ce de
gre
e
value
h
.
As
sho
w
n
in
Figure 2, t
w
o
neig
hbo
r p
o
i
n
ts
i
P
and
1
i
P
resp
ectively
stay on
o
ne sid
e
of
the line
yx
. If we
co
nne
ct the
two
neigh
bo
r
points with
a l
i
ne, there
will
be
cross
poi
nt with th
e
line
yx
. We d
o
t
he
same
thin
g to e
a
ch two nei
ghb
or
p
o
ints
acro
ss
the line
yx
. Then we
cal
c
ulate the
total numbe
r
of the cross p
o
ints on th
e line
yx
. To ac
c
o
mplis
h this
, our firs
t s
t
ep
is to judge
wheth
e
r the
r
e is a cross
point bet
wee
n
the neigh
b
o
r point
s. We use the ve
ctor
triangle a
r
ea
method to judge wh
ethe
r the two nei
gh
bor poi
nts are sepa
rate
d on both sid
e
s of
the line
yx
. considerin
g the ne
ighbo
r point
s
i
P
and
1
i
P
in the geometri
c figu
re, we choi
ce
any
two poi
nts,
named
1
t
and
2
t
, on the lin
e
yx
. C
o
or
d
i
na
te
s
o
f
i
P
and
1
i
P
are
(,
)
ii
x
y
an
d
11
(,
)
ii
x
y
, while
coo
r
di
nate of
1
t
and
2
t
are
11
(,
)
ab
and
22
(,
)
ab
. W
e
c
o
nn
ec
t th
e
po
in
t c
o
u
p
l
es
to
obtain some
vectors
12
tt
,
2
i
tP
,
1
i
Pt
,
21
i
tP
and
11
i
Pt
. Then we cal
c
ulate a
r
eas of the two vecto
r
triangle
s
a
s
follows:
12
1
2
1
12
1
1
2
1
11
1
1
1
1
ii
ii
i
i
aa
x
a
a
x
S
b
by
S
b
by
(
4
)
If
1
0
ii
SS
, there i
s
a
cross p
o
int
on the lin
e
yx
. If
1
0
ii
SS
, there i
s
n
o
cro
ss
point bet
wee
n
two
neig
h
b
o
r p
o
ints.
Ne
xt step is to
calcul
ate the t
o
tal num
ber
of the cro
s
s p
o
ints
on the line
yx
. Becau
s
e th
e dynamic a
ttribute has
an increa
sin
g
seq
uen
ce
s and every
positio
n in the seq
uen
ce i
s
a samplin
g time point over a pe
riod
of time, we reg
a
rd the lin
e
yx
in the geom
e
t
ric figu
re a
s
a time axis. T
he attr
ibute v
a
lue poi
nts a
r
e distri
buted
near th
e line
in
the increa
sin
g
dire
ction a
c
ross the lin
e. At any time p
o
int t on
yx
, we use a
circle
with radi
us
f
as an
ob
servation
wind
ow, which can sli
de a
c
ro
ss th
e time l
i
ne
yx
. We cal
c
ulate th
e
numbe
r of cross point
s in the win
d
o
w
at time
t
with the followin
g
eq
uation:
1
()
n
ff
i
i
nI
t
(
5
)
Whe
r
e the n
u
mbe
r
of attribute points i
n
the windo
w is
n
, and
the variable
()
fi
It
is
defined a
s
be
low:
1
1
10
()
00
ii
fi
ii
if
S
S
It
if
S
S
(
6
)
Here we discuss the time
points. In ap
plic
atio
ns
su
ch as n
e
two
r
k resource
po
pularity
ran
k
ing, attri
bute value
s
of rece
nt peri
od of ti
me are more referentially important. Accordi
ngly,
we ad
d a we
ight
()
f
wt
to each
time point. The wei
ght fu
nction i
s
in
creasi
ng an
d satisfies the
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02-4
046
TELKOM
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KA
Vol. 12, No. 6, June 20
14: 4814 – 4
824
4818
equatio
n
0
()
1
T
f
wt
. Here
T
is the perio
d of observati
on time. To normali
ze the j
udgin
g
value
s
,
we u
s
e th
e
ratio of
cro
s
s poi
nt amo
unt and
attribute poi
nt a
m
ount
()
f
Nt
in the wind
ow to
expre
ss the j
udgin
g
value
at time t as bellow:
1
()
()
(
)
()
n
fi
i
ff
f
I
t
pt
w
t
Nt
(
7
)
As the
win
d
o
w
a
c
ross th
e
time line
yx
over a p
e
rio
d
of ti
me
T
,
w
e
c
a
n e
x
p
r
es
s
th
e
freque
ntly ch
angin
g
judgin
g
value as foll
ow:
0
1
()
d
T
ff
pp
t
t
T
(
8
)
2.2.3. Greatl
y
Changing
Judging Val
u
e
In this pa
rt, we di
scuss t
h
e
situatio
n in
whic
h
some
attribute
point
s
are
far from
the time
line
y=x
in a
great
dista
n
ce. We
analyze the featu
r
e
s
of attrib
ute
points
both a
bove an
d bel
ow
the time axi
s
y=
x
.
One
of
the mo
st imp
o
rtant featu
r
e
is th
e
di
stan
ce from attri
b
ute point to
the
line
y=
x
. This feature som
eho
w pre
s
e
n
ts the domina
n
ce extent o
n
one attribut
e point. In this
situation,
we
use
a re
ctan
gle wi
ndo
w a
c
ro
ss the ti
m
e
line to o
b
se
rving the attri
bute poi
nts.
Half
of the windo
w length is gre
a
ter than the
ma
xim distan
ce from a p
o
i
n
t to the line
y=
x
.
In the windo
w at time t, we can find a
ma
x-di
stan
ce
point on both side of time line
y=
x
.
we exp
r
e
s
s t
he jud
g
ing
va
lue at time
t
a
s
the ratio of max-di
stan
ce
on
o
ne side
to
the sum of
the
max-di
stan
ce
s on both
si
des. As
sho
w
n in Fig
u
re
3, in the windo
w at time
t
,
(,
)
ii
i
Px
y
rep
r
e
s
ent
s the max-di
stan
ce poi
nt abov
e the time axis, while
(,
)
jj
j
P
xy
rep
r
ese
n
ts the m
a
x-
distan
ce p
o
in
t below the time axis. The
judging valu
e at time t is
defined a
s
fol
l
ow:
()
()
ii
gg
ii
j
j
xy
pt
w
t
x
yx
y
(
9
)
Whe
r
e
()
g
wt
is an
increa
sing
weight functio
n
who
s
e valu
e
large
r
a
c
ro
ss the timelin
e
and satisfyin
g
0
()
1
T
g
wt
. As the re
ct
angle
wind
ow across the ti
me axis ove
r
a peri
od of time
T
,
we can obtai
n the greatly cha
ngin
g
jud
g
ing value b
e
l
ow:
0
1
()
d
T
gg
pp
t
t
T
(
1
0
)
2.2.4. Dominance Degre
e
Value
To su
mma
rize the cases
above, we o
b
tain thre
e ju
dging valu
es
about the
do
minan
ce
relation
between two dyn
a
mic attri
but
e se
que
nces.
Thre
e jud
g
in
g value
s
all
contri
bute to
the
domina
n
ce d
egre
e
value
d
. and the b
a
s
ic j
udgin
g
value is
also u
s
ed in th
e jud
g
ing of si
gn.
We
defined the d
o
minan
ce d
e
g
ree valu
e as follow:
s
g
n(
0.
5
)
bb
f
g
dp
p
p
p
(
1
1
)
We al
so
give
a domin
an
ce thre
shol
d
T
d
. Whe
n
the d
o
m
inan
ce d
e
g
r
ee value i
s
g
r
eater
than
T
d
, we ap
prove of the
domina
n
ce re
lation.
Co
rrespondi
ngly, we ca
n de
ny the domi
nan
ce
relation if the domina
n
ce d
egre
e
is le
ss
than
T
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Dom
i
nance
Degree for
Rough Sets a
n
d
Its App
licati
on in Ra
nki
n
g
Popularit
y (Ji
a
Zhao
)
4819
2.3. Rough S
e
ts
w
i
th D
y
n
a
mic Attribu
t
es
There is a co
rrespon
ding bi
nary relatio
n
betwe
en two
obje
c
ts
A
and
B
in roug
h set. The
relation
of
A
do
minating
B
ca
n be
rega
rd as the
rel
a
tion o
f
B
dominate
d
by
A
. The d
o
mi
nan
c
e
degree threshold
T
d
should
b
e
expre
s
sed i
n
two format
s of
T
d
and
T
d
.
We u
s
e
d
yP
x
to prese
n
ts the d
o
m
inan
ce relat
i
on.
P
is a dyn
a
mic attrib
ute
set.
d
is the
domina
n
ce d
egre
e
value.
Obje
ct
x
and
y
all belon
g to the obje
c
t set
U
. The domina
n
ce
set,
who
s
e me
mb
ers all d
o
min
a
te obje
c
t
x
, is defined a
s
fol
l
ows:
Defini
tion 1.
On the dyn
a
m
ic attrib
ute
set
P
, Given an
obje
c
t
x
, for objec
t
s
,'
yy
U
, i
f
'
d
yP
x
, we define the set
'
()
{
:
,
'
0
}
dd
P
Dx
yU
y
P
x
d
d
as the
dominan
ce
set, and if
'
'
d
yP
x
,
then
we
defin
e the
set
()
{
'
:
'
,
'
0
}
dd
P
Dx
y
U
y
P
x
d
d
as the d
o
minate
d
set. A
c
cordin
g to th
e
definition ab
o
v
e, we give two prope
rtie
s
about the do
minan
ce set and the domi
nated set.
Property
1.
On the dyna
mic attribute
set
P
, for the thres
h
old
T
d
, two domina
n
ce
degree value
s
12
,[
,
1
]
T
dd
d
and the obj
ect
x
U
, if
12
0
T
dd
d
，
then
the dominan
ce sets
sat
i
sf
y
12
()
()
dd
PP
Dx
D
x
.
Property
2.
On the dyna
mic attribute
set
P
, for the thres
h
old
T
d
, two domi
nan
ce
degree valu
e
s
12
,[
1
,
]
T
dd
d
and the
ob
ject
x
U
, if
12
0
T
dd
d
, then
the domi
nate
d
set
s
sat
i
sf
y
12
()
()
dd
PP
Dx
D
x
.
Defini
tion 2.
On the
dyna
mic attrib
ute
set
P
, for the objec
t
s
e
t
U
, dominan
ce d
e
g
r
ee
value
d
and th
e deci
s
ive set
X
, the up and down app
roxi
mations a
r
e d
e
fined a
s
follows:
[,
1
]
[,
1
]
()
{
:
,
(
)
,
(
)
}
,
()
{
:
,
(
)
,
(
)
}
T
T
dd
dd
PP
PP
dd
dd
PX
y
U
x
U
y
D
x
D
x
X
PX
y
U
x
U
y
D
x
X
D
x
Defini
tion 3.
On the
dyna
mic attrib
ute
set
P
, for the objec
t
s
e
t
U
, dominan
ce d
e
g
r
ee
value
d
and th
e de
ci
sive
co
mpleme
nt set
C
X
, the u
p
a
n
d
down a
pproximations a
r
e
defined
a
s
follows
:
[1
,
]
()
{
:
,
(
)
,
(
)
}
T
Cd
d
C
PP
dd
PX
y
U
x
U
y
D
x
D
x
X
[1
,
]
()
{
:
,
(
)
,
(
)
}
T
Cd
d
PP
dd
PX
y
U
x
U
y
D
x
X
D
x
Theorem 1.
On the dyna
mic attribute
set
P
,
f
o
r t
he deci
siv
e
set
X
, if the dominan
ce
degree value
[,
1
]
T
dd
, then the up a
nd do
wn ap
proximati
ons
ca
n be expre
ssed as follo
ws:
11
()
{
:
,
(
)
,
(
)
}
,
()
{
:
,
(
)
,
(
)
}
TT
dd
PP
P
P
P
X
y
U
x
U
y
Dx
Dx
X
P
X
y
U
x
U
y
D
x
X
D
x
Proof .
T
h
e
d
o
m
in
an
ce
de
g
r
ee
va
lu
e
s
a
tis
f
ies
th
e
c
o
nd
itio
n
[,
1
]
T
dd
. We
can
get that
that any degree value
i
d
is not less than
the thresh
ol
d value
T
d
. Accordin
g to the prope
rty 1,
from the relation
iT
dd
, we
can g
e
t the
relation
bet
ween th
e two
domin
an
ce
set
s
a
s
()
()
i
T
d
d
PP
D
xD
x
. For all possi
ble
i
d
, we get
[,
1
]
[,
1
]
()
(
)
()
i
TT
iT
i
T
d
dd
PP
P
dd
d
d
D
x
Dx
Dx
.
Also, the
belon
ging
relation
[,
1
]
TT
dd
lead
s to
the incl
udi
ng rel
a
tion
[,
1
]
()
()
i
T
T
d
d
PP
dd
Dx
D
x
. Then we ge
t the relation
[,
1
]
()
()
i
T
T
d
d
PP
dd
Dx
D
x
. For the defin
ition of the up
approximatio
n, if the unio
n
[,
1
]
()
i
T
d
P
dd
Dx
X
, then
()
T
d
P
D
xX
. Therefore, the
up
approximatio
n
is expre
s
sed
as theo
rem 1.
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Vol. 12, No. 6, June 20
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4820
Acco
rdi
ng to the prop
erty 1, when
1
Ti
dd
, the
relation b
e
tween the two
domina
n
ce
s
e
ts
is
1
()
(
)
i
d
PP
Dx
D
x
. We can get the rel
a
tion belo
w
:
11
[,
1
]
[,
1
]
()
()
(
)
i
iT
i
T
d
PP
P
dd
d
d
Dx
D
x
Dx
T
h
e
do
mina
nc
e
s
e
ts
s
a
tis
f
ie
s
1
[,
1
]
()
()
i
iT
d
PP
dd
Dx
D
x
. if
[,
1
]
()
i
iT
d
P
dd
X
Dx
, then
1
()
P
X
Dx
.
So the down
approximatio
n is
expre
s
se
d as theo
rem
1.
Theorem 2.
On the dyna
mic attribute
set
P
,
f
o
r t
he deci
siv
e
com
p
l
e
ment
set
C
X
, if
the
domina
n
ce d
egre
e
value
[1
,
]
T
dd
, then the up a
n
d
down app
ro
ximations a
r
e
as follows:
11
()
{
:
,
(
)
,
(
)
}
,
()
{
:
,
(
)
,
(
)
}
TT
dd
CC
C
C
PP
P
P
PX
y
U
x
U
y
D
x
D
x
X
PX
y
U
x
U
y
D
x
X
D
x
Proof.
Fo
r a
n
y possibl
e d
o
minan
ce
de
gree
value
[1
,
]
iT
dd
, accordi
ng to
p
r
ope
rty 2
and the in
clu
d
ing an
d belo
nging p
r
op
erti
es in sets, we
can get the relation
s belo
w
:
[1
,
]
[1
,
]
(
)
()
()
i
TT
iT
iT
d
dd
PP
P
dd
dd
D
x
Dx
Dx
,
[1
,
]
()
()
i
T
iT
d
d
PP
dd
Dx
D
x
Then the
un
ion of domi
nan
ce
sets
satisfie
s the
relation
[1
,
]
()
(
)
i
T
iT
d
d
PP
dd
Dx
D
x
. if
[1
,
]
()
i
iT
d
C
P
dd
Dx
X
, then
()
T
d
C
P
D
xX
. Theref
ore, the up a
pproxim
ation
follows as the
o
rem 2.
For
1
iT
dd
, we c
an get the relation:
11
[1
,
]
[1
,
]
()
()
()
i
iT
iT
d
PP
P
dd
dd
Dx
D
x
D
x
The domin
a
n
ce
sets sa
tisfies
1
[1
,
]
()
(
)
i
iT
d
PP
dd
Dx
D
x
. If
[1
,
]
()
i
iT
d
C
P
dd
X
Dx
, then
1
()
C
P
X
Dx
. So the down
approxim
atio
n is expre
s
se
d as theo
rem
2.
Theorem 3.
The obje
c
t set
U
can
be
gro
upe
d int
o
two
de
cisi
ve set
X
and
its
compl
e
ment
C
X
. When a ne
w obje
c
t
y
joins the set
U
and nee
d to be classifie
d
, for the
obje
c
ts
x
X
and
'
C
x
X
, with the
dom
inan
ce
deg
re
e value
d
of
y
, if
T
dd
, then
yX
; if
T
dd
, then
C
yX
.
Proof.
Con
s
i
derin
g the thre
shol
d
T
d
and the obje
c
t
x
X
, we can
see that if
()
T
d
P
D
xX
, then
()
T
d
C
P
Dx
X
. But
the prop
erty that object
s
in set
C
X
are domi
nated by
x
contradi
cts t
he definitio
n
of
()
T
d
P
D
x
. Theref
ore
,
if
T
dd
, acco
rdin
g to the p
r
o
perty 1, we
get
()
()
T
d
d
PP
yD
x
D
x
X
.
For t
he th
re
shold
T
d
and th
e
obje
c
t
'
C
x
X
, if
('
)
T
d
C
P
D
xX
,then
('
)
T
d
P
Dx
X
. The
prop
erty that
obje
c
ts i
n
X
do
minate
'
x
contradict
s the
def
inition of
('
)
T
d
P
D
x
. Th
erefo
r
e, if
T
dd
,
according to the pro
p
e
r
ty 2, we can g
e
t the relatio
n
:
('
)
(
'
)
T
d
dC
PP
yD
x
D
x
X
Theorem 4.
On the dyn
a
m
ic attribute set P, for two object
s
,
x
yU
, in
the relations
d
yP
x
and
d
x
Py
, where
0
d
and
0
d
, if
ma
x
dd
, then
mi
n
dd
.
Proof.
Con
s
i
derin
g
the
eq
uation (11
)
, we ca
n see
,,
0
bf
g
pp
p
. Given the
co
nstant
f
p
,
we can get:
2
2
bg
fb
g
f
pp
dp
p
p
p
,
2
2
(1
)
(
1
)
2
bg
fb
g
f
pp
dp
p
p
p
.
If
ma
x
dd
, then
bg
pp
. When
bg
pp
,
mi
n
dd
.
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TELKOM
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ISSN:
2302-4
046
A Dom
i
nance
Degree for
Rough Sets a
n
d
Its App
licati
on in Ra
nki
n
g
Popularit
y (Ji
a
Zhao
)
4821
3. Resul
t
s
and
Discus
s
ion
In this section, we will ev
aluate the perform
a
nce of our proposed dynami
c
attribute
deci
s
ion maki
ng method. F
i
rstly, we give a simp
l
e
example to illustrate
rough
set
based ranking
deci
s
io
n with
dynamic attributes. The
n
, we em
ploy our propo
se
d
method in network service
resou
r
ce ran
k
ing
with ou
r camp
us n
e
tworkin
g
flow
statistics. Fin
a
lly we exam
efficiency of
a
netwo
rk
re
so
urce se
archi
n
g engin
e
impl
emented
wi
th
rough
set ba
sed dyn
a
mic
attribute ra
nki
n
g
deci
s
io
n.
Table 2. Information Tabl
e About Web Vi
deo
s
Web video
Dur
a
tion
Flo
w
Visiting time in
5
da
y
s
rank
x
1
13
124.5
{46
7
,
7
71, 110
9, 1415,
20
07
}
1
x
2
19
158.4
7
{43
6
,
8
64, 105
1, 1662,
19
32
}
2
x
3
11
76.9
{89
,
20
1, 2
27,
45
3, 53
9}
2
x
4
17
58.4
{43
,
89
, 41
5, 4
4
7
,
486
}
2
x
5
22
160.3
{22
5
, 4
23,
671
, 8
49, 1
070
}
1
Table 3. Do
m
i
nan
ce Judgi
ng Re
sult
s
Relatio
n
coupl
e
P
f
P
b
P
g
d
Domina
nce
(
x
1
, x
2
)
0.2
0.6
0.223
0.028
No
(
x
1
, x
3
)
1
1
1 1 Y
e
s
(
x
1
, x
4
)
1
1
1 1 Y
e
s
(
x
1
, x
5
)
1
1
1 1 Y
e
s
(
x
2
, x
3
)
1
1
1 1 Y
e
s
(
x
2
, x
4
)
1
1
1 1 Y
e
s
(
x
2
, x
5
)
1
1
1 1 Y
e
s
(
x
3
, x
4
)
0.6
0.8
0.373
0.179
No
(
x
5
, x
3
)
1
1
1 1 Y
e
s
(
x
5
, x
4
)
1
1
1 1 Y
e
s
W
e
b
vide
os
ha
ve
s
o
me
flow
s
t
a
t
is
tic
featu
r
e
s
that
can
be u
s
e
d
a
s
d
y
namic
attrib
utes fo
r
their p
opul
ari
t
y ranki
ng
de
cisi
on. To
cl
a
r
ify the
ranki
ng d
e
ci
sion
pro
c
e
ss, l
e
t’s wo
rk thro
ug
h a
web
video
ra
nkin
g exa
m
pl
e containi
ng
three
domi
n
a
n
ce
relation
attributes,
on
e of
whi
c
h
is a
dynamic
attri
bute. Table
2
sho
w
s ra
nki
ng de
ci
si
on i
n
formatio
n of
the five web
videos. Th
ere
are
three statisti
c
attribute cont
aining duratio
n,
flow
an
d visiting time
s in
five days. T
he first col
u
m
n
of the table display
s
the video name
s
list
ed in ord
e
r from
x
1
to
x
5
. In se
con
d
col
u
mn of the table,
visiting d
u
rati
on i
s
di
splay
ed
with time
unit of h
our.
The thi
r
d
col
u
mn
sho
w
s fl
ow
data fo
r e
a
ch
video
with the
unit
of GB. B
o
th this two a
ttribut
es emb
ody do
minan
ce
rel
a
tion
be
tween
ea
ch
two
web vid
e
o
s
and
sho
w
p
opula
r
ity exp
r
esse
d by th
is
p
r
eferrin
g
relation.
The
values of t
h
is
dynamic attri
bute for ea
ch
video are shown in t
he format of seq
uen
ce. The
r
e
are also so
me
feature
s
that
we can
see
from the fou
r
th co
l
u
mn.
Relatio
n
of value sequ
en
ces b
e
twee
n two
videos al
so p
r
esents
prefe
r
en
ce. And th
e attri
bute val
ue se
que
nce
s
are increa
si
ng se
que
nce
s
.
It is easy to
unde
rsta
nd that the popul
ar attribute
like visiting times is an a
c
cu
mulative variable
who
s
e val
ue
alway
s
in
cre
a
s
e
s
a
s
mo
re
and mo
re
pe
ople
click a
n
d
visit the resource. Th
e fifth
colum
n
di
spl
a
ys the
de
ci
sive ran
k
in
gs.
Acco
rdi
ng to
the attribute
s
and
de
ci
sive ran
k
in
g g
r
ou
ps
we
ca
n p
r
o
c
e
s
s this info
rm
ation tabl
e a
nd d
o
the
mu
ltiple attribute
de
cisi
on
ma
king
with
rou
g
h
set b
a
sed
dynamic attrib
u
t
e ra
nki
ng. T
able
3
sh
o
w
s the
analysi
s
of the
domi
nan
ce
relatio
n
s.
The first colu
mn lists the d
o
minan
ce
rel
a
tion co
uple
s
. The se
con
d
column
displ
a
ys the value
of
freque
ntly ch
angin
g
judg
ment variabl
e for each
d
o
minan
ce
rel
a
tion co
uple.
Values of b
a
si
c
judgme
n
t vari
able calculat
ed by Equati
on (3
) for
ea
ch do
minan
ce relation
co
uple are sho
w
in
the third column. The fourth c
o
lu
mn
sh
ows the
valu
es
of greatly
cha
ngin
g
jud
g
ment va
riabl
e.
The fifth column lists th
e domina
n
ce
degre
e
values for e
a
ch domina
n
ce
relation cou
p
le.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4814 – 4
824
4822
Acco
rdi
ng to
domina
n
ce d
egre
e
valu
es in fifth colu
mn, domi
nan
ce
de
cisi
ons
are
sh
own in
the
last column.
Notice the
se
con
d
ro
w in t
he table,
the
domina
n
ce d
egre
e
value
h is little than
the
threshold val
ue
T
d
, which i
s
given by
T
d
=0.3
. So, the dom
inan
ce relatio
n
between
x
1
and
x
2
on
the attribute o
f
visiting times is de
nied. In
the same
way, the dominance relatio
n
betwe
en
x
3
a
nd
x
4
on
this dyn
a
mic
attribute
are
de
nied.
You c
an
se
e
all the oth
e
r
cou
p
le
s have
a de
gree val
ue
equali
ng to 1
,
and these
cou
p
le
s defin
itely have
a domina
n
ce relation. Fro
m
the data of the
table, we
ca
n
see th
at too l
i
ttle degre
e
value
will be u
s
ed to
deny a
domina
n
ce relation altho
u
gh
one obj
ect ha
s more domin
ance point
s than an
other.
Table 4. Ra
n
k
ing
Rule
s fro
m
Discrimi
nat
e Matrix
Rank 1
to
ra
nk 2
x
2
x
3
x
4
Domina
ting Rule
s
x
1
dfc fc
Ø
f
≥
124
.5, c
≥
c(
x
1
)
x
5
dfc dfc
dfc
d
≥
22,
f
≥
160.
3, c
≥
c(
x
5
)
Domina
ted Rules
d
≤
19
f
≤
158
.47
c
≤
c(
x
2
)
d
≤
11
f
≤
76.
9
c
≤
c(
x
3
)
f
≤
58.
4
c
≤
c(
x
4
)
The next ste
p
of this example is to ma
ke a
multiple
attribute de
ci
sion by some
deci
s
ion
rule
s. As sho
w
n i
n
T
able
4, the
web
video
s a
r
e
di
splay in t
w
o
g
r
oup
s by thei
r ran
k
ing
val
ue.
Firstly, in each position of the ro
w
co
rre
s
po
ndin
g
to the domin
ated
group
x
2
,
x
3
and
x
4
, there
is
an attribute v
a
riabl
e nam
e
cha
r
a
c
ter
string, each ch
ara
c
ter of
wh
ich exp
r
e
ss t
hat the attrib
ute
can
di
scrimin
a
te the
two
o
b
ject
s by
defi
n
ite do
minan
ce
rel
a
tion. A
c
cordi
n
g
to th
e data
in
Tabl
e 2
and
Tabl
e 3,
we
ca
n fill thi
s
attri
bute
ch
ara
c
ter st
ring
in th
e p
o
siti
on
relate
d
wi
th a
domin
an
ce
relation
coup
le. Then, f
r
o
m
this ta
ble,
we
can
extract
ra
nki
ng
deci
s
io
n rule
s by
usi
ng t
he
discrimi
nate functio
n
.
We
re
cord th
e network traffic stati
s
tics o
v
er
a p
e
ri
od
of time and
a
nalyze
many
netwo
rk
flow featu
r
e
s
that ca
n be
u
s
ed
to de
scri
be a
nd d
e
ci
d
e
the p
opul
arity. We collected two
mont
h
statistics, totally 425.73 T
B
upload a
n
d
downloa
d flows and 1
9
9079
44 time
s re
so
urce views.
500 regi
stere
d
se
rvice
s
a
r
e cla
s
sified i
n
to
we
b
pa
g
e
,
video,
ima
ges and oth
e
rs. We obta
i
n
totally 16 kinds of flow attributes fro
m
o
u
r statisti
cs.
Our go
al is to
make a multi
p
le attribute a
n
d
multi-rel
a
tion
based roug
h set ran
k
in
g de
cisio
n
. In these attri
butes,
categ
o
ry and
si
ze
are
indiscri
minate
relatio
n
ba
se
d stati
c
attrib
utes.
C
ontent
and
protocol
are
simil
a
rity relatio
n
ba
se
d
static
attribut
es. T
here
are 9
domi
nan
ce-rel
ati
on-ba
sed
dyna
mic attribute
s
: a
c
cess tim
e
, d
a
ily
views, daily visitors, key wo
rds,
comm
ent
s, fl
ow, duration, resou
r
ce view and u
n
iq
ue visitor.
Figure 4 sho
w
s the comp
arison of the
ranki
ng re
sults with and
without the dynamic
attribute
red
u
c
tion
betwee
n
two
resources. T
he
ba
sic judgi
ng val
u
e is g
r
eate
r
t
han
0.5, but
the
domina
n
ce d
egre
e
valu
e i
s
le
ss th
an t
he th
re
shol
d. Each
re
sou
r
ce i
s
ra
nked
by p
e
rcenta
g
e
numbe
r
of re
sou
r
ces b
e
lo
w it.
Re
sults of Fig
u
re
4
(
a)
and
(b
) li
e in th
e to
o
little freq
ue
ntly
cha
ngin
g
jud
g
ing value, which lea
d
s to
the dominan
ce deg
re
e value less than
the threshol
d.
Without thi
s
j
udgin
g
value,
one
re
sou
r
ce is
cla
ssifie
d
to a high
ra
n
k
set whil
e th
e other re
so
u
r
ce
is g
r
ou
ped i
n
to a lo
w ra
n
k
set. With t
h
is ju
dgin
g
value, do
mina
nce
rel
a
tion
betwe
en the
two
resou
r
ces i
s
denie
d
. Therefore, two
re
sou
r
ces
ar
e
ran
k
ed
nea
rl
y. As to effect of the gre
a
tly
cha
ngin
g
jud
g
ing val
ue
shown in
Fig
u
re
4(c) a
n
d
(d
), it is an
alogo
us to t
he a
nalyzi
n
g
of
freque
ntly ch
angin
g
judgin
g
value abov
e.
Figure 5
sho
w
s the
com
p
arison
of sea
r
chi
ng
re
sult
relevan
c
e
wit
h
an
d
without
ran
k
in
g
function in 1
0
queri
e
s. We use this
re
sult to
evaluate the efficiency of re
so
urce ra
nkin
g
in
sea
r
ching. We evaluate the sea
r
ching result item
s wi
th the Normal
Discounte
d
Cumul
a
tive Gai
n
(NDCG) val
u
e, whi
c
h i
s
widely used in
evaluati
ng t
he pe
rforman
c
e of
se
archi
ng en
gine
s [
18].
We ca
n see the
searchi
n
g
en
gine wit
h
the
p
opul
a
r
ity ran
k
ing
functio
n
sho
w
highe
r val
u
e
of
NDCG
than
j
u
st
key
wo
rd
sea
r
ching
wit
hout reso
u
r
ce ra
nki
ng. Ex
planatio
n i
s
t
hat amo
ng
all
the
key-wo
rd mat
c
he
d re
sults,
more p
opul
ar reso
ur
ce
s ha
ve a high po
ssibility to satisfy use
r
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Dom
i
nance
Degree for
Rough Sets a
n
d
Its App
licati
on in Ra
nki
n
g
Popularit
y (Ji
a
Zhao
)
4823
0
1
0
2
03
04
0
5
06
07
0
8
09
0
0%
20
%
40
%
60
%
80
%
10
0%
Reso
u
r
ce
1
Reso
u
r
ce
2
Ranking %
Below
Ob
ser
v
a
t
i
o
n
da
y
s
(a
)
0
1
0
2
03
04
0
5
06
07
0
8
0
9
0
0%
20%
40%
60%
80%
1
00%
Re
sou
r
c
e
1
Re
sou
r
c
e
2
Ranking %
Bel
o
w
Obser
v
at
i
o
n
day
s
(b
)
(c)
(d)
0
1
0
2
03
04
0
5
06
07
0
8
09
0
0%
20
%
40
%
60
%
80
%
10
0%
Re
sou
r
c
e
3
Re
sou
r
c
e
4
Ranki
ng % Bel
o
w
Ob
ser
v
a
t
i
o
n
da
y
s
0
1
02
0
3
0
4
05
0
6
0
7
08
0
9
0
0%
20%
40%
60%
80%
1
00%
Re
sou
r
c
e
3
Re
sou
r
c
e
4
Ranki
ng % Bel
o
w
Obser
v
at
i
o
n
day
s
Figure 4. Co
mpari
s
o
n
of Two Resource
Ran
k
in
g with
and with
out Dominan
ce
Ju
dging Valu
es
123456
7
8
9
1
0
0.
0
0.
2
0.
4
0.
6
0.
8
1.
0
NDC
G
qu
ery
num
ber
s
w
i
th
r
ank
w
i
th
out r
a
nk
Figure 5. Co
mpari
s
o
n
of NDCG in
We
b S
earchin
g with and
with
out Popula
r
ity Ran
k
ing
4. Conclu
sion
In this pap
er,
we propo
se
a dynami
c
attribute b
a
sed
domina
n
ce d
egre
e
value f
o
r ro
ugh
set ran
k
ing
d
e
ci
sion.
Domi
nan
ce
relatio
n
bet
wee
n
t
w
o
obje
c
ts
m
a
y be
deci
d
e
d
by a
dyna
mic
attribute wh
o
s
e value i
s
n
o
t a single n
u
mbe
r
but a seq
uen
ce. Items of the se
quen
ce a
r
e the
sampli
ng val
ues at differe
nt time over an ob
servatio
n time. To sol
v
e the proble
m
on domin
a
n
ce
relation
jud
g
i
ng by
dynam
ic attri
bute
s
,
we
propo
s
e
th
r
e
e ju
dg
in
g
va
lu
e
s
re
s
pec
tive
ly in
thre
e
geomet
ric
ca
se
s ab
out di
stributio
n of
attribute
valu
e co
uple p
o
i
n
ts. With the
three ju
dgin
g
values,
we
ob
tain the
domi
nan
ce
deg
ree
value, by
whi
c
h we
can de
cide
the domi
nan
ce relatio
n
.
Then
we bui
ld the domin
ance rel
a
tion
base
d
ro
ug
h sets
with
the dynami
c
attributes a
nd
domina
n
ce d
egre
e
value
s
.
The mo
st im
portant a
ppli
c
ation of domi
nan
ce relatio
n
ba
sed
rou
g
h
set lie
s in
multiple attri
bute ranki
n
g
deci
s
io
n. We use rough
set ba
se
d
dynamic
attri
bute
redu
ction
by the domina
n
ce d
e
g
r
ee
value to ra
n
k
the camp
u
s
net
work
service
re
sou
r
ce
s.
Evaluation Warning : The document was created with Spire.PDF for Python.