TELKOM
NIKA
, Vol.11, No
.11, Novemb
er 201
3, pp. 6686
~6
692
e-ISSN: 2087
-278X
6686
Re
cei
v
ed Ma
y 11, 201
3; Revi
sed
Jun
e
23, 2013; Accepted July 2
5
,
2013
An Indeterminacy Temporal Data Model based on
Probability
Ren Shuxia
1,
2
, Zhao Zhen
g
*
1
, Zou Xiaojian
3
1
Colle
ge of Co
mputer Scie
nc
e and T
e
chno
l
o
g
y
, T
i
anjin Un
iversit
y
, C
h
i
n
a
2
College of Computer Sc
ienc
e and Soft, T
i
anjin P
o
ly
technic Un
iversit
y
, T
i
anjin 300072, China
3
Militar
y
T
r
ans
portatio
n
Univ
e
r
sit
y
, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zhengz
h@tju
.
edu.cn
A
b
st
r
a
ct
T
here
are
ma
ny ki
nds
of i
n
deter
mi
nacy t
e
mp
oral
d
a
ta
in
tempor
al
data
base. T
h
erefor
e, man
y
re
se
a
r
ch
e
r
s
ha
ve
fo
cu
sed
on
bu
i
l
d
i
ng
i
n
de
te
rmi
na
cy tem
p
o
r
a
l
da
ta
mo
d
e
l
s
. U
n
fo
rtun
a
t
e
l
y,
e
s
ta
bl
ished
mo
de
ls can
’
t
a
deq
uate
l
y ad
dr
ess the ch
all
e
nges
pose
d
by
indet
ermin
a
cy
temp
oral
infor
m
ati
on, a
nd ca
n
’
t
ada
pt to al
l sor
t
s of involv
ed
a
pplic
atio
ns. In this
p
a
p
e
r, w
e
prop
ose
a te
mpora
l
dat
a
mod
e
l, na
med BPT
M
(T
emp
o
ral
mod
e
l b
a
se
d o
n
pr
oba
bil
i
ty), to mana
ge th
e
i
nde
termi
nacy te
mpora
l
se
ma
ntic
s of ind
e
ter
m
i
n
ac
y
data. F
i
rstly, w
e
pres
ent o
u
r tupl
e-
timesta
m
p metho
d
to re
prese
n
t an
d store thes
e te
mp
oral
data i
n
cl
u
d
in
g
deter
mi
nacy a
nd in
deter
mi
n
a
cy data. T
h
e
n
w
e
introduc
e
the temp
ora
l
pri
m
itives to
process temp
oral
relations needed in
BPT
M. A
new probability method
is br
ought forwar
d to get
potential
in
formation among
these i
n
d
e
ter
m
inacy
data. At
last
a
query
e
x
ampl
e b
a
sed
on CP
R (C
omputer-b
ase
d
P
a
tient R
e
cor
d
)
is
give
n to show
that our
meth
od
is effective an
d feasib
le.
Ke
y
w
ords
:
in
d
e
termin
a
cy, a tempor
al dat
a mo
de
l, prob
abi
lity, CPR (Co
m
puter-b
ase
d
Patient Rec
o
rd)
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1
．
Introduc
tion
Many appli
c
ations
su
ch
as AI, datab
ase
m
ana
ge
ment, multimedia sy
stem,
history
manag
eme
n
t syste
m
, me
dical
informa
t
ics, et
c., ine
v
itably encou
nter in
dete
r
m
i
nacy tem
p
o
r
al
data be
ca
use
of the dyna
mic
cha
nge
s
of the re
al
wo
rld. They
c
a
n
not be
efficie
n
tly represent
ed
and
sto
r
ed
in
datab
ase, e
s
peci
a
lly the v
a
lid time
of
some in
cid
ent
s a
nd th
eir te
mporal
relatio
n
s
can
not be a
c
curately dete
r
mined [1, 2]. Therefor
e, m
any re
sea
r
ch
ers
have fo
cu
sed
on b
u
ildi
ng
indetermina
cy temporal d
a
t
a model
s. Th
ere a
r
e
two b
r
oad
cate
gori
e
s of ap
proa
ches
emerged
in
the previou
s
resea
r
ch. On
e is point-ba
s
ed
sema
ntics model a
n
d
the ot
her is interval-b
ased
sema
ntics m
odel. Th
e typ
i
cal
point-ba
s
ed mo
del i
s
C. Combi
propo
sed
mod
e
l ba
sed
on
time
point, whi
c
h i
s
suita
b
le to deal with a va
riety of medical data. But the model h
a
s some limitati
ons
in copi
ng
with
data ba
sed
on interval. T
he typica
l int
e
rval-ba
s
ed
model i
s
HA
MP in whi
c
h
use
r
s
can d
e
fine ti
me point an
d
time interval
with
indete
r
minacy [3]. HAMP is focu
sed on q
ueryi
n
g
informatio
n about natural langu
age ex
pre
ssi
on
s,
while it can not express a
finite union of
intervals an
d
rep
r
e
s
ent
rel
a
tive time. NL
TM (T
empo
ra
l model
of Na
tural la
ngu
ag
e) mo
del i
s
al
so
a interval-based model
which ha
s overcome HAMP
’s
limitations
,
but
NLT
M
still exists som
e
faults [4]. For example, da
te element
s
and time
-of-d
a
y are
rep
r
e
s
ente
d
sepa
rately, so spa
c
e
co
st is very hi
gh than mod
e
l
s that store them unity.
Above-me
ntioned mo
del
s, HAMP and NLTM a
ll
ca
n expre
ss d
e
t
ermina
cy informatio
n
and in
determinacy info
rmation. But query
re
sult
s are o
n
ly “u
nce
r
tain
” wh
en u
s
ers q
u
e
ry
indetermina
cy informatio
n. Potential i
n
formatio
n am
ong th
ese in
d
e
termin
acy
d
a
ta can
not
b
een
get wh
en
u
s
ers
are
qu
erying i
n
HAMP or
NL
TM mod
e
l. In order to
overcome th
ese
sho
r
tco
m
ing
s
, we pro
p
o
s
e
an indete
r
mi
nacy tempo
r
a
l
data model
based on p
r
o
bability, named
BPTM (Tem
poral m
odel
base
d
on
prob
ability), to manag
e
the indete
r
m
i
nacy temp
o
r
al
sema
ntics of medical data.
Firstly, Sectio
n 2 a
nd
se
ction 3
pre
s
e
n
t our tu
ple
-
timestamp
meth
od to rep
r
e
s
e
n
t an
d
store
the
s
e t
e
mpo
r
al d
a
ta
inclu
d
ing
de
termina
c
y an
d indete
r
min
a
cy dat
a. In se
ction
4,
we
introdu
ce the
temporal p
r
imitives to process temp
oral relation
s needed in
BPTM. A ne
w
prob
ability m
e
thod i
s
bro
u
ght
forward t
o
get
potenti
a
l information
amon
g the
s
e ind
e
termi
n
acy
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
An Indeterm
i
nacy Tem
poral Data Mo
d
e
l
base
d
on Probabilit
y (Ren
Shuxia
)
6687
data. At last a query example ba
sed
on CPR (C
o
m
puter-ba
s
e
d
Patient Re
cord) i
s
given in
se
ction 5 to show that ou
r me
thod is eff
e
ctive and fe
asibl
e
.
2. Temporal Conc
epts an
d Terms
Tempo
r
al DB
MS has three
kind
s’ styles’
of time:
a)
Valid-time [1, 5]: a period time in whi
c
h a
real event re
mains true.
b)
Tran
sa
ction-t
i
me: the time whe
n
a datab
ase o
b
je
ct ha
ppen
s.
c)
Use
r
-define
d
time [6]:
the time that
use
r
s input a
c
cording to their n
eed
s.
Events a
r
e
al
ways a
s
soci
a
t
ed with
valid
time an
d tran
sa
ction tim
e
i
n
temp
oral
da
tabase.
We o
n
ly de
al
with valid tim
e
be
cau
s
e
th
e main
pu
rpo
s
e of th
e latte
r on
e is valid
ating data
b
a
s
e
,
and mo
reove
r
, it brings a
powerful cost
in term
s of computing
co
mplexity, storage capa
city and
perfo
rman
ce.
The time
sta
m
p types for rep
r
e
s
entin
g
BPTM ar
e ti
me poi
nts, in
tervals, d
u
ration an
d
temporal ele
m
ents. In ge
neral, the
st
anda
rd
G
r
e
g
o
rian
cal
end
ar is
ado
pte
d
, whi
c
h allo
ws
timestamp
s
t
o
be
de
clare
d
at any of t
he follo
wi
ng colle
ction of gran
ula
r
ity:
year,
mo
nth, day,
hour, min
u
te and second.
Tempo
r
al DB
MS has five kinds
st
yles of temporal data
[7-10]:
a)
Chro
non:
We assum
e
time domai
n TD is a no
n-e
m
pty,
fi
nite, totally ordered
set. TD
with the co
rresp
ondi
ng d
o
main ELEM
, models the
time domai
n. Its eleme
n
ts are te
rm
ed
Chrono
n. Chronon is a n
o
n
-
de
com
p
o
s
ab
le time interval of some
fi
x
ed minimal d
u
ration. Se
co
nd
is utilized as t
he Chronon i
n
this paper.
b)
Instant: a fixed time point on time axis. It relates to in
stantan
eou
s
situation
s
.
c)
Interval [7]: a
n
movable an
d contin
uou
s
time perio
d.
d)
Period: an i
mmovable int
e
rval
A perio
d is a
n
immovable
interval an
d very usef
ul da
ta style, but it is not
supp
o
r
ted by
busi
n
e
ss
se
rvice DBMS a
nd SQL9
2. This pa
pe
r
introdu
ce
s a me
thod to simul
a
te peri
od wi
th
both in
stant, one in
stant m
ean
s the b
egi
n of the pe
rio
d
, the other
mean
s t
he e
nd of the p
e
ri
od.
In addition, period
s
are no
t entirely ord
e
rly and have
seven tempo
r
al relatio
n
s
[
5
, 11]. Figure 1
sho
w
s the se
ven temporal relation
s of two pe
riod
s.
Duration: Du
ration is the le
ngth between
two ti
me points. Du
ration
of unce
r
tain i
n
terval
is un
ce
rtainty
and it h
a
s the minim
u
m
and m
a
xi
mal
values.
The
expre
s
sion
of duration i
s
an
orde
re
d se
qu
ence of time value on time
domain. It can be differe
nt granul
aritie
s su
ch a
s
ye
ar,
month, day and hou
r and
so on.
Figure 1. Seven Temp
oral
Relatio
n
s of
Period
s
3. Indetermi
n
ac
y
Temporal Informati
on
Valid-time
ca
n be exp
r
e
s
sed by a or
ma
ny poi
nts, an
interval, duration and
a pe
ri
od. We
adopt a
pe
rio
d
to show a
valid time. For exam
pl
e, Disea
s
e
attri
bute
in CPR (Co
m
pute
r
-b
ase
d
Patient Reco
rd) i
s
a temp
oral on
e (cha
nge over ti
m
e
), its valid time is someti
me determin
a
cy,
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 668
6 – 6692
6688
sometim
e
in
d
e
termin
acy (Disea
se begi
ns and
en
ds
at a m
o
vable
time).
We
h
a
ve re
solve
d
the
probl
em by providing upp
er bound a
nd lo
wer b
oun
d for the begin an
d end time of dise
ase.
a. The rep
r
e
s
entation of in
determi
na
cy data
Attributes
set
of temporal relation
shi
p
i
s
compo
s
e
d
of non-te
mpo
r
al attrib
utes
(Value
s
do n
o
t
chan
g
e
ove
r
time
)
and te
mpo
r
al
attribute
s
(v
alue
s
cha
nge
with
time) [8
]. We
expre
s
s a
temporal attri
bute a
s
a
cou
p
le of
attribut
e value
and
p
e
riod,
nam
ely (v, <t1, t2
>),
v is a
tempo
r
al
attribute n
a
m
e
, <t1,t2> i
s
a co
uple
of
begin tim
e
a
nd en
d time
of temporal
attribute, na
mely
tuple-time
sta
m
p. If the val
i
d time
of te
mporal a
ttri
b
ute is d
e
term
inacy,
t1 and t2 become time
points
and
be
gin time a
nd
end time i
s
e
qual. If one o
f
t1 and t2 i
s
a pe
riod at l
e
ast, valid tim
e
of
temporal attribute is
indeterminac
y [9].
In the BPTM
,
all types of
time are re
pre
s
ente
d
a
s
a tuple fo
rm
<t1, t2>, t1
or t2 i
s
expre
s
sed a
s
a period to show a valid time. When
d
e
t
ermina
cy temporal inform
ation is a inst
ant,
the insta
n
t is
denote
d
a
s
<t1, t2>, t1 is
equal to
t2. If the insta
n
t is indetermina
cy, it is denote
d
as <t1, t2>, t
1
is not equ
a
l
to t2. When the i
ndeterm
i
nacy tempo
r
al informatio
n
is a perio
d, the
perio
d is still
denote
d
as
<t1, t2>, but t1
and t2 ar
e al
l two-tuple
s
, namely t1 or
t2 has sta
r
t time
and e
nd tim
e
. Comp
ared
with HAT
M
and
NLTM
in flexibility, BPTM mod
e
l ha
s a g
r
eat
advantag
e in the unified
fo
r
m
of
expre
s
si
on.
b. The storag
e stru
ctur
e of indetermina
cy data
Indetermi
na
cy and dete
r
minacy valid
time are all
store
d
in the
same ta
ble
stru
cture.
Although O
r
a
c
le do
not provide data
style about pe
riods,
we can
stimulate p
e
r
iod
with Dat
e
style. If valid time i
s
d
e
termin
acy,
we
nee
d two date
field
s
to i
m
itate. If valid tim
e
is
indetermina
cy (at least
on
e of t1 and t2
is a p
e
rio
d
),
we u
s
e fo
ur
Date field
s
to
determi
ne u
pper
and lo
we
r bo
und of be
gin
and en
d poi
n
t
of valid time
. In the Ora
c
l
e
DBMS, a field of date
style
can d
enote y
ear-month
-
d
a
y
and hour-m
i
nute-se
con
d
simultan
eou
sl
y.
If indetermina
cy temporal d
a
ta is <t1, Du
rati
on > o
r
<Duration, t2>,
we ado
pt thre
e kind
s
of databa
se
schem
as to
so
lve the Du
rati
on probl
e
m
. The forwa
r
d
mode
can
sol
v
e <t1, Du
rati
on
>, Backward
mode
ca
n sol
v
e <Duration,
t2>. Th
e
two
mode
s
can fi
gure
out the
other
un
kno
w
n
t1 or t2 by means of ad
ding
and su
btra
ction.
4. Temporal Relatio
n
s of
Indetermina
c
y
Temporal Information
The tem
poral qu
ery la
ngua
ge
and
pro
c
e
s
sing
are
key contents in t
e
mpo
r
a
l
manag
eme
n
t and h
a
ve cl
o
s
e
con
n
e
c
tio
n
. This
pap
er introdu
ce
s a
temporal mo
del BPTM ba
sed
on relatio
n
s,
so the temp
o
r
al que
ry lan
guag
e is al
so
relational
qu
ery one in
clu
d
ing exten
s
io
n of
SQL. Relatio
nal data mod
e
l is able to p
r
ocess the ad
ded valid-tim
e and tran
sa
ction time.
Snodg
ra
ss
brought fo
rward proba
b
ility method to
so
lve the relations of ind
e
te
rmina
c
y
temporal dat
a by defining
the “B
efore” relation of in
determi
na
cy
instant. Base
d on which, the
pape
r exten
d
s
thi
s
meth
o
d
by ad
ding
two
new te
m
poral
pri
m
itive definition
s
of indete
r
min
a
cy
instant
as
well as ind
e
termin
acy p
e
r
iod:
“Bef
ore
I
” and
“simu
l
taneity”. By introd
uci
n
g
an
argu
ment
ca
lled “Fu
zzi
n
e
ss” to d
e
scrib
e
th
e d
egre
e
of
in
determi
na
cy, mea
n
whil
e
the
“Fu
zzi
ne
ss” i
s
mo
dified
by NiaveB
ay
e
s
cla
ssif
i
e
r
t
o
e
n
su
re ac
cu
ra
cy of the
min
ed in
determi
n
a
cy
temporal data
.
a.
Tempo
r
al rel
a
tions of ind
e
t
ermina
cy period.
Seven relatio
n
s of peri
o
d
s
can be
sum
m
ed up
to “<”or “<<” relati
on between
a kind of
time point
s. If two en
d-poin
t
s of a p
e
rio
d
are
det
ermin
a
cy, its temp
oral
relatio
n
can be
achiev
ed
by using te
m
poral
relatio
n
of time points. If tw
o end
-points of a
p
e
riod
are i
n
d
e
termin
acy, the
query result may be ambi
guity. The pa
per a
dopt
s pr
obabili
stic a
p
proa
ch to
re
solve the pro
b
l
e
m
about ind
e
terminacy temp
oral info
rmati
on.
(1) Proba
bilistic approa
ch [12]
There is a p
r
ereq
uisite
bef
ore
usi
ng p
r
o
babili
stic a
p
p
r
oa
ch th
at an
y incide
nt ha
ppen
s at
any time i
n
st
ant du
rin
g
th
e pe
riod
with
equal
pr
oba
bi
lity. In additio
n
, one
in
cide
nt and
the
ot
her
incid
ent ha
s no any relatio
n
s.
Proba
bilisti
c Orde
rin
g
[7, 12]: Given there a
r
e two i
ndetermina
cy
time points
α
and
β
,
the probabilit
y of
α
before
β
, that is probability of
α≤β
, namely Before (
α
,
β
), ca
n be define
d
as:
(
1
)
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An Indeterm
i
nacy Tem
poral Data Mo
d
e
l
base
d
on Probabilit
y (Ren
Shuxia
)
6689
(2)
“Simultan
e
ity” temporal
primitive
In orde
r to ob
tain more flexibility to query
indetermina
cy temporal inf
o
rmatio
n, we
define
two ne
w temporal p
r
imitives ba
se
d on
seven temp
o
r
al rel
a
tion
s in Figure 1: “simultan
e
ity” and
“non
-simultan
e
ity”.
Given in
cide
n
t
A occu
rs at
a an
d finishe
s
at
b,
in
cide
nt B occu
rs a
t
c a
nd fini
sh
es
at d.
Obvious
l
y, “
a
﹤
b’ and “c
﹤
d
”
are all tru
e
. a, b, c and d can b
e
time points an
d also time perio
d
s
.
Definition 1 “sim
ultaneity”:
Given
“a
≤
c
﹤
b” o
r
“c
﹤
a
﹤
d” i
s
tru
e
，
then in
cide
nt A and
incid
ent B will
have simulta
neity relation.
“simulta
neity” definition in
clud
es five of all the relatio
n
s
in Figure 1 (o
verlap, du
ring
, equal, start, end).
Definition 2 “non-sim
u
ltan
eity”: Given “b
≤
c” or
“d
≤
a
”
is true, then incid
ent A and
incide
nt
B will h
a
ve
non-sim
u
ltan
eity relation.
“Non
-sim
ultaneity” d
e
fini
tion in
clude
s two
relatio
n
s in
Figure1 (m
ee
t, before).
(3)
Ne
w temp
oral p
r
imitive “BeforeI
” and
Fuzzine
ss
The q
uery
of
indetermina
cy temporal inf
o
rmat
io
n ofte
n ha
s n
o
t an
explicit an
swer. If the
comp
uted p
r
o
bability is too
small, it is n
o
good h
e
lp
u
s
ers’
de
cisi
on-makin
g
s. In o
r
de
r to re
solv
e
the problem,
we int
r
od
uce
an a
r
gu
men
t
“
γ
”, whi
c
h
i
s
p
r
ob
able v
a
lue that
ca
n
be a
c
hi
eved
at
least a
c
cordi
ng to use
r
’s e
x
perien
c
e.
Definition 3 F
u
zzine
s
s:
We call “
γ
” as “fuzzi
ne
ss”, whi
c
h the value of “
γ
” is b
e
t
ween ‘0’ to ‘1’. If the value
of “
γ
” is
bigge
r, and then the que
ry result
of indetermi
na
cy tempo
r
al information is mo
re meani
ngful
for
use
r
s.
In SQL, “Before [6, 8]” is algeb
ra rel
a
tion “
≤
”, the “Before
”
relat
i
on of any b
o
th time
points can
b
e
de
scri
bed
as B
e
fore
(
α
,
β
)=
α≤
β
. But f
o
r i
ndete
r
min
a
cy tem
poral
inform
ation
can
not use “B
efore
”
op
eratio
n [12]. So we define
a
ne
w
op
er
a
t
io
n “
B
e
f
o
r
e
I
”
w
h
ic
h
inc
l
ud
es
th
r
e
e
argu
ment
s su
ch a
s
f
u
z
z
ine
ss
“
γ
”, incid
e
n
t A and incid
ent B with indetermin
a
cy valid-time.
Definition 4 “BeforeI” op
eration:
BeforeI (
,
,
γ
)
＝
{True |Pr[
]
γ
}
{Fals
e
|Pr[
<
]
γ
}
(2)
The result s
e
t of BeforeI (a, b,
γ
) in
clu
des fo
ur el
e
m
ents
su
ch
as {
}
, {True},
{False},
{True, Fals
e}. If BeforeI
(a, b,
γ
) ={
True
}, the
relation
of ”a
b” is true.
If BeforeI (a, b
,
γ
)=
{False}
或
{
}
,
the relation
of “a
b” is
fals
e. If BeforeI (a, b,
γ
)
= {T
rue, False}, th
e que
ry re
sult
is
indetermina
cy, but the value of proba
bility, which re
sult is true o
r
f
a
lse, mu
st no
t be small
e
r t
han
f
u
zzi
ne
ss “
γ
”.
b.
Modifying fuzzine
s
s “
γ
”
Before
minin
g
the i
ndete
r
mina
cy tem
poral
data, t
he a
r
gu
ment
“
γ
”
as fuzzi
ness i
s
inputted by u
s
ers. But different
“
γ
” by
different users offered a
ll
has
som
e
deviation whi
c
h will
influen
ce the
accuracy
of the minin
g
re
sults.
Ni
aveB
ayes cla
ssifie
r
is used
to modify
fuzzin
ess
“
γ
” for en
su
ri
ng better a
c
cura
cy of the mined ind
e
terminacy temp
oral data.
The modifyin
g pro
c
ed
ure is as follo
ws:
(1) Initializing
arguments
“
γ
” an
d “p”
whi
c
h is step width.
(2)
Prepa
ring d
a
ta set for an e
v
aluation fun
c
tion---f
it(x
), whi
c
h can get
classification
accura
cy
given a “
γ
” by
NiaveBayes
cla
ssif
i
e
r
t
r
ain
i
ng.
S = load('
D
at
a.mat');
x =
S.Data;
De
cA: a deci
s
ion
-
ma
kin
g
attribute
（
Th
e
second
colu
mn of X, DecA = x(:,2)
）
;
ConA: a co
nd
ition attribute
（
The firs
t column of X, ConA =
x(:,1)
）
;
The metho
d
of 10 fold cro
ss valid
ation i
s
us
ed to co
mpute the cla
ssifi
cation a
c
curacy of
sampl
e
. The i
m
pleme
n
tatio
n
pro
c
ed
ure of
the func
tion fit(x) is
as
follows
:
indic
e
s =
cr
o
ssv
ali
nd('Kfold',De
cA,10);
cp =
cla
s
s
per
f
(
De
cA
);
fo
r
k
=
1
:
10
tes
t
=
(indic
es
==
k);
train =
~
t
es
t;
nb =
NaiveBayes
.fit(ConA
(t
rain,:),Dec
A
(
train,:));
c
l
as
s
=
nb.predic
t
(ConA(tes
t,:));
c
l
as
sperf
(
cp,c
las
s
,tes
t
);
end
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Vol. 11, No
. 11, Novemb
er 201
3: 668
6 – 6692
6690
Fit =
c
p
.Correc
t
Rate;
end
(3)
For a given fu
zzi
ne
ss “
γ
”, computing p
r
o
bability value and its cl
ass
mark.
for j = 1:lengt
h(x)
if x(j,1) >
=
r
x(j,2) =
1;
els
e
x(j,2) =
0;
end
end
(4)
Initializing the
best cla
s
sification accu
ra
cy. pbest = fit(x);
(5)
Thro
ugh ma
n
y
times iterations to find th
e optimal fuzzine
s
s “
γ
”
.
Spe
c
ific
pr
oc
es
s is
a
s
follows
:
for i =
1:m
r =
r +
s
t
ep;
for j = 1:lengt
h(x)
if x(j,1) >
=
r
x(j,2) =
1;
els
e
x(j,2) =
0;
end
end
pref =
fit(x);
if
pref <
pbes
t
pbest = pref;
rbes
t = r;
end
end
P = pbest;
R =
rbes
t;
End
Figure 2 is a
prog
ram flo
w
cha
r
t for Modi
fying fuzzin
e
ss “
γ
”.
Figure 2. The
Progra
m
Flo
w
Ch
art for M
odifying Fuzzi
ness “
γ
”
5. The Mining of Indeter
m
inac
y
Temporal Inform
ation
Usi
ng ab
ove-mentione
d m
e
thod,
indete
r
mina
cy temp
oral info
rmati
on in CP
R is mined.
First,
som
e
d
a
ta ab
out hy
perten
s
io
n a
n
d
arte
rio
s
clerosi
s
h
a
s bee
n filtered
fro
m
Data
ba
se,
and
then
we
wan
t
to continu
e
analyzi
ng
“simultaneity”
relation
wh
en
we
find
time
of illn
ess
attack
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
An Indeterm
i
nacy Tem
poral Data Mo
d
e
l
base
d
on Probabilit
y (Ren
Shuxia
)
6691
and
re
covery
is in
determi
nacy. Fo
r ex
ample, di
se
a
s
e A
and B
have valid
-time a
s
follo
ws in
Table 1, ES i
s
the e
a
rlie
st
time of on
set
of illness,
LS
is the late
st time of on
set
of illness, EF
is
the earlie
st time of illness recovery, and
LF
is
the lates
t
time of illnes
s
rec
o
very.
Table 1. Stimulation of Valid-time
Name
LS
ES
EF
LF
A 1999-5
-
30
1999-6
-
18
2000-2
-
10
2000-10
-1
B 1999-6
-
8
1999-6
-
29
2002-10
-10
2002-12
-3
Given time
of disea
s
e A
attack is ‘a’ a
n
d
the ti
me
of
recovery i
s
‘b
’, the time of
dise
ase
B attack i
s
‘
c
’
and the tim
e
of re
covery i
s
‘d’, then tem
poral
rel
a
tion
s of 19
99
-5-3
0
≤
a
≤
19
99-6-18
,
2000
-2
-10
≤
b
≤
200
0-10-1, 1999
-6
-8
≤
c
≤
1999
-6
-29 a
n
d
2002
-1
0-1
0
≤
d
≤
200
2-1
2
-3 are
all true,
the
modified fuzziness “
γ
” i
s
e
qual to 0.6 which i
s
obtain
ed by NiaveB
ayes
c
l
ass
i
fier
tr
a
i
n
i
ng
. N
o
w
,
we n
eed to
confirm the
relation
s of a,
b, c
an
d d
by estimating
if the relatio
n
of “a
≤
c
﹤
b” or
“c
﹤
a
﹤
d” i
s
true. Becau
s
e
a, b, c and d
are a
ll indet
ermin
a
cy, we
need proba
bility method to
comp
ute their relation
s.
First, we
com
pute Pr(a
≤
c) by usin
g formula 1. L
eng
th of ‘a’ and
‘
c
’ is
20
and
22 day
s
respectively as
granularity with
a day. ‘
a
’ and ‘c’
hav
e equal prob
ability in each own peri
od.
So
the probabilit
y is computed as follows:
Pr(a
≤
c) =(1/2
0
×1/2
2)×12
+
(1/20×1/22)×1
3+ ……
+(1/
2
0
×1/2
2)×21
+
[
(
1/20
×1/22
)
×22] ×10
=
0.8
7
5
Usi
ng p
r
ob
a
b
ility appro
a
c
h, othe
r p
r
oba
bility re
sults
of ind
e
termin
acy t
e
mpo
r
a
l
informatio
n are comp
uted a
s
follows:
Pr[a>c
]=
0.125 Pr[c
<
b
]=1 Pr[
c
≥
b]=0
Comp
ared wi
th
γ
=
0
.6, Pr[a
≤
c
]
=
0
.8
75>
γ
Pr[a>c]
=
0.12
5<
γ
Pr[c<
b
]=1>
γ
P
r
[
c
≥
b]=0<
γ
our goal will
be to obtain
Before I (a, c,
γ
)={True}
a
nd Before I (c, b,
γ
)=
{
T
r
ue}
. T
h
is
s
h
ows th
a
t
‘a
≤
c’ a
nd ‘c
﹤
b’ are all true, namely ‘
a
﹤
≤
c
b
’ is tru
e
. The co
ncl
uded
re
sults
are d
e
termin
acy,
namely di
se
a
s
e A
and
B i
s
“sim
ultaneit
y
” rel
a
tion.
If one
re
sult i
s
{T
ru
e}, the
other is {T
rue,
False
}
, a
nd t
hen
we
ne
ed
to comp
ute “Pr[a
≤
c<b]” o
r
“Pr[
c<a<
d]” and sh
ow
the
i
r
ind
e
termi
n
a
c
y
results for all
users. For
computing
“Pr[
a
≤
c<b]
” or “P
r[c
<
a
<
d]” is v
e
ry
com
p
lex
,
we intro
d
u
c
e a
s
i
mple method for a c
a
s
e
of “Pr[a
≤
c<b]
” as follo
ws:
Pr[a
≤
c
<
b] =
Pr[c<
b
] +
Pr[a
≤
c]
﹣
1
(
3
)
Usi
ng above
-
mentione
d method
s, a temporal
DBM
S
based on
CPR is
con
s
t
r
ucte
d to
implement the mining
of indetermi
nacy medical te
mporal data. Figure 3
i
s
probability computing
res
u
lts of CP
RS.
Figure 3. Probability
Computing Result
s
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 668
6 – 6692
6692
6. Conclusio
n
In orde
r to o
v
erco
me so
me sh
ortcom
ings of
curre
n
t temporal
model
s,
an
op
ti
m
i
zatio
n
m
odel
is prop
ose
d
[13], na
med BPTM (Tempo
ral m
o
del ba
sed
on
prob
ability), to manag
e th
e
indetermina
cy temporal
sema
ntics of
indete
r
mi
n
a
c
y
data. Firstly,
we pre
s
ent our
tu
ple-
timestamp m
e
thod to re
p
r
esent an
d store the
s
e tempo
r
al data
includi
ng d
e
termin
acy a
n
d
indetermina
cy data. Then
we intro
d
u
c
e the tempo
r
al primitives
to pro
c
e
ss te
mporal rel
a
tions
need
ed in B
P
TM. A new prob
ability method i
s
br
ought forwa
r
d to get pot
ential inform
ation
among the
s
e
indetermin
a
c
y data. At last a tempor
al CPRS is
con
s
tru
c
ted t
o
implement
the
mining of in
d
e
termin
acy
medical temp
oral d
a
ta.
Th
is CP
RS is
uncertain
system to sup
p
l
y
a
good
help fo
r docto
rs to
make
a
clinical diag
no
sis [
14]. This
CP
RS exampl
e
related to
qu
ery
also
sho
w
s that our metho
d
is effective and fea
s
ible.
Ho
wever, ou
r model still has so
me faults.
For exampl
e, the query spe
ed will slo
w
whe
n
data re
co
rd
s excee
d
one h
undred thou
sand or m
o
re
. And therefo
r
e
we sh
all opti
m
ize the q
uery
algorith
m
on
temporal info
rmation a
nd the extens
i
on
of temporal i
ndex and joi
n
operator in t
h
e
future.
Ackn
o
w
l
e
dg
ment
This wo
rk wa
s
su
p
ported
by
Tianjin
Nat
u
ral S
c
ie
nce Fo
undatio
n (Gra
nt
No.07
J
CZD
J
C06
700
).
Referen
ces
[1]
Z
hang
Shic
ha
o
,
Yan
Xi
ao
w
e
i,
Nie W
e
nlo
ng.
A fe
w
pr
obl
em
s intemp
oral
d
a
tabas
e.
Jour
n
a
l of Gu
an
gxi
Nor
m
al U
n
iv
ersity
.1995; 1
3
(4
): 10-14.
[2]
Z
hou
Xia
o
n
i
ng.
Researc
h
on
CPR.
Medic
a
l information.
19
98; 11(1): 6-8.
[3]
C Comb
i, G Pozzi. HMAP - A temporal
dat
a mode
l ma
n
a
g
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g interv
als
w
i
t
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differe
nt g
r
anu
lariti
es an
d
i
n
de
te
rmi
na
cy
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he VLDB Jou
r
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08; l9(
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11.
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Xi
ao
w
e
i Z
H
A
N
G. A
T
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mpora
l
Data
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e
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li
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mpora
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e
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3
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[6]
D
y
r
e
sso
n CE,
RT
Snodgrass.
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i
mest
amp Semantics a
nd
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epres
entati
on.
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s
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93
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18(3): 14
3-1
6
6
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[7]
Jense
n
CS, L Mark.
T
e
mporal Spec
ial
i
zati
o
n
and Ge
nera
l
i
z
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a
ta Eng
i
neer
ing
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994;
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97
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[8]
M
y
rac
h
T
,
GF Knolma
ye
r, R Barnert. On
Ensuri
ng Ke
ys
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enti
a
l Integrit
y
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e
mpor
a
l
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e
La
n
gua
ge T
S
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ation s
y
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g
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e
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d
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o
r
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a
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