TELKOM
NIKA
, Vol.11, No
.3, Septembe
r 2013, pp. 6
11~616
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v11i3.1271
611
Re
cei
v
ed Ap
ril 25, 2013; Revi
sed
Jul
y
4, 2013; Accept
ed Jul
y
18, 2
013
Balanced the Trade-offs Problem of ANFIS using
Particle Swarm Optimization
Dian Palupi Rini
1
, Siti Ma
riy
a
m Shamsuddin
2
, Siti
Sophia
y
ati Yuhaniz
2
1
F
a
cult
y
of Co
mputer Scie
nc
e, Sri
w
i
j
a
y
a
Un
iversit
y
, In
don
e
s
ia
2
Soft Computin
g Rese
arch Group UT
M, Skudai Jo
hor b
ahr
u Mala
ys
ia
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: dian
_rin
i@u
n
s
ri.ac.id, {mari
y
am, sophi
a}@u
tm.my
Abs
t
rak
Peni
ngkat
an n
ilai
perkir
aan
akuras
i da
n i
n
terpreta
bil
i
tas
pada s
ebu
ah
sistem sa
ma
r adal
ah
perso
ala
n
pe
n
t
ing ba
ik pa
d
a
teori siste
m
samar at
aup
un pa
da a
p
lik
asiny
a
. T
e
lah
diketah
u
i b
a
h
w
a
opti
m
is
asi sec
a
ra si
l
m
ulta
n
p
ada k
e
d
ua
per
soal
an ters
eb
u
t
adal
ah
sal
i
ng
sei
m
b
a
n
g
, na
mu
n h
a
l
ini
ak
a
n
m
e
ningkatkan pencapaian
syst
em
dan m
e
nghindari
pelatihan
berleb
ihan. Partic
le Sw
arm
Optim
i
s
a
s
i
(PSO)
ada
lah
ba
gia
n
dari
alg
o
ritma evol
usio
ner
y
a
n
g
mer
u
p
a
kan
ca
lon
al
gorit
ma
yang
ba
ik
unt
uk
me
meca
hkan
mas
a
l
ah terse
but dan
me
miliki ru
ang
p
e
n
cari
an gl
oba
l
yang leb
i
h
baik. Tulisa
n
ini
m
e
n
g
e
n
a
l
k
an
se
b
u
a
h
i
n
teg
r
asi
an
ta
ra
PSO
d
a
n
AN
FIS u
n
t
u
k
op
tim
i
sa
si
pe
mb
el
a
j
a
r
a
n
n
y
a
te
ru
tama
pada
peny
esu
a
ia
n n
ilai
par
a
m
eter
fungsi k
epe
mi
lika
n
d
an
mene
ntuka
n
ju
ml
ah at
uran y
ang
opti
m
a
l
u
n
tu
k
me
mper
ole
h
ni
lai kl
asifikas
i y
ang
leb
i
h b
a
ik.
Usula
n
a
l
gor
itma
ini te
la
h dit
e
s pa
da 4(
e
m
p
a
t) dataset sta
nda
r
dari
mesi
n pe
mb
el
ajar
an UC
I, yaitu:
dataset Iris
F
l
ow
er, H
aber
man
’
s Sur
v
ival Data, Bal
l
oon d
an T
h
yro
i
d
.
Hasil
me
nun
ju
kkan bahw
a
ni
l
a
i
kl
asifik
asi
y
a
ng leb
i
h ba
ik p
ada
al
gorit
ma
PSO-ANF
IS yang
dius
ulk
an
d
a
n
kompl
e
ksitas w
a
ktunya
me
nur
un bers
e
su
aia
n
.
Ka
ta
k
unc
i:
ANF
I
S, interpretabil
i
tas, akuras
i, algor
itma evo
l
usio
ner, partic
l
e sw
arm opti
m
i
s
asi
A
b
st
r
a
ct
Improv
in
g the
appr
oxi
m
ati
on
accuracy a
nd i
n
terpreta
bil
i
ty of fu
z
z
y
syste
m
s is a
n
i
m
p
o
r
t
ant issue
either
in fu
z
z
y
system
s theory
or in
its applic
ations
. It is
known that simu
lt
aneous
optimi
z
ation bot
h iss
u
es
was the trade-
offs problem
,
but it
will im
pr
ov
e perfor
m
anc
e of the system
and avoid overtraining of
data.
Particle sw
ar
m opti
m
i
z
at
ion (
PSO) is part o
f
evoluti
o
n
a
ry
alg
o
rith
m that i
s
goo
d ca
ndi
d
a
te al
gorith
m
s
to
solve
mu
ltipl
e
opti
m
a
l
sol
u
tio
n
an
d better g
l
oba
l searc
h
sp
ace. T
h
is p
ape
r introduc
es a
n
integr
ation
of PSO
dan A
N
F
I
S for opti
m
is
e its le
a
r
nin
g
esp
e
ci
all
y
for t
unin
g
me
mb
ershi
p
funct
i
on
para
m
eters
and fi
nd
ing t
h
e
opti
m
a
l
rul
e
for
better cl
assific
a
tion. T
h
e pro
pose
d
me
tho
d
h
a
s
be
en
te
sted
o
n
fo
u
r
stan
da
rd
da
ta
se
t fro
m
UCI mac
h
i
ne l
earn
i
ng i.
e. Iris F
l
ow
er, Haber
ma
n
’
s Su
rv
ival
Data, Ball
oon
and T
h
yro
i
d d
a
taset. T
he resu
lts
have
show
n
b
e
tter class
i
ficat
i
on
usi
ng t
he
prop
osed
PSO
-ANF
IS and
th
e ti
me c
o
mp
le
xity has r
e
d
u
c
ed
accordingly
.
Ke
y
w
ords
: AN
FIS, interpretability, accur
a
cy
, evolutio
nary a
l
gorit
hms, p
a
rti
c
le sw
arm o
p
ti
mi
z
a
t
i
o
n
1.
Introduc
tion
The strength
of neuro
-
fuzzy system
s involves
two
contradi
ctory
requi
rem
ents in fuzzy
modellin
g: interp
retability
and accu
racy. Im
provi
ng the ap
proximatio
n
accura
cy and
interp
retabilit
y of fuzzy system
s is an i
m
porta
nt
issue either in f
u
zzy system
s theory o
r
in its
appli
c
ation
s
[
1
]. An ada
ptive neu
ro
-fuzzy infere
n
c
e
system
(ANF
IS) ba
sed
on
TSK mod
e
l i
s
a
spe
c
ific
app
roach of ne
uro-fuzzy
that has sh
own
significa
nt
re
sult
s
in cla
ssif
i
cat
i
on pro
b
le
m.
The structu
r
e of adaptive neuro-fu
zzy system (ANFIS) is sim
ilar with gen
eral ne
uro
-
fu
zzy
system. It le
a
r
ns featu
r
e
s
i
n
the
data
se
t, and
adju
s
t
s
the
sy
stem
paramete
r
s
according
to
a
given erro
r
criterion [2]. Bu
t in the rul
e
l
a
yer,
it
gives a
num
ber of node
s
that re
pre
s
ent
s
a self
gene
rating
al
l possibl
e fu
zzy rul
e
s i
n
n
euro
-
fu
zzy
st
ructu
r
e. T
he
self ge
ne
rati
ng rule
s give
a
cha
n
ce to produ
ce effecti
v
e or ineffecti
v
e rule
s. So, a simulta
neo
usly tech
niqu
e that gene
ra
tes
the ANFIS that has go
od a
c
cura
cy and
has effe
ctiv
e rule
s is ne
ce
ssary in this
re
sea
r
ch.
Particle
swa
r
m optimizatio
n (PSO) is o
ne of
evolutionary alg
o
rit
h
ms (EA
s
) te
chni
que
s
that is wid
e
ly use
d
and
ra
pidly develop
ed by re
se
arche
r
s, d
ue to
its easy impl
ementation
a
n
d
few pa
rticl
e
s
requi
re
d to b
e
tuned.
Furt
herm
o
re
PSO is
a very
simple
con
c
e
p
t
and p
a
ra
dig
m
s
whi
c
h can b
e
impleme
n
ted in a fe
w lines of
co
mputer
cod
e
.
It require
s only primiti
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 11, No. 3, September 20
13: 61
1 – 616
612
mathemati
c
al
operators, and is
co
m
putationally
i
nexpen
sive
i
n
term
s of both mem
o
ry
requi
rem
ents and spe
ed [3-4]. The re
search on
co
n
f
licting fuzzy neural network (F
NN) probl
em
by using PSO
has be
en pu
blish by [5],
but in this
re
search, the rul
e
s is g
ene
rat
e
s by an exp
e
rt.
Based
on th
e
advantag
es
of PSO and t
he ne
ede
d of
ANFIS to st
abilise the
co
nflicting
crite
r
ia in neu
ro-fu
z
zy probl
em, this stud
y w
ill examined parti
cle swarm optimization to balan
ce
accuracy an
d
interpretabilit
y tr
ade-offs in
ANFIS struct
ure.
The o
r
g
ani
sa
tion of the
p
aper is a
s
d
e
t
ail
ed. Sectio
n 2
de
scribe
s the
ad
aptive ne
uro
-
fuzzy
con
c
e
p
t
s. Section
3
descri
b
e
s
the
pro
p
o
s
ed m
odified n
euro
-
fuzzy cl
assifi
er u
s
ing
PSO
in
detail. Sectio
n 4 de
scrib
e
s the
pe
rfo
r
man
c
e
eval
uation p
r
o
c
e
dure fo
r the
cla
ssifie
r
. T
he
con
c
lu
sio
n
s a
r
e presented i
n
Section 5.
2.
Adap
tiv
e
Neuro Fuzz
y
Sy
stem
As the gene
ral fuzzy mod
e
lling structu
r
e, ANFIS
is mainly cha
r
a
c
teri
sed by two feature
s
that assess the quality of the obtained fu
zzy
models: int
e
rp
retability and a
c
cura
cy [6].
Interpretabilit
y refers to the ability of fuzzy model
s
to represent the
habitual
of its systems. S
o
me
of re
sea
r
che
r
s
agreed th
at the interpretability cove
rs
seve
ral i
s
sue
s
, such a
s
the m
o
d
e
l
stru
cture, the numbe
r of
input variable
s
,
and the num
ber of fuzzy rules, the num
ber of lingui
st
ic
terms, a
nd th
e sh
ape of th
e fuzzy set
s
. The inte
rp
retability is impo
rtant issue
s
i
n
ANFIS process
becau
se it is affecting t
he co
mplexit
y
and pr
o
c
e
ssi
ng time o
f
the system
. Based on
[1],
interpretabilit
y can be im
proved
by fine-tuni
ng
the fuzzy rules with re
gularisation such
as
gro
w
ing
and
pruni
ng fu
zzy
rule n
u
mb
er
to find the effective on
e fro
m
all po
ssi
bl
e fuzzy rul
e
s
in
neuro-fu
zzy structu
r
e.
The accu
ra
cy
has straightf
o
rwar
d definit
ion. It refers to the cap
abili
ty of
the fuzzy model
to faithfully repre
s
e
n
t the
modelle
d
system. The
clo
s
er the m
ode
l to the
syste
m
, the a
c
curacy
clo
s
en
ess i
s
highe
r a
s
the
simila
rity betwee
n
the
respon
se
s of th
e real
sy
ste
m
and th
e fu
zzy
model is u
n
d
e
rsto
od. One
of the neuro
-
fuzzy adv
anta
ges i
s
neu
ro-f
uzzy can be
desi
gne
d based
solely on
app
roximation a
n
d
the lingui
sti
c
informat
ion.
Therefore, b
a
se
d on [7] t
he satisfa
c
tory
level of accu
racy can be
achi
eved by tuning t
he ne
twork structu
r
e and pa
ram
e
ter lea
r
ning
of
neuro-fu
zzy and ba
se
d o
n
[8], there are a hi
gh relation
ship b
e
twee
n mem
bership fun
c
t
i
on
para
m
eter
a
nd accu
ra
cy. This state
m
ent has
l
ed
to ideas
on
how to tuni
n
g
membe
r
ship
function
s to improve the a
c
cura
cy of ne
uro
-
fuzzy systems.
Based o
n
the two co
ntradicto
r
y req
u
ir
em
ents in
fuzzy mode
lling, ANFIS can b
e
formulate
d
wi
th two obje
c
tives that
will simultaneo
usly
optimised, i.e.
1.
Tuning
the
p
a
ram
e
ter lea
r
ning
of ANFI
S to obtai
n a
goo
d p
e
rfo
r
mance
(Accu
r
acy
)
of fu
zzy
modellin
g ba
sed o
n
Mean
Squared Erro
r (MSE). It is given as:
m
i
n
1
(1)
Whe
r
e
and
are the net
work o
u
tput an
d the desi
r
ed
output, resp
ectively, and
is the
numbe
r of da
ta.
2.
Gro
w
ing
an
d
pruni
ng fu
zzy rule
num
ber
to obtain
a go
od Interpreta
bility of fuzzy
modellin
g. It
is given a
s
:
m
i
n
Ο
(2)
Whe
r
e
is the maximum numbe
r of rule node
s, and
Ο
Ο
is a binary value used to
indicate wh
ether the rule n
ode
exists or not. It works
as a swit
ch to turn a rule node on or off.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Balanced the
Trad
e-off
s
problem
of ANFIS Using PS
O (Dia
n Palu
pi Rini)
613
3.
Modified Ad
aptiv
e
Neuro
Fuzzy
Sy
stem using PSO
Particle
swarm optimizatio
n (PSO) i
s
p
a
rt
of evoluti
onary al
go
rithm that will
use
by
ANFIS as a l
earni
ng meth
od to optimise both conflic
ting crite
r
ia.
A definition o
f
PSO based
on
descri
b
e
s
PSO as a swa
r
m of particle
s
, where p
a
rti
c
le rep
r
e
s
ent a
potential sol
u
tion.
Particle
swarm optimization con
s
ist
s
of par
ti
cle
where
po
sition
of the pa
rticle i
s
influen
ced by
velocity. Let
denote the positio
n of particle
in the sea
r
ch sp
a
c
e at time
st
ep
; unless otherwise sta
t
ed, t denotes discrete ti
me step
s. Th
e positio
n of the particle
is
cha
nge
d by adding a velo
ci
ty,
to the current positio
n:
(3)
(4)
Whe
r
e
and
are a
c
cele
ration coeffici
ent,
and
are ran
dom v
e
ctor an
d
and
local be
st and glo
bal
best re
sp
ecti
vely.
PSO is a
po
tential tech
ni
que to
solve
the
ANFIS
probl
em
s. In the context
of PSO,
ANFIS is
co
nsid
ere
d
a
s
one p
a
rti
c
le
and p
a
rame
t
e
rs that influ
ence the A
N
FIS pro
c
e
s
s is
con
s
id
ere
d
a
s
a dimen
s
io
n of the particle. Wh
il
e in the PSO, there are som
e
particl
es; me
ans
there a
r
e
so
me ANFIS p
r
oce
s
se
s that
com
pete
to achi
eve
the potential solu
tion
of
obje
c
t
i
ve
function of A
N
FIS.
Figure 1. The
adaptive neu
ro
-fu
z
zy archi
t
ecture.
Layer 1 is in
put layer, wh
ile
1
…
are input signal
s; Layer 2 is fuzzif
i
cation
pro
c
e
ss of antece
dent pa
ramete
r nam
ely membership function
,
that each no
de con
n
e
c
ted
with
single
n
ode
of layer
2a. The
conn
ection
s
pre
s
e
n
t modify the
memb
ership
functio
n
val
ue;
Layer 3 is th
e fuzzy rul
e
base layer; while layer
4 is the norm
a
li
zation laye
r. In this layer, the
optimized fuzzy rule
will selected. Lay
er 5 is the defuz
zification layer while the layer is
affected by consequ
ent pa
ramete
r
, and C is outp
u
t cl
assificatio
n
.
As illustrated in Fig.
1, each
node
in
l
a
yer
2 has single c
onnectiv
i
ty with node
in layer
2a, means each mem
bersh
ip function parameter in layer 2 will modi
fied in layer 2a to obtain the
approp
riate
membe
r
ship
whi
c
h will u
s
ed to me
a
s
u
r
e the outp
u
t and get si
g
n
ificant mini
mum
error. Fu
rthe
r, each
no
de i
n
layer
3 is conne
cted
wit
h
ea
ch
node
in layer
4, wh
ere
ea
ch of t
he
connection represents
a fuzzy
rule.
The optimal fuzzy
rule
will selected based
on how
importa
nce of each fu
zzy rule in the co
rresp
ondi
ng sy
stem.
In the
pro
p
o
s
ed
PSO-A
NFIS, PSO wil
l
used
to tun
e
all
the
parameters l
e
a
r
ning
of
ANFIS and
si
multaneo
usly
will g
r
owi
ng
and p
r
uni
ng f
u
zzy rul
e
nu
mber i
n
ANFI
S stru
cture to
get
the be
st valu
e of pa
ram
e
ters lea
r
nin
g
and fu
zzy
rul
e
num
ber,
re
spe
c
tively. The p
r
op
ose PSO-
ANFIS
will used
to design the
ANFIS wi
th
a small
number of fuzzy
rules with hi
gh
performance
ac
cur
a
cy
.
T
h
i
s
t
a
sk
i
s
p
e
rf
orme
d t
h
rou
g
h
max
i
mi
zing
the
accu
ra
cy, minimizin
g
the
numb
e
r
o
f
sele
ct
ed r
u
le
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 11, No. 3, September 20
13: 61
1 – 616
614
Figure 2. An overview of the ANFIS-PS
O pro
c
e
ss
Figure 2 presents the
process of
ANFIS
PSO. Be
low
is illustration
of PSO used
to tune
all the param
eters l
earning
of ANFIS and simult
a
neo
usly will g
r
o
w
and prune fu
zzy rule num
ber
in ANFIS s
t
ruc
t
ure:
4. Experimenta
l
studies
To evaluate
perform
an
ce of the propo
s
ed al
go
rithms, seve
ral expe
rime
nts are
con
d
u
c
ted
on four real
-world data
s
ets from
UCI machi
ne l
earni
ng
(http://archive.ics.uci.edu/m
l
/dataset
s.html): Iris Flower, Balloon,
Haberm
an’
s Survival Data and
Thyroid. Tabl
e 2 is su
mma
rise
s the
cha
r
acteri
st
ics of the data
s
ets u
s
ed in thi
s
experim
ents.
Table 2. Ch
aracteri
stics of
datasets
Datase
t
Samples
Inpu
t N
o
.
Ou
tpu
t
N
o
.
Class
No. o
f
Ins
t
anc
e
in Each
Class
Iris Flow
e
r
150
4
1
3
C1= 50 inst, C2
=50, C3=50
Haberma
n’s
306
3
1
2
C1= 255 inst, C2
= 81
Balloon
20
4
1
2
C1= 8 inst, C2 = 12
Th
yroid
215
5
1
2
C1= 150 inst, C2
=35, C3=30
1.
Initializ
e partic
l
e positi
on
usin
g equ
atio
n (16)
and vel
o
cit
y
wi
t
h
numb
e
r o
f
dimensi
ons.
2.
Initializ
e fitness
function
for ANF
I
S-PSO. F
i
tness functio
n
of
ANF
I
S-PSO i
s
the objective
functio
n
of the ANF
I
S i.e. equati
on (1)
and (2).
3.
F
i
nd ob
jectiv
e
function of A
N
F
I
S using e
quati
on (5) –
(10). Based
o
n
the fitness functio
n
find
particl
e’s positi
on (
) in each local best (
). If
fitness (
) is better than fitness (
) th
en
=
.
4.
F
i
nd best val
u
e
of
. Set best of
as
5.
Upd
a
te vel
o
city a
nd pos
itio
n usin
g eq
uatio
n (3) and (4)
6.
F
o
r each partic
l
e, find ne
w
fit
ness functio
n
. Check
as fitness function b
a
s
ed on ste
p
3) and fin
d
the
gbest val
ue b
a
s
ed on ste
p
4)
7.
Check
w
h
eth
e
r
the val
ue h
a
s
conver
genc
e t
hen sto
p
, othe
r
w
i
s
e b
a
ck to
5). Check, if g
best_fitness
better that stop
pin
g
criteria th
en proc
ess stop, else got
o step 5)
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TELKOM
NIKA
ISSN:
1693-6
930
Balanced the
Trad
e-off
s
problem
of ANFIS Using PS
O (Dia
n Palu
pi Rini)
615
To ensure th
e con
s
iste
ncy of
the data, val
ues of the datasets
are no
rmali
s
ed in the
rang
e of [0,
1] usin
g no
rmalisatio
n formula. The
n
h
o
ld-o
ut cro
s
s validation i
s
use
d
to te
st the
perfo
rman
ce
of the system
. Hen
c
e, t
he
datasets a
r
e partition
ed
into two sets: a traini
ng
set and a testing
set. The trainin
g
set is use
d
to train the net
work in orde
r to get the ANFIS
learni
ng
whil
e the te
stin
g set i
s
u
s
ed to
te
st the ge
neralisati
on pe
rformance of A
N
FIS
and i
s
not
se
en du
ring th
e
training
process. The
s
e d
a
taset
s
are p
a
rtitioned
ra
n
domly i.e. 80
% of
data are u
s
e
d
for the trainin
g
set and
the
rest 20% fo
r the testing
set
.
Table 3. Spe
c
ificatio
n of propo
se
d meth
od
PSO
Parame
ter
Value
Number of
particle
50
Number of lingui
stic fuzzy
set
3
Number of ite
r
ati
ons
1000
Obj. Function 1
(
1
)
Mean Square
Err
o
r (MSE)
Obj. Function 2
(
2
)
Optimal Numbe
r
of rule
acceleration coefficient
0
,
5
1
random vector
and
random
Initial values that requi
re
d in ANFIS-PSO
pro
c
e
s
s are de
scri
bed in table
3. The
experim
ents
of ANFIS-PSO are cond
u
c
ted ba
s
ed o
n
ten run
s
on
each data
s
e
t. The mean and
SD (indi
cate
s the mea
n
value and
st
anda
rd d
e
vi
ation, respe
c
tively) result about the M
SE
(sati
s
fy accuracy), the num
ber of rul
e
an
d time con
s
u
m
e are
cal
c
ul
ated and rep
o
rted
Table 4
sho
w
s th
e mea
n
and
stand
ard d
e
viation
of ANFIS learni
ng b
a
se
d PSO
algorith
m
s. T
he table
sho
w
s that the
b
e
st e
r
ror
rate
on the
trai
ning p
r
o
c
e
s
s is Balloon
and
on
the testin
g p
r
oce
s
s i
s
Iri
s
Flowe
r
. T
he
result i
ndi
cate
s that th
e e
r
ror
rate
might
not be
influe
n
c
ed
by the numb
e
r of input pa
ramete
rs a
n
d
sample
s
but
it might be due to the dist
ribution
s
of the
datasets itsel
f. For exampl
e, al
though
Haberman
s
’
s
d
a
taset
s
have
three in
put variable
s
, but th
e
distrib
u
tion
of its
cla
s
ses i
s
extremely i
m
balan
ce
d
(there
a
r
e
255
insta
n
ces fo
r
class 1
and
81
instan
ce
s fo
r cla
s
s
2), th
us it
be
see
n
that th
e
si
gnifica
nt e
rro
r of it
s val
u
e
is not
so
g
ood
comp
ared to
the ball
oon
and i
r
i
s
dat
a. Ballo
o
n
has fewer i
n
stan
ce
s the
n
others
and
the
distrib
u
tion
d
a
ta is
rathe
r
norm
a
l, but t
here
is
a
sig
n
ifican
ce
differen
c
e
of e
r
ror results
bet
wee
n
training a
nd testing. On th
e contrary, Iris
data have
more vari
abl
e than Hab
e
rman’s a
nd m
o
re
instan
ce
s tha
n
ballo
on, b
u
t
it has
norm
a
l dist
ri
butio
n
.
The o
u
tput
sho
w
s mini
mal erro
r val
u
e
either i
n
trai
ni
ng o
r
te
sting
data. Fu
rthermore, th
yroid
data obtai
ned
the worse
re
sults in b
o
th
set
of data i
n
whi
c
h it
ha
s m
o
re varia
b
le th
a
n
othe
rs a
nd
has ab
normal
dist
ribution
d
a
ta. So, it mig
h
t
be co
ncl
ude
d
that the distri
bution of ea
ch cla
ss gi
ve
s
a large effe
ct to the erro
r ra
te value.
Table 4. Re
sult of ANFIS
PSO
Dataset Experiments
Training
Testing
No of Optimal Ru
le
(
2
)
Ti
me (s
)
MSE (
1
)
Error
Rate
(
1
)
Iris Flow
e
r
Mean
0.151
0.155
30.2
80.2
SD 0.057
0.103
9.64
25.5
Haberma
n’ s
Mean
0.163
0.195
16.1
38.9
SD 0.005
0.004
2.85
0.57
Balloon
Mean
0.116
0.241
12.5
13.6
SD 0.055
0.127
8.86
0.52
Th
yroid
Mean
0.189
0.580
115.4
147.4
SD 0.021
0.063
40.313
2.675
In numb
e
r
of optimal
rule
2
colu
mn, the
small
e
st n
u
m
ber
of rul
e
is o
b
tained
by
balloo
n
, while
thyroid ha
s the mo
st one.
From the
tab
l
e 3, it is kno
w
n that Ballo
on data ha
s t
he
smalle
st num
ber of data
and thyroid
has the mo
st
one. It seems that there is a co
rrel
a
tion
betwe
en
nu
mber of in
pu
t and
numb
e
r
of
optimal
rule. However, Hab
e
rm
an’
s ha
s le
ss in
p
u
t
variable
but t
he optim
al n
u
mbe
r
of rule
is mo
re th
an
balloo
n
. If seeing f
r
om n
u
mbe
r
of
sa
mple
(insta
nce), th
e Habe
rma
n
’
s
ha
s more
numbe
r of
instan
ce
s than
Balloon. Wh
ile Iris data
has
more
optimal
numbe
rs du
e to it has
more i
nput t
han
Hab
e
rm
an’s
and m
o
re in
stan
ce
s
than
balloo
n
. So, it might be
con
c
lu
ded th
at numb
e
r
o
f
input an
d i
n
stan
ce
s giv
e
a
sub
s
tant
ial
contri
bution t
o
find optimal
numbe
r of ru
les.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 11, No. 3, September 20
13: 61
1 – 616
616
Table 4
sh
ows that the tim
e
pro
c
e
s
s is
balan
ce
d wit
h
the num
ber of rule. The
more th
e
numbe
r of
rul
e
the mo
re th
e time process is
obtain
ed.
For a
n
exam
ple, Balloon
data have l
e
ss
numbe
r
of op
timal rul
e
s co
mpared to
time
spent
le
ss tha
n
oth
e
rs. Thyroid
ha
s mu
ch
numb
e
r
of
rule than othe
rs, then it also spen
d more
time in
it proce
ss. So, it can be co
ncl
u
ded that the time
compl
e
xity will reduced
whi
l
e the optim
al
number of rule is obtained.
Table 5. Cla
s
sificatio
n
Mea
s
ureme
n
t of propo
se
d meth
od
Dataset Sensitiv
ity
Specific
ity
Accur
a
cy
Iris Flow
e
r
0.891155
0.029563
0.941667
Haberma
n
0.794521
0.24
0.790984
Balloon 1
0
1
Th
yroi
d
0.63081
0.086873
0.854651
In the conte
x
t of evaluation of the cl
as
sificatio
n
measurement
of PSO-ANFIS, an
averag
e of sensitivity, spe
c
ific
ity, and p
r
edi
cting a
c
cura
cy of mod
e
l wa
s perfo
rmed in Tabl
e
5
.
Based
on th
e table 5, when the
sen
s
itivity is
high and the
spe
c
ificity gives
low value
s
, the
accuracy i
s
b
e
tter du
e to t
he
correlatio
n bet
ween
thes
e two
meas
urements
. I
n
this
res
u
lt,
the
highe
st cla
s
si
fication a
c
curacy is obtai
n
ed by
balloo
n
dataset (Accuracy eq
ual
s to one mea
n
s
that all the dataset
s have
been
cla
ssifi
ed preci
s
ely)
,
while Iri
s
flo
w
er
and
Hab
e
rma
n
’s i
s
in
the
se
con
d
an
d third
ran
k
ing
score,
re
spe
c
tively and t
he worst re
sult is obtai
ne
d by thyroid.
By
observing fro
m
the behavi
our of data, I
r
is flo
w
er, Ba
lloon an
d thyroid h
a
ve mo
re inp
u
t varia
b
le
and have le
ss numb
e
r of i
n
stan
ce
com
pare
with Ha
berm
an’
s, but the classifica
tion accuracy
is
bigge
r than Haberman’
s. Howeve
r,
the distributio
n of each cla
s
s in
Habe
rma
n
’s
dataset is mo
st
un-n
o
rm
al co
mpared to th
e other. So i
n
this c
ontext, the distrib
u
tion data of e
a
ch
cla
s
s mi
ght
result to a la
rge effect in
cl
assificatio
n
m
eas
ure
m
ent besi
d
e
s
in
co
nsi
s
t
ent
data cla
ss of
data
s
et.
Ho
wever, for
over all the result
s given feasi
b
le
ac
cu
r
a
cy
in cla
ssif
i
cat
i
on f
o
r all
dat
a set
s
whi
c
h
in all datasets accura
cy mo
re than 0.75 i
s
obtain
ed.
5. Conclu
sion
In this pape
r,
an approa
ch
multiple solu
tions ba
se
d o
n
PSO is pro
posed an
d a
pplied to
develop
gen
e
r
alisation
and
cla
s
si
ficatio
n
accu
ra
cy of
several o
b
je
ctives for ada
p
t
ive neuro-fu
zzy
system
(A
NF
IS). This is d
one
by si
mul
t
aneou
sly o
p
timising
the A
N
FIS a
r
chite
c
ture
ba
se
d
on
two crite
r
ia: enha
nce the accu
ra
cy an
d redu
ce
the
complexity based on int
e
rp
retability. The
finding
s indi
cated that the
pro
p
o
s
ed
m
e
thod p
r
ov
id
es p
r
omi
s
in
g
accu
ra
cy wh
ich
coul
d red
u
ce
time c
o
mplexity.
Referen
ces
[1]
Paiva, R.P. an
d A. Doura
do,
Interpretab
ilit
y and l
earn
i
n
g
in ne
uro-fuzz
y s
y
stems. Else
vier.
Fu
z
z
y
Sets and Syste
m
s
. 20
04. 14
7: 17-38.
[2]
Neg
nevitsk
y, M., Artificial Inteli
genc
e: A gui
de
to intel
l
i
gent s
y
st
ems. second e
d
itio
n ed. 200
5,
Engl
and: Pe
ar
son Educ
atio
n Limite
d. 415.
[3]
Bai, Q., Analysis of Particle
S
w
arm O
p
timization Algorithm.
Co
mp
ute
r
an
d Infor
m
at
ion
Scie
nce
.
201
0; 3(1): 180
-184.
[4]
Enge
lbrec
h
t, A.P., F
undamen
tal of Com
put
ation
a
l S
w
a
r
m
Intelig
ent. F
i
rst ed. 20
05,
T
he atrium,
Souther
n Gate, Chich
e
ster, W
e
st Susse
x PO
19 8SQ, Engl
a
nd: John W
i
l
e
y & Sons Ltd.
[5]
Ma, M., et al.,
Fuzzy
Neural
Net
w
ork Optimization by
a
Particle
S
w
arm Optimization Algorithm, in
Advanc
es
in
N
eura
l
N
e
t
w
orks
- ISNN
2
006,
J. W
ang,
et
a
l
., Editors. S
p
ri
nger
Berl
in
/
Heid
el
berg.
200
6: 752-
761.
[6]
Di Nuovo, A.G.
and V.
Catania.
Li
ng
uistic M
odifi
ers to I
m
pr
ove th
e Acc
u
ra
cy-Interpretab
i
l
i
ty T
r
ade-Off
in Mu
lti-Objecti
v
e Genetic
De
sign
of
F
u
zz
y
Rule
Bas
ed C
l
a
ssifier Syste
m
s
. in Intelligent Sy
stems
Desig
n
an
d Ap
plicati
ons, 2
0
0
9
. ISDA '
09.
Ninth Internati
o
n
a
l Co
nferenc
e
on. 200
9.
[7]
Lee, C.-H. a
n
d
C.-C. T
eng, F
i
ne T
unin
g
Of Members
h
ip F
unctio
n
s F
o
r F
u
zz
y
Ne
ural S
y
stem.
Asian
Journ
a
l of Co
ntrol
. 200
1; 3(3): 216-
225.
[8]
Zeng,
X
.
-J. and M.G. Singh.
A Relationship Bet
w
een M
e
mbers
h
ip
Functions
and A
pproximation
Accurac
y
in F
u
zz
y
S
y
stems.
IEEE Trans
actions
On S
ystem
s, Ma
n, And
Cybernetics-Part
B:
Cyber
netics
, 1996. 26(
1): 176
-180.
Evaluation Warning : The document was created with Spire.PDF for Python.