Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
3
,
No
. 5, Oct
o
ber
2
0
1
3
,
pp
. 69
6~
70
1
I
S
SN
: 208
8-8
7
0
8
6
96
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Mapping Fuzzy Petri Net to
Fuzzy Extended
Markup Language
Z
a
hra Mas
o
u
d
i
n
ez
ad*,
Al
i
Har
o
o
n
abadi*
*, M
o
hamma
d
Teshnehl
ab*
* Departement o
f
Computer, Scien
ce
and R
e
sear
ch branch
, Islamic Azad
University
, khouzestan-Ir
an
** As
is
tent P
r
of
es
s
o
r, Com
puter
Departm
e
nt,
Is
la
m
i
c Azad
Unive
r
s
i
t
y
,
cen
tral
T
e
h
r
an bran
ch
***Control Dep
a
rtmant K
.
N. Toosi University
of
Technolog
y
S
e
y
e
d Khand
a
nbr
idge, Tehran
, Ir
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 14, 2013
Rev
i
sed
Ju
l 28
,
20
13
Accepted Aug 10, 2013
Use of model gives the knowled
g
e and
information about th
e p
h
enomenon
als
o
erad
ic
ates
the
cos
t
,
the
effort
and th
e haz
a
rd of us
ing the
rea
l
phenomenon.Ch
aracteristics an
d
concepts of Petri ne
ts ar
e in
a way
th
at
makes it simple
and strong
to
describe
and stud
y the
information
processing
s
y
stem
; espe
cia
l
l
y
it is shown
in t
hos
e which
are de
al
i
ng with discrete,
concurren
t
, d
i
str
i
buted
, par
a
llel
and inde
cisiv
e
e
v
ents. Ye
t, du
e t
o
Petri n
e
ts
inabil
it
y to fa
ce
with s
y
stem
s working
on obscure data and contin
ues events,
the interest to d
e
velop fundamental co
n
cept of
Petri nets has been raised
which is led to
new sty
l
e of presente
d model named "fuzzy
Petr
i nets". Th
e
differen
ce
in P
e
t
r
i nets
is
in th
e
elem
ents
th
at ha
ve been fu
zz
ed.
Trans
itions
,
plac
es
, s
i
gns
and arcs
can be fu
zzed
. P
M
NL, on the other hand
as
a m
a
rkup
languag
e
has
b
een
engag
e
d in
uttering Petri
nets in
previous
resear
ches
.
Fuzzy
markup nets can model the uncertainty
of concurr
e
n
t
scenarios
differen
t
from a d
y
namic s
y
stem
b
y
a boa
rd of p
a
rameters and u
s
e of fuzzy
membership dependencies. Th
erefore, in
ord
e
r to
define
these uncertain data,
it is vital to use a formal language to
describ
e
fuzzy
Petri nets. To support
this version in
t
h
is thesis,
a m
a
rkup
languag
e
will be present
e
d stating
the
structure
and gr
ammar of mark
up langua
g
e
and
covering fu
zzy
concep
ts in
Petri nets as w
e
ll
. Presenting
t
h
e suggested gr
am
m
a
r accom
m
odates the
support of fuzzy
developed mar
kup la
nguage an
d includes the combination
of uncer
tainty
an
d XML.
Keyword:
FPNML
Fuzzy Pet
r
i Ne
t
FXML
Pet
r
i
Net
M
a
rk
up
La
ng
ua
ge
XM
L
Copyright ©
201
3 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Zahra
Masoudinezad,
Depa
rtem
ent of Com
puter, Sc
ience and Res
e
arch branc
h
,
Isl
a
m
i
c
Azad Uni
v
ersi
t
y
, kh
ouze
s
t
a
n-
Ira
n
Em
ail: z.
m
a
soudi
nezad@yahoo.com
1.
INTRODUCTION
Petri n
e
ts
were d
i
scu
ssed
b
y
Carl Ad
am
Petri in
h
i
s PHD
'
s th
esis in 19
62
[1
] &
[
14]. Th
ey ar
e
gene
ral
l
y
use
d
as a
de
vi
ce t
o
st
udy
a
n
d
m
odel
sy
st
em
s. I
n
fact
he
pr
esent
e
d
t
h
e
rel
a
t
i
ons
hi
p am
ong
t
h
e
sy
st
em
co
m
ponent
s
by
a gra
ph
or a
net
w
or
k. Fi
r
s
t
and
fo
r
e
m
o
st
a Pet
r
i
net
i
s
a
m
a
t
h
em
at
i
cal
descri
pt
i
on
b
u
t
i
t
gi
ves a grap
hi
cal
or vi
su
al
di
spl
a
y
of sy
st
em
as wel
l
.
A Pet
r
i
net
can be use
d
t
o
det
e
rm
i
n
e im
p
o
rt
a
n
t
i
n
f
o
rm
at
i
on ab
out
t
h
e m
odel
sy
st
em
st
ruct
ure
.
N
o
rm
al
Pet
r
i
net
s
are
u
s
ed t
o
m
odel
sy
st
em
descri
b
e
d i
n
d
e
tails, bu
t t
o
th
o
s
e wh
ich hav
e
u
n
certain
an
d ob
scu
r
e
da
ta they are
inappropriate,
wh
ile in
p
r
actice we
are
dealing
with c
o
m
p
licated syste
m
s that have a degree
of
unce
r
t
a
i
n
t
y
and t
h
ey
ar
e
not subject to
precise
math
e
m
atica
l
m
o
d
e
lin
g
.
Regard
i
n
g th
e
o
s
ten
s
ib
ly of
ob
sc
u
r
e d
a
ta with
fu
zzy
log
i
c,
the
coalesce
nce
of fuzzy
th
eory in
Pet
r
i
n
e
ts is
u
s
efu
l
to
en
h
a
n
ce t
h
e
ab
ility o
f
Petri
n
e
ts m
o
d
e
lin
g. It
h
a
s
b
een do
n
e
with th
e
wo
rk
of
Loo
n
e
y an
d some au
th
ors
o
f
Petri n
e
ts and
asso
ciatio
n
of
artificial in
telli
g
e
n
c
e in
19
88
. D
i
ff
er
en
t typ
e
s of
fu
zzy Petri n
e
ts co
m
p
atib
le
with
th
e th
eo
ry o
f
Petri
net
s
were de
si
g
n
e
d
[
2
]
.
These
d
i
ffere
nt
way
s
whi
c
h
synthesize Pet
r
i net a
n
d
fuz
z
y sets are cal
led fuzzy Pe
tri n
e
ts
[
3
] & [4
] &
[
5
]. Th
e d
i
ff
er
en
ce is
in
th
e
ele
m
ents that have
bee
n
fuz
zed. T
r
ansitions, places, si
gns and a
r
cs ca
n be fuzzed. Al
l these things can be
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 3
,
N
o
. 5
,
O
c
tob
e
r
20
13
:
696
–
7
01
6
97
fuzze
d.
PNM
L
, o
n
t
h
e
ot
her
han
d
,
as a m
a
rku
p
l
a
ng
ua
ge
has
ut
t
e
red
Pet
r
i
net
s
.
F
u
zzy
m
a
rku
p
net
w
or
ks ca
n
m
odel
t
h
e uncert
a
i
n
t
y
of co
n
c
ur
rent
sce
n
ari
o
s di
f
f
ere
n
t
fr
o
m
a dy
nam
i
c sy
st
em
by
a board o
f
pa
ram
e
t
e
rs an
d
use o
f
f
u
zzy
m
e
m
b
ershi
p
de
p
e
nde
nci
e
s. T
h
e
r
ef
ore
usi
n
g a fo
rm
al l
a
ngua
ge i
s
ur
gent
t
o
descri
be
fuzz
y
Pet
r
i
n
e
ts to d
e
fin
e
th
ese
un
certain
d
a
ta. To
sup
port th
is
v
e
rs
i
o
n i
n
th
is article the related
wo
rk
will b
e
rev
i
ewed
in
th
e first p
a
rt, i
n
th
e second
a
m
a
rk
up
lan
guag
e
will b
e
p
r
esen
ted
ex
pressin
g
th
e
g
r
ammar an
d
stru
ctu
r
e i
n
mark
up
lang
u
a
g
e
as well as co
v
e
ring
fu
zzy co
n
c
ep
ts in
Petri n
e
ts, in
th
e th
ird
a case stud
y will b
e
d
one and
co
n
c
l
u
sion
and fu
tu
re work
s
will b
e
p
r
esen
t
e
d
in th
e last
part.
2.
RELA
TE
D WORK
Fu
zzy set th
eor
y
, pr
opo
sed
by Zad
e
h
in
196
5, is no
t to
rep
r
esen
t non
d
e
term
in
istic s
itu
atio
n
of
unce
r
t
a
i
n
t
y
s
u
ch as
ra
nd
om
ness o
r
st
ocha
st
i
c
pr
ocess
,
b
u
t
rath
er to represen
t
d
e
term
in
istic u
n
c
ertain
ty b
y
a
class or classe
s which do
not
possess
s
h
arpl
y de
fi
n
e
d
b
ound
ar
ies
[6
]. In cr
isp
set, th
e char
acter
istic fu
nctio
n
assign a val
u
e of either
1or 0
to each indi
vidual in th
e uni
versal set, there
b
y discrim
i
nating
betwee
n m
e
m
b
ers
an
d
no
n-
m
e
mb
er
s
of
th
e cr
isp
set und
er c
onsi
d
erat
i
o
n.
The c
once
p
t
o
f
fuzzy set howeve
r
allows
a give
n
ele
m
en
t to
h
a
ve its
m
e
m
b
ersh
ip
fun
c
tion
between
n
on-
m
e
mb
e
r
s
h
ip
a
n
d
f
u
l
l
-
me
mb
e
r
s
h
ip in a
given
class or
fu
zzy set. In
d
e
termin
istic u
n
c
ertain
ty o
f
fu
zzy set,
on
e m
a
y
su
bj
ectiv
ely
d
e
ter
m
in
e m
e
m
b
ershi
p
function of a
gi
ve
n el
em
ent
by
hi
s
k
n
o
w
l
e
dge
. I
n
ot
he
r
w
o
r
d
s,
k
n
o
wl
e
d
ge
pl
ay
s i
m
port
a
nt
r
o
l
e
s i
n
de
t
e
rm
i
n
i
ng
or
d
e
fi
n
i
ng
a fu
zzy set. Si
m
i
larly, so
m
e
b
a
sic co
n
c
ep
t
s
su
ch
as equality, co
n
t
ain
m
en
t, co
m
p
le
men
t
atio
n
,
un
i
o
n
an
d
in
tersection
are red
e
fi
n
e
d
.
In ad
d
ition
b
y
fu
zzy con
d
itional p
r
o
b
a
b
ility
relatio
n
as
p
r
op
o
s
ed
i
n
[8
] & [15
]
,
gra
n
ul
ari
t
y
of
kn
o
w
l
e
d
g
e i
s
g
i
ven i
n
t
w
o f
r
a
m
ewor
ks, c
r
i
s
p
gra
nul
a
r
i
t
y
and f
u
zzy
gra
n
ul
ari
t
y
. Pet
r
i
net
s
are a
gra
p
hi
cal
an
d
m
a
t
h
em
at
i
cal m
odel
i
ng t
o
o
l
appl
i
cabl
e
t
o
m
a
ny system
s. They
are a p
r
om
i
s
i
ng
t
ool
f
o
r
descri
bi
n
g
an
d st
udy
i
n
g i
n
fo
rm
ati
on p
r
o
cessi
ng sy
st
e
m
s t
h
at
are
charact
e
r
i
zed as bei
ng c
o
n
c
ur
rent
,
asy
n
ch
ro
n
o
u
s
,
di
st
ri
b
u
t
e
d,
par
a
l
l
e
l
,
non
det
e
r
m
i
n
i
s
t
i
c
, and/
o
r
st
ocha
st
i
c
. A
s
a gra
phi
cal
t
ool
,
pet
r
i
net
s
can be
u
s
ed
as a v
i
su
al-co
m
m
u
n
i
cati
o
n
aid
sim
ilar t
o
flow ch
arts,
b
l
o
c
k
d
i
agrams, an
d
n
e
two
r
ks. In
ad
d
ition
,
to
k
e
n
s
are u
s
ed
in
th
ese n
e
ts to
si
m
u
late th
e d
y
n
a
mic an
d
con
c
u
rren
t
activ
ities o
f
syste
m
s [9
]. Petri Net (PN) (also
known as a
place/transition
net or P/T net
)
is one
of sev
e
ral m
a
th
e
m
a
tical
m
o
d
e
lin
g lan
g
u
a
g
e
s fo
r th
e
descri
pt
i
on
of
Di
scret
e
Ev
ent
Sy
st
em
s (DES
). P
N
s we
re e
m
erged i
n
1
9
6
2
f
r
om
t
h
e Ph
D t
h
esi
s
o
f
C
a
r
l
Adam
Pet
r
i
and
pr
o
v
e
d t
o
be
qui
t
e
effect
i
v
e t
o
ol
f
o
r
gra
phi
cal
m
odel
i
n
g, m
a
t
h
em
at
i
cal
m
odel
i
ng
, si
m
u
l
a
ti
on,
and
real ti
m
e
control by the use
of
pl
aces and
transitions. Howeve
r, there
was an i
n
tuitive nee
d
for a syste
m
,
wh
ich
wou
l
d
be ab
le t
o
ad
dress un
certain
ties and
im
p
r
ecision
of the
real
world system
s,
beca
use
of inc
r
ease
i
n
t
h
e com
p
l
e
xi
t
y
of i
n
d
u
st
ri
al
and c
o
m
m
uni
cat
i
on sy
st
em
s. Fuzzy
l
ogi
c p
r
ove
d t
o
be a
n
a
p
p
r
op
ri
at
e
com
p
le
m
e
nt because
of its possiblistic
nature to ha
ndle vague
data.
Up
till
the date, num
b
ers of
way
s
have
been
pr
o
p
o
s
ed
fo
r om
bi
ni
n
g
P
N
wi
t
h
fuzzy
l
ogi
c, acc
o
r
di
n
g
t
o
di
ffe
rent
a
ppl
i
cat
i
o
ns. B
u
t
wi
t
h
t
h
e i
n
cre
a
si
ng
ap
p
lication
s
of th
ese n
e
ts, there is an
in
crease in
th
e a
m
b
i
g
u
ity ab
ou
t their typ
e
s an
d
stru
ctures.
Almo
st in
every
ne
w re
s
earch
on
Fuzz
y
Pet
r
i
Net
s
(F
PN)
,
resea
r
c
h
e
r
s cl
aim
t
o
have com
e
up wi
t
h
ne
w t
y
pe of
FPN.
There
f
ore, for
the ease of
fut
u
re
res
earche
r
s
and enginee
r
s, it was essentia
l to categorize
FPN
on the
ba
sis of
som
e
criteria. Owi
ng t
o
this
fact, in c
u
rrent
researc
h
FPN are classified accordin
g to
their structure
s
, and
alg
o
rith
m
s
. Fu
rth
e
r, literatu
re rev
i
ew
o
f
th
e app
licatio
ns o
f
FPN h
a
s b
een
don
e in
th
e lig
h
t
of th
eir
cl
assi
fi
cat
i
ons.
As
P
N
ca
n
be
t
i
m
e
d and/
or
c
o
l
o
red
,
si
m
i
l
a
rly
FPN
ca
n al
s
o
be
t
i
m
e
d an
d/
or
col
o
re
d t
o
i
n
cl
u
d
e
th
e te
m
p
o
r
al effect and
/
or enh
a
n
ce t
h
eir v
i
sib
ility. Li
k
e
th
at o
f
Neu
r
al
Netwo
r
k
s
(NN), FPN can
also
do
l
earni
n
g
, a
n
d
can be
t
r
ai
ne
d
i
n
o
r
de
r t
o
ge
t
adapt
t
o
t
h
e
chan
gi
n
g
si
t
u
a
t
i
ons.
A
nd a
s
Fuzzy
l
o
gi
c i
s
bei
n
g
co
m
b
in
ed
with PN t
o
g
e
t FPN, i
n
th
e sam
e
way FPN
can
b
e
co
m
b
in
e wi
th
o
t
h
e
r
Artificial In
tellig
en
ce (AI)
t
ool
s, a
nd m
a
them
ati
cal
m
odel
s
t
o
b
ecom
e
m
o
re efficient, and powerful.
In
[
1
4]
on t
h
e
basi
s o
f
st
ruct
u
r
es an
d
algorithm
s
FPNs
have
bee
n
classified as;
Basic Fuzzy
Petri Nets
(BFPN), Fu
zzy
Timed
Pet
r
i Nets
(FTPN),
Fu
zzy Co
lored Petri Nets (FCPN), Ad
ap
tiv
e Fu
zzy Pe
tri Nets (AFPN), and
Co
m
p
o
s
ite Fu
zzy Petri Nets
(C
FP
N)
[1
0]
&[
11]
. M
a
p
p
i
n
g
bet
w
ee
n IF
-T
HEN
rul
e
s a
n
d
fuzzy
Pet
r
i
ne
t
s
i
s
obvi
o
u
s
.
Any
I
F
-T
HE
N
rul
e
o
f
t
h
e p
r
e
v
i
o
us
de
fi
ne
d f
o
rm
:
I
F
X
1
is
A
1
AN
D …
AN
D Xn
is
A
n
TH
EN
Y
is B
can
b
e
ex
pressed
b
y
th
e fo
llowing
p
e
tri n
e
t[7
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ma
ppi
ng
Fu
zz
y Pet
r
i
N
e
t
t
o
Fuzzy
Ext
e
n
d
e
d
M
a
rk
up
L
a
n
g
u
a
g
e (
Z
ahr
a
Mas
o
u
d
i
n
e
z
a
d
)
69
8
Fi
gu
re
1.
Si
m
p
l
e
pet
r
i
net
Th
e Petr
i
N
e
t Mar
k
u
p
Languag
e
(PN
M
L)
is an
X
M
L-b
a
sed
in
ter
c
h
a
n
g
e
f
o
r
m
at f
o
r
Petr
i n
e
ts.
In
o
r
d
e
r t
o
su
pport d
i
fferen
t v
e
rsio
n
s
of
Petri
n
e
ts, its fo
cu
s i
s
on
un
iv
ersality an
d
flex
ib
ility, w
h
ich
is ach
i
ev
ed
by
a t
ech
ni
q
u
e
fo
r
defi
ni
n
g
n
e
w Pet
r
i
net
t
y
pes. F
o
r
pres
ent
i
n
g
an
d
p
r
e
c
i
s
el
y
defi
ni
n
g
t
h
e
XM
L-s
y
nt
ax,
PNM
L
uses U
M
L
m
e
t
a
m
odel
s
:
The PNM
L
C
o
re M
o
d
e
l
defi
nes t
h
e concept
s
sha
r
ed
by
all
ki
nds
of Pet
r
i
n
e
ts; ad
d
itional Petri n
e
t ty
p
e
d
e
fin
itio
ns are UML m
e
t
a
m
o
d
e
ls for d
e
fi
n
i
ng
th
e co
n
c
ep
ts th
at are
speci
fi
c t
o
par
t
i
c
ul
ar ki
nd
s
of
Pet
r
i
net
s
. T
h
e co
ncret
e
XM
L-sy
nt
a
x
i
s
t
h
e
n
defi
ned
by
m
a
ppi
ng
t
h
e
co
n
cept
s
of these
UML
meta
m
odels to XML elem
ents.
Currently, PNML is standa
rdized as
P
a
r
t
2
o
f
t
h
e
I
n
t
e
r
n
a
t
i
o
n
a
l
S
t
a
n
d
a
r
d
I
S
O
/
I
E
C
1
5
9
0
9
a
s
t
h
e
transfer sy
ntax for three pa
rticular
versi
o
ns
of
Petr
i nets:
Place/Transition-Nets,
High-l
evel Petri Nets, and
Sym
m
et
ri
c Net
s
[
12]
& [
1
3]
.
To s
u
p
p
o
r
t
of
t
h
i
s
ve
rsi
o
n
i
n
t
h
i
s
pa
per
wi
l
l
be
p
r
esent
e
d
a m
a
rkup
l
a
n
g
u
age
.
F
X
M
L
havi
ng
t
a
gs
(lab
els) t
o
su
pp
ort th
e fu
zzy
co
n
c
ep
ts en
ab
le u
s
to s
upp
ort
th
e
fu
zzy fo
rmal
m
o
d
e
l. In
th
is p
a
p
e
r in ad
d
iti
on
to
sup
p
o
r
t of th
e fu
zzy con
c
ep
ts in
Petri Nets, to
ex
press
th
e stru
ct
u
r
e an
d
g
r
amm
a
r in
m
a
rk
up
lan
guag
e
, in
ot
he
r
wo
rd
s ca
n
be s
u
pp
ort
t
h
e el
em
en
ts of Fu
zzy Petri
Nets with
FXML.
3.
THE PROPOSED GRAMMAR
Gramm
a
r p
r
opo
sal th
at will
b
e
d
i
scu
ssed
i
n
th
is
p
a
p
e
r called
FPNML
(Fuzzy Petri
Net Markup
Lan
gua
ge)
w
h
i
c
h i
s
a
ne
w sy
n
t
ax ba
sed
o
n
F
X
M
L
f
o
r
descr
i
bi
ng
pet
r
i
net
s
.
Tag
s
and
lab
e
l
s
in
t
h
is lang
u
a
g
e
an
d th
eir child
are listed b
e
lo
w:
<net>:
Petri
Nets
A Pet
r
i n
e
t is
defin
e
d
with
th
e ele
m
en
t <n
et>. Th
is elem
en
t h
a
s t
h
e fo
llowin
g
attribu
t
es:
a)
id:
U
n
i
que
i
d
e
n
t
i
f
i
e
r .al
l
ows
t
h
e
net
t
o
be
r
e
fere
nced
f
r
om
ot
he
r
net
s
.
b)
typ
e
: Th
e Petri
n
e
t typ
e
:
The net's places, transitions,
arcs an
d subne
t
s are childre
n of the <net>
ele
m
ent; and it
m
a
y furthe
r c
ontain
th
e fo
llowing
ele
m
en
ts:
c)
graphics:
Th
is ele
m
en
t is op
tio
n
a
l; it is u
s
ed
if
an
ov
erv
i
ew
p
a
g
e
ex
ists
with
an
item
fo
r
all n
e
ts in the
d
o
c
u
m
en
t. It sp
ecifies the
p
o
sitio
n
an
d op
tio
n
a
lly th
e
size
o
f
th
e item
wit
h
in
t
h
e
o
v
e
rv
iew.
d)
name
:
Opti
onal, The
elem
e
n
t <nam
e> contains t
h
e name
o
f
th
e elem
en
t.
A
n
a
m
e
is
o
p
tion
a
l an
d no
t
n
ecessarily u
n
iq
u
e
.
It h
a
s
no
attribu
t
es and
th
e nam
e
is in
serted
i
n
the ele
m
en
t <te
x
t>. Op
tion
a
lly,
gra
p
hi
cal
i
n
f
o
r
m
at
i
on can
be
adde
d
wi
t
h
<
g
r
a
phi
cs>
.
e)
description
: Op
tio
n
a
l.
Th
e el
e
m
en
t <d
escri
p
tio
n
>
con
t
ains th
e d
e
scrip
tio
n
o
f
an
elemen
t. It is op
tion
a
l
and
not neces
sarily unique.
This elem
ent
doe
sn'
t
have
a
ttributes and t
h
e val
u
e of the descri
ption i
s
in
serted in
to th
e elem
en
t <t
ex
t>.
Op
tion
a
l
l
y, g
r
a
phi
cal
i
n
f
o
rm
at
i
on ca
n
be
adde
d
with the elem
ent
<gra
phics>.
f)
D
:{d1
,d
2,…,dn
}
was a fin
ite
set o
f
pro
p
o
s
itio
n
s
.
…………
……
…………
……
…………
……
1.
<place>
: places
A
place is
defi
ned with the ele
m
ent <p
la
ce>. T
h
is element ha
s the
followi
ng attributes:
a)
id:
Unique ide
n
tifier; allows
the place to
be
refe
renc
e
d
.
Such re
fere
nces a
r
e m
a
de in <re
f
ere
n
cePlace>
s
and <arc>s
.
A
<place> m
a
y furt
her c
o
ntain t
h
e
following el
e
m
ents:
b)
graphics
: Op
ti
o
n
a
l;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 3
,
N
o
. 5
,
O
c
tob
e
r
20
13
:
696
–
7
01
6
99
c)
name
:
Op
tio
nal; Th
e elem
e
n
t <n
am
e> con
t
ain
s
the n
a
m
e
o
f
th
e elem
e
n
t.
A n
a
m
e
is o
p
tion
a
l an
d no
t
n
ecessarily u
n
i
q
u
e
–
it is leg
a
l fo
r t
w
o
d
i
fferen
t elem
en
ts to
carry th
e sam
e
n
a
m
e
. It h
a
s no
attribu
t
es and
th
e n
a
m
e
is
i
n
serted
in
th
e ele
m
en
t <tex
t>. Op
tion
a
lly, g
r
aph
i
cal in
fo
rm
atio
n
can
b
e
add
e
d
with
<gra
phics>.
d)
description
: Op
tio
n
a
l; Th
e el
e
m
en
t <d
escri
p
tio
n
>
con
t
ains th
e
d
e
scri
p
tio
n of an
elemen
t. It is
op
tion
a
l
and
not neces
sarily unique.
This elem
ent
doe
sn'
t
have
a
ttributes and t
h
e val
u
e of the descri
ption i
s
in
serted
i
n
to
t
h
e elem
en
t <t
ex
t>. Op
tion
a
lly, g
r
ap
h
i
cal in
fo
rm
atio
n
can
b
e
add
e
d
with
th
e elem
e
n
t
<gra
phics>.
e)
initia
lMa
r
king
: Op
tion
a
l. Th
e <in
itialMark
i
ng
> elem
en
t
p
r
ov
id
es t
h
e
in
itial
m
a
rk
in
g o
f
a p
l
ace. It
s
require
d
s
ub el
e
m
ent <text> specifies the
va
lue; fo
r un
co
lored
n
e
ts, it is a n
onn
eg
ativ
e
deci
m
a
l n
u
m
b
e
r.
This elem
ent
may have a sub elem
ent <graphics> to
s
p
eci
fy
a rel
a
t
i
v
e po
si
t
i
on f
o
r di
s
p
l
a
y
i
ng t
h
e co
nt
e
n
t
in a
diagram
.
f)
typ
e
:
a place can
either be a
store or
a
c
h
annel. A
c
h
a
n
nel is a re
gula
r
Petri net
pla
ce, while a store
serve
s
as a data storage c
o
mpone
n
t. Optional; a place
is a
ssum
e
d to be
a channel. The
ele
m
ent <
t
ext>,
whi
c
h i
s
req
u
i
r
ed
fo
r <t
y
p
e>,
hol
ds t
h
e t
y
pe i
n
f
o
rm
at
i
on.
g)
α
:
P
[0,1] wa
s an association
fu
nction, a
mappi
ng from
places to
r
eal values betwee
n
ze
ro
and one.
h)
β
:
P
→
D was a
n
association function, a
obj
e
c
tive m
a
pping
from
places to
propositions.
…………
……
…………
……
…………
……
……
<transition>:
Transitio
n
s
A tran
sitio
n is
d
e
fi
n
e
d b
y
t
h
e
ele
m
en
t <tran
s
itio
n
>
. Th
is elemen
t h
a
s t
h
e
follo
wing
attributes:
a)
id
: Un
i
q
u
e
id
en
tifier, allows
th
e tran
sitio
n
t
o
b
e
re
fere
nce
d
.
Suc
h
refe
re
nces a
r
e m
a
de in <arc>
s
a
n
d
<refe
r
ence
Place>s. A <tra
nsition> m
a
y fu
rt
her c
ontain the
followi
ng elements:
b)
graphics
:
c)
description
:Op
tio
n
a
l.
d)
tra
n
sf
orm
a
ti
o
n
: The <trans
form
ation> element specifies
th
e t
o
ke
n val
u
e t
r
a
n
sf
o
r
m
a
ti
on
per
f
o
rm
ed by
th
e tran
sitio
n.
Th
is elem
en
t is op
tion
a
l. The transfo
r
m
a
ti
o
n
is th
e co
n
t
en
t
o
f
t
h
e
requ
ired
sub
elemen
t
<tex
t>. Op
tionally, in
form
ati
o
n abou
t relativ
e
p
o
siti
oni
n
g
can
be a
dde
d
wi
t
h
t
h
e
el
em
ent
<g
ra
phi
cs>.
e)
CF (µ)
:
CF
wa
s the “Ce
r
tainty Factor”; a
larger CF
va
lue i
ndicated a
higher certai
n
ty of the
rule.
…………
……
…………
……
…………
……
……
<arc>:
Ar
cs
An arc is d
e
fined
b
y
th
e elem
en
t <arc>. Th
is ele
m
en
t h
a
s t
h
e fo
llo
wi
n
g
attribu
t
es:
a)
id:
Unique ide
n
tifier, allows the arcs t
o
be refere
nced
. the
id of a <tra
nsit
ion>,
<
p
lace>
within the sa
me
<net> or <
p
a
g
e
>
as the
<arc>
itself.
b)
Source
:
{X
1
,
X
2
,…,
X
n
}
wa
s a i
nde
pe
nde
nt
va
ri
abl
e
s
an
d {P
1
,
P
2
,…,
P
n
} was a input places.
c)
tar
g
et
: {
Y
1 ,
Y2 ,…
, Yn}
was a de
pe
nde
nt
varia
b
les and
{
P
1
, P2 ,…, Pn} was a
output
places An <a
rc
>
may furthe
r c
o
ntain the
following elem
ents:
d)
graphics:
For an
<arc>, th
is
ele
m
en
t can
o
ccu
r
0
,
1, or m
u
ltip
le ti
mes;
it
sp
ecifies in
termed
iate su
p
port
poi
nt
s fo
r l
a
y
o
u
t
pu
r
poses
. It
i
s
up t
o
t
h
e d
r
a
w
i
n
g t
ool
to
interp
ret th
e v
a
l
u
es. Start an
d
end
po
in
ts are not
speci
fi
ed;
t
h
e l
a
y
out
al
g
o
r
i
t
h
m
s
m
u
st
be de
duci
n
g
t
h
em
fr
om
source
an
d
t
a
rget
.
e)
name
: Op
tio
nal; Th
e ele
m
e
n
t <n
am
e> co
n
t
ain
s
th
e n
a
me o
f
th
e ele
m
e
n
t. A n
a
m
e
is
o
p
tion
a
l and
not
n
ecessarily u
n
i
q
u
e
–
it is leg
a
l fo
r t
w
o
d
i
fferen
t elem
en
ts to
carry th
e sam
e
n
a
m
e
. It h
a
s no
attribu
t
es and
th
e n
a
m
e
is
i
n
serted
in
th
e ele
m
en
t <tex
t>. Op
tion
a
lly, g
r
aph
i
cal in
fo
rm
atio
n
can
b
e
add
e
d
with
<gra
phics>.
f)
description
:Op
tio
n
a
l; Th
e el
e
m
en
t <d
escrip
tio
n
>
co
n
t
ains th
e d
e
scrip
tion
o
f
an
ele
m
en
t. It is
o
p
tio
nal
and
not neces
sarily unique.
This elem
ent
doe
sn'
t
have
a
ttributes and t
h
e val
u
e of the descri
ption i
s
in
serted in
to th
e elem
en
t <t
ex
t>.
Op
tion
a
l
l
y, g
r
a
phi
cal
i
n
f
o
rm
at
i
on ca
n
be
adde
d
with the elem
ent
<gra
phics>.
g)
inscriptio
n
:
Op
tio
n
a
l; its v
a
lu
e m
u
st b
e
in
th
e sub
elem
e
n
t <tex
t>. A su
b
elem
en
t <g
raph
ics> m
a
y
b
e
adde
d wi
t
h
rel
a
t
i
v
e
p
o
si
t
i
oni
ng
f
o
r
l
a
y
out
p
u
r
p
oses.
…………
……
…………
……
…………
……
…….
<IF>: if
… th
en
a)
THEN:
the el
e
m
ent <THEN> contains the
main part of
<IF>. Th
is ele
m
en
t d
o
e
sn
't h
a
ve attrib
u
t
es and
th
e v
a
l
u
e
o
f
the d
e
scrip
tion
is in
serted
in
t
o
t
h
e elem
en
t <tex
t>.
…………
……
…………
……
…………
……
<THE
N>
Newi
nitial
m
ar
king.place ID:
this elem
en
t is new initial
m
arking a
f
ter
firing.
New
α
.place
ID: this elem
ent is ne
w
α
a
f
ter
firin
g
.
…………
……
…………
……
…………
……
Sub nets
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ma
ppi
ng
Fu
zz
y Pet
r
i
N
e
t
t
o
Fuzzy
Ext
e
n
d
e
d
M
a
rk
up
L
a
n
g
u
a
g
e (
Z
ahr
a
Mas
o
u
d
i
n
e
z
a
d
)
70
0
N
e
ts
can
con
t
ain
subn
ets.
D
i
ff
er
en
t
v
a
r
i
an
ts of
Petr
i
n
e
ts suppo
r
t
d
i
ff
er
en
t no
tio
ns o
f
subnets;
o
n
e
diffe
re
nce
between them
is how the
subnet
can
be c
o
nnect
ed
with its e
nvi
ronm
ent.
1)
<page>:
Su
bnet d
e
fi
ni
t
i
ons
It
h
a
s th
e fo
llo
wi
n
g
attribu
t
es:
a)
id:
Un
i
q
u
e
id
en
tifier, all
o
ws th
e sub
n
e
t t
o
b
e
referen
ced.
A <
p
a
g
e>
may furthe
r c
o
ntain the
following elem
ents:
b)
description
: Op
tio
n
a
l; Th
e el
e
m
en
t <d
escri
p
tio
n
>
con
t
ains th
e
d
e
scri
p
tio
n of an
elemen
t. It is
op
tion
a
l
and
not neces
sarily unique.
This elem
ent
doe
sn'
t
have
a
ttributes and t
h
e val
u
e of the descri
ption i
s
in
serted in
t
o
t
h
e elem
en
t <tex
t>.Op
tion
a
lly, grap
hical i
n
form
ation ca
n
be a
d
ded
with the elem
ent
<gra
phics>.
c)
THEN
: Requ
ired
; th
is elem
en
t h
a
v
e
on
e attri
b
u
t
e and
th
is is
β
.
d)
New
α
:
th
is elemen
t is n
e
w
α
after firi
n
g
an
d it is ca
lcu
l
ate
fo
llows:
α
.p
sour
ce
*
CF(µ). its valu
e m
u
st b
e
i
n
the s
u
b elem
en
t <text>.
…………
……
…………
……
…………
……
……
2.
Com
m
on ele
ments
:
1)) <
g
raphics
>:
Gra
phi
cs
Th
e <g
raph
ics> ele
m
en
t is op
tio
n
a
l.
It
can
ha
ve t
h
e
fol
l
o
wi
n
g
s
u
b
el
em
ent
s
:
<pos
i
t
i
on> an
d <
d
i
m
ensi
on>
.
These elem
ents, whe
n
t
h
ey occur,
h
a
v
e
two
requ
ired
attribu
t
es:
x T
h
e
x c
o
or
di
nat
e
o
f
t
h
e el
e
m
ent
.
y The y c
o
ordinate of t
h
e ele
m
ent.
They
do
n
o
t
ha
ve a
n
y
f
u
rt
her
cont
e
n
t
.
C
o
o
r
di
nat
e
v
a
l
u
es
de
not
e
n
u
m
bers of
scree
n
pi
xel
s
.
Sizes are ab
so
l
u
te, i.e. relative to
th
e in
cl
u
d
i
n
g
<n
et>.
Po
sition
s
are al
ways relativ
e t
o
th
e po
sition
o
f
th
e
n
earest co
n
t
ain
i
n
g
elemen
t.
The
x c
o
ordi
na
te increases t
o
the right; the y
coordina
te in
creases
d
o
wn
ward
; th
e orig
in is th
e co
n
t
ain
i
ng
el
em
ent'
s up
pe
r l
e
ft
han
d
c
o
rn
er.
The <position> sub elem
ent
is used for <
p
lace>s, <tra
nsition>s, and
<page>
s. It is require
d
. It is not
u
s
ed
an
ywh
e
r
e
e
l
s
e
.
The <
o
ffset> s
u
b elem
ent is use
d
for
nod
e
attrib
u
t
es th
at
may b
e
d
i
sp
lay
e
d
in th
e
d
i
agra
m
,
It is op
tional;
wh
en
u
s
ed
, it is relativ
e t
o
th
e ob
j
ect t
o
wh
ich
it refers.
The <
d
im
ension> elem
ent is
use
d
to
d
e
no
te
th
e size of an ele
m
en
t with
in
its containi
ng ele
m
ent, eve
n
for
<page>
s a
n
d <
n
et>s.
…………
……
…………
……
…………
……
……
<name>
:
Nam
e
The elem
ent <nam
e> contains the
nam
e
o
f
th
e elem
en
t. A n
a
m
e
is o
p
tion
a
l and
no
t n
e
cessarily un
ique it is
leg
a
l for two
differen
t
elem
e
n
ts to
carry the sam
e
n
a
m
e
.
It h
a
s
n
o
attri
b
u
t
es and
th
e
na
m
e
is in
serted
in
th
e
ele
m
en
t <tex
t>. Op
tion
a
lly, grap
h
i
cal i
n
fo
rm
at
i
on ca
n
be a
d
ded
wi
t
h
<g
ra
p
h
i
c
s>.
…………
……
…………
……
…………
……
……
<description>
:
Descri
p
tio
n
The el
em
ent
<descri
p
t
i
on>
c
ont
ai
n
s
t
h
e
des
c
ri
pt
i
o
n o
f
a
n
el
em
ent
.
It
i
s
opt
i
o
nal
a
nd
n
o
t
necessa
ri
l
y
uni
que
.
Thi
s
el
em
ent
doe
sn'
t
have a
t
t
r
i
but
es a
nd t
h
e val
u
e
of
t
h
e d
e
scri
p
tion
is in
serted
in
to th
e elem
en
t
<tex
t>.
Opt
i
o
nal
l
y
, g
r
a
phi
cal
i
n
f
o
rm
ati
on ca
n
be
added
with
th
e elemen
t <g
raph
ics>.
…………
……
…………
……
…………
……
……
<
id>:
Id
en
ti
fi
ers a
n
d
re
fere
nc
es
Every <
n
et>,
<page>
, <tra
nsition>, <
p
lace
> and <a
rc>
m
u
st have a
n
id attribute; T
h
e s
o
urce a
nd target
attrib
u
t
es
o
f
<arc>s IDREF
attrib
u
t
es: th
ei
r v
a
l
u
es m
u
st o
c
cu
r as th
e v
a
lu
e of so
me id
attribu
t
e
in
th
e
doc
um
ent
.
4.
CASE ST
UDY
In th
is
p
a
p
e
r, a p
e
tri
n
e
t is
b
e
i
n
g stud
ied in
wh
ich
d
e
si
g
n
ru
les fo
r system
b
a
n
k
facilities usin
g fu
zzy
scenari
o
.
To
de
scri
be t
h
i
s
net
w
o
r
k
,
use
d
t
h
e
pr
o
pose
d
g
r
am
m
a
r i
n
t
h
e
p
r
e
v
i
ous
sect
i
o
n
an
d al
l
t
h
e
com
pone
nt
of
t
h
e net
w
or
k and
f
u
zzy
beha
vi
o
r
i
s
e
x
p
r
ess
e
d usi
n
g FPN
M
L
l
a
ng
ua
ge.
Fig
u
re
2
:
Fu
zzy Petri n
e
t syst
e
m
o
f
b
a
n
k
facilit
ies
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 3
,
N
o
. 5
,
O
c
tob
e
r
20
13
:
696
–
7
01
7
01
Fuzzy
rul
e
s
de
scri
bi
n
g
t
h
e
pe
t
r
i
net
i
n
fi
gu
re
2:
•
I
f
p1
an
d p2
•
I
f
p4
and
p5
t
h
en p6
•
I
f
p2
th
en
p3
•
I
f
p3
an
d p6
t
h
en
p
7
•
I
f
p2
an
d p6
t
h
en
p
9
•
I
f
p9
th
en
p1
0
•
If
p
7
a
n
d
p1
0 t
h
en
p
8
In this
figure, a
ll the places a
s
the elem
ent <place> and their
properties
by s
u
b elem
ent using
pr
o
pose
d
t
a
gs i
n
F
P
NM
L
l
a
n
g
u
age
.
T
r
an
si
t
i
ons a
n
d A
r
cs
an
d t
h
ei
r
pr
ope
rt
i
e
s are e
x
pres
se
d as
wel
l
as
pl
a
ces
usi
n
g t
a
gs <t
ra
nsi
t
i
on>
an
d <
a
rc>.
Fuzzy
rul
e
s t
h
at
are
d
e
fi
ned
i
n
fi
g
u
re
2
,
are
desc
ri
be
d
usi
n
g t
a
gs <
I
F
>
an
d
<THE
N>.
5.
CON
C
LUS
I
ON
What
i
s
hi
g
h
l
i
ght
e
d
i
n
t
h
i
s
pape
r i
s
p
r
ese
n
t
e
d a m
a
rku
p
l
a
n
gua
ge t
o
su
pp
ort
t
h
e
f
u
zzy
f
o
rm
al
m
o
d
e
l.A
lth
ou
gh
so
far is done activ
ities o
n
X
M
L tag
s
an
d also
in
j
ection
u
n
c
ertain
ty in
fu
zzy p
e
t
r
i n
e
t
,
bu
t
m
a
ppi
n
g
a
f
u
z
z
y
fo
rm
al
m
odel
t
o
f
u
zzy
m
a
rku
p
l
a
ng
ua
ge i
s
i
n
no
vat
i
o
ns t
h
at
di
sc
usse
d i
n
t
h
i
s
pa
per
.
REFERE
NC
ES
[1]
Fellow T
.
Petri Nets:
Properties,
Analysis and
Applica
tion
”.
P
r
oceed
ing of
the
I
EEE
.
1989; 77(4
)
.
[2]
Intan R, Mukaidono M and Emoto M. Knowle
dge-based
R
e
prisentation of
Fuzzy
sets.
I
EEE In
ternaton
al
conferen
ce on 2
002
. 2002; 1: 59
0-595.
[3]
Intan R, Mukaidono M.
Conditional
Probabilit
y Relations
in Fuzzy Rela
ti
onal Database
.
P
r
oceedings
o
f
RSCTC’00, Springer. 2000
: 251-
260.
[4]
Intan R, Mukaidono M, Yao
YY.
Generalization of Rough Sets with
α
- cov
e
r
i
ngs
of the Univer
s
e
Induced
b
y
Conditional
Pro
babilit
y
Rela
tion
s
. Proceedings o
f
Intern
ation
a
l
Workshop
on Rough Sets and
G
r
anular
Computing,
LNAI- 2253, Sp
ringer-Verlag,
y
.
2001: 311-315
.
[5]
Tsuji K. A New T
y
p
e
of Ext
e
nde
d Petri Nets and
its Applica
tions.
International symposium on circuits and systems
.
2000; 1: 192-19
5.
[6]
Chen SM. Weighted Fuzzy
R
e
asoning
Us
ing
Weight
ed F
u
zz
y
P
e
tri Nets
.
IEEE
Transaction on knowledge an
d
data eng
i
neering
. 2002: 14.
[7]
Pavliska V. Pet
r
i nets
as fuzzy modeling tool.
Submitted/
to appear: Internal public
at
ion Uni
versity of Ostrava
Institute for
Res
e
arch and
App
l
i
c
ations o
f
Fuzzy
Modeling
. 2006
.
[8]
Aziz MH, Er
ik
LJ Bohez, Manu
kid P and Chan
chal S.
Classifi
c
a
tion of Fuz
z
y
Petri
Nets, and
Their Applicatio
ns.
World Acad
emy
of Science,
Eng
i
neering and
Technology.
2010.
[9]
Kindler E.
Con
c
epts, sta
t
us, and
future d
i
rection
s
Paper for th
e
invited
talk at
EKA 2006
. In E.
Schnieder
(ed
.
):
Entwurf Komplexer Automatisier
ungs
s
y
steme, EKA 2006, 9. Fachtagung, Br
auns
chweig, German
y
.
2006, pp. 35-
55.
[10]
KonarA, Mandal AK. Uncertain
ty
management in expert s
y
st
em using fuzzy
p
e
tr
i nets.
Transaction on Knowledge
and Data Eng
i
n
eering, IEEE
. 19
96: 96-105.
[11]
Paul B, Konar
A, Mandal AK.
Estmation of certanty fa
ctor o
f
knowledg
e wit
h
fuzzy petri ne
ts.
Intern
ation
a
l
Conferenc
e
on
Fuzz
y
S
y
stem
s Proceed
ing, IEE
E
.
1998: 951-955.
[12]
Cardoso J, Prad
in-chezalviel B.
Logic
and fuzzy petri
n
e
ts.homep
ages.iaas
.fr/ Rob
e
rt/works
hop.d/janete.ps.gz.
199
6.
[13]
Chaoui A, Hadjadj I.
PNTools: a
multi-language environment
to In
tegrate petri
net
s
tools.
2009
.
[14]
http://www
.bibs
onomy.org/
bibtexkey/con
f
/ciia
/2
009.
[15]
www.esoa.ir
,
Iran
,
s Information
Artichecture co
mmittee,
[onlin
e]
2010.
Evaluation Warning : The document was created with Spire.PDF for Python.