Jurnal ILMU DASAR, Vol. 10, No. 2, hal: 190-198, 2009
ISSN: 1411-5735
V o l u m e1 0 N o mo r2
J u r n a lI LMUD A S A R V o l .1 0 No.2
Hlm. 109-244
Jem ber
Juli 2009
ISSN
14',11-5735
lssN 1411-57:5
,
Jurnal ILMUDASAR
Volume10 Nomor2 Juli2009
PimpinanEditor
I MadeTirta
Sekretaris
KartikaSenjarini
EditorPelaksana
EvaTyas Utami
EdySupriyanto
DewanEditor
Moh.Hasan
Sujito
WuryantiHandayani
SattyaArimurti
EditorTeknik
Kusbudiono
Adminisffi:'g,,ilfffansan
Nur SyamsiyahHarpanti
JurnalllmuDasarditerbitkan
oleh:
FakultasMatematika
dan llmuPengetahuan
Alam,Universitas
Jember.
TerbitsejakJanqpri2000denganfrekuensi
penerbitan
dua kalisetahun.
Terakreditasi
berdasarkan
SK DirjenDiktiNOMOR:65a/DlKTl/Kep/2008
tanggal15 Desember
2008
AlamatEditor/Penerbit:
Jl. Kajimantan
37 KampusTegalboto,
Jember68'12'l
Telp.(0331)334293;Fax.(0331)330225
E-mail: jid@fmipa.unej.ac.id
ataujurnalilmudasar@gmail.com
http://www.unej.ac.id/fakultaslmipa/
atauhttp:l/r,vww.mipa.unei.ac.id
Keterangan
sampul:
Atas
: Cormelexplantswithshootintiationof threegladiolus
(a) Nabila,
cultivars;
(b) Claraand (c) Kaifain 18 days"afterplantingon MS freehormonemedia.
(a)cv. Nabilaon 2 mgilBAr
Bawah : Plantletperformance
of gladiolus
cultivars:
(b)cv.Claraand (c)cv. Kaifa on 3 mg/lBA supplemented
in MS + 0.5 mg/l
NAA after60 daysculture.
UCAPANTERIMAKASIH
Diucapkan
terimakasihkepadaMITRABESTARIatas kontribusinya
pada penerbitan
Jurnal
ILMUDASARVolume10tahun2009:
1.
2.
Prof.AgusSubekti,
M.Sc.,Ph.D.
ph.D.
Prof.Prof.Dra.SusantiLinuwih,
M.Stats.,
4.
Prof.Dr.rer.nat.
KarnaWijaya,M.Eng.
Prof.Dr.WiwikTriWahyuni,
M.Sc.
5.
Triyanta,
Ph.D.
6.
Prof.Dr.Tejasari,
M.Sc.
7.
Slamin.
Ph.D.
B.
Drs.Moh.Hasan,M.Sc.,Ph.D.
L
Prof.Kusno,DEA.,Ph.D.
3.
10. Prof.Endang
Semiarti,
M.Sc.,Ph.D.
11. Prof.Dr.Mammed
Sagi,M.S.
12. Prof.EndangSoetarto,
M.Sc.,ph.D.
13. PepenArifin,Ph.D.
14.
15.
Prof.Dr.Bambang
Sugiharto,
M.Sc.Agr.
Prof.Dr.I NyomanBudiantara,
M.Si.
16. Drs.Siswoyo,
M.Sc.,Ph.D.
17. Drs.AchmadSjaifullah,
M.Sc.,ph.D
18. Drs.Zulfikar,
Ph.D.
19. Drs.Bambang
Kuswandi,
M.sc.,ph.D.
20. TriAtmojo
Kusmayadi,
M.Sc.,ph.D.
21.
Dr.Sekartedjo
22.
Dr.HidayatTeguhWiyono,M.pd.
23.
Drs.BudiLestari,
M.Si.
24.
Dr.dr. Supangat,
M.Kes.
25.
Dra.HariSulistyowati,
M.Sc.
26.
Dr.WiwikSriWahyuni,
M.Kes.
27.
Dr.M. lsa lrawan,M.T.
Volume10 Nomor2 Juli 2009
lssN 1411-5735
Jurnal ILMU DASAR
DAFTAR ISI
ln Vitro Regeneration
of Three GladiolusCultivarsUsing Cormel Explantsby Kurniawan Budiarto
(109-1
13).
SolusiAnalitikPersamaanSchrddinger
SistemOsilatorHarmonik1 DimensidenganMassaBergantung
Posisimenggunakan
MetodeTransformasi
(AnatyticatSotutionol Schrodinger
Eq-uation
oi tneUarmonic
Oscillator
SystemwithPositionDependent
MassUsingTransformation
Method")ofefr'suiisna
(114-120).
Peningkatan
KualitasMinyakJelantahMenggunakan
AdsorbenHs-NZAdalamReaktorsistem Fluidfixed
bed [he lmprovementof_WasteCookingOil QuatityusingH5-NZAAdsorbentin FtuidFixed Bed Reactor)
olehDonatussetyawanp. Handoko,Triyono,Narsito,tutlr owi (121-1g2).
Konsistensi
dan AsimtotikNormalitas
ModelMultivariale
AdaptiveRegression
Spline(Mars)ResponBiner
(Consistency
and AsymptoticNormatityof MaximumLiketihoodEstimior in MniS ainiry iisponse Model
olehBambangWidjanarko
Otok(133-140).
AnalisisReservoar
DaerahPotensiPanasbumi
GunungRajabasa
Kalianda
denganMetodeTahananJenis
dan Geotermometer(GeothermatReservoir Anatysisof ilount RajabasaKaianda pitency Area using
ResistivityMethod and Geothermometer)
oleh Nandi Haerudin, Vina Jaya parOeOe,'
Syamsurijai
Rasimeng
(141-146).
AplikasiSistemInformasiGeografi(SlG) untuk-Mempelajari-Keragaman
StrukturHabitatLaba-labapada
LansekapPertaniandi DaerahAliranSungai(DI\q).cialJul (AppticZtion
of Geographical
tnfomationSystem
Diyersityof HabitatStructureof Spider i; Ag'ri;itturat Landscapein Cianjur Watershed)oteh
(!-tp) to S_tudy
I WayanSuanadan Yaherwandi(147-152).
ModifiedNewtonKantorovich
problemsby AgungTjahjo
Methodsfor SolvingMicrowave
InverseScattering
Nugroho(153,159).
ldentifikasi
FraksiAktifBakterisida
pada RimpangLempuyang
(ZingiberramineumBlume)
(tdentification
of
TheBactericide
ActiveFractionon Zinqiberqiamineum'8iumdearxio'lehI Madeoira Swairtara(160-170).
Embe.dding
Grat Kz,s,npada Torus (EmbeddingK23,, Graphson Torus)oleh Liliek Susilowati, Nency
RosyidaY, YayukWahyuni(171-180).
Uji Sitotoksisitas
EkstrakMetanolBuahBuni(An.tidesma
bunius(L)Spreng)terhadapSet Hela(Cytotoxicity
Effectof Methanolic
Extract.of.
Buni-'s
Fruits(Anldcsmgbunius1Ly'sjreng)'against
Hiti ceirg otenEndah
Puspitasari
& Evi UmayahUtfa(181-185).
LaserInduced
ThinFilmProduction
(LITFP)
UsingNitrogen
(N2)LaserDeposition
by SyamsirDewang(186189).
ConstructingFuzzy Time Series Model Using Combinationof Table Lookup and Singutarvalue
Decomposition
Methodsgnd lts Application
to Foiecasting
InflationRateby Agus MamanAbadi,Subanar,
Widodo,Samsubar
Sateh(190-i9S).
SimulasiModelJaringanSelularmelaluiPemrogramanInte-ger
(Simutation
of CeilularNetworkModetby
Integer Programming)otehAgustinapradjaningsih (199-206j.
Jurnal ILMU DASAR
DAFTAR ISI
Efek ProtektifPropolisDalamMencegahstres oksidatifAkibatAktifitas
Fisik Berat (swrmming stress)
(PropotisProtectiveEffect to Prevent-oxidarive^
stress cai;;J-oy' itrenous pnyiiiit \iiii,ty (swimming
Sfress))ofeh Hairrudindan DinaHetianti(207-211).
Pusatdari BeberapaGelanggang
PolinomMiring(rhe centreof some skewpotynomialRings)
oleh Amir
Kamaf Amir(212-2181.
EfekKondisiHiperglikemik
terhadapstrukturovariumdan siklusEstrusMencit(Mus musculusL)
(Effectof
Hyperglikemic
conditionson ovarianstructure.andestpui)icte i'ui"r(Mus musculus
L))
oteh
'
Eva
Tyas
Utami,RizkaFitrianti, Mahriani,SusantinFajariyah
tZtg-iiil.
Generalized
ReducedGradientUntukoptimasiAmunisiKaliber57 mm c-60 Het (Generalized
Reduced
Gradientoptimizationfor Ammunitioncaiiber57 mm c-oo ieo-olii Muhammad
ev sjahid
vre"rv Akbar,
Bambang
WidjanarkoOtok,dan LestiAnggraini(225-23s)
^^vr
BeberapasenyawaHasillsolasidari Kulit BatangTumbuhanKedoya(Dysoxylum
gaudichaudianum
(A.
Juss.) Miq.) (Metiaceae)
compoundi tsotatedrroi-'dtem Bark of Kedoya
.(p9v9r7t
erqvlur
oaudichaudianum
(A. JussJ.Miq
oleh ruliran, i"yutr" Hamdani,RosyidMahyudi,
) (Meliaceie))
sri
HidayatiSyariefdan NurutHidayati(296-244i.
I
(AgusM amanAbadi dkk)
ConstructingF uzzyTime.............
190
ConstructingFazzy Time SeriesModel Using Combination of Table Lookup
and Singular Value DecompositionMethods and
Its Application to ForecastingInflation Rate
Agus Maman Abadir),Subanar2),
widodo2),SamsubarSaleh3)
1)Department
andNaturalSciences,
of Mathematics
Education,
Facultyof Mathematics
Yogyakarta Stat e Univ ersity
Student, Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Gadjah Mada University
2)Department
of Mathematics, Faculty of Mathematics and Natural Sciences,
Gadjah Mada University
3)Department
of Economics, Faculty of Economics and Business, Gadjah Mada University
t)Ph.D
ABSTRACT
Modellingfuzzy time sedes
Fuzry time seriesis a dynamicprocesswith linguisticvaluesasits observations.
datadevelo@ by someresearchers
useddiscretemembership
functionsandtablelookupmethodfurm taining
data.Thispaperpresents
a newmettrodto modellingfuzzytime seriesdatacombiningtablelookupandsingular
value decompositionmethodsusing continuousmembershipfunctions.Table lookup methodis used to
of fuing strengthmahix and QR
constuctfuzzy relationsfrom frainingdata.Singularvaluedecomposition
this methodis appliedto forecastinflationratein
factorizationareusedto rcducefuzz] relations.Furthermore,
Indonesiabasedon six-factors
one-orderfuz4r time series.Thisresultis comparedwith neuralnefivorkrnethod
methodgetsa higherforecasting
ratethantheneuralnetworkmethod.
andtheproposed
accuracy
inflationrate.
Keywords:Fuzrytimeseries,tablelookup,singularvaluedecompositioq
(Sah& Degtiarev2004, Chen
someresearchers
& Hsu 2004).
Fuzzy time series is a dynamic processwith
Forecastinginflation rate in Indonesia by
linguistic values as its observations.Many fuzzy model resultedmore accuracythan that
researchershave developedfizzy time series by regression method (Abadi et al. 2006).
model. Song & Chissom (1993a) developed Following the abovepaper,Abadi et al. (2007)
fuzzy time series model based on fuzzy also constructedflzzy time seriesmodel using
relational equation using Mamdani's method. table lookup methodto forecastinterestrate of
In their paper, determination of the fuzzy Bank Indonesiacertificate and the result gave
relation needslarge computation.Meanwhile, high accuracy. Abadi et al. (2OO8a,2008b)
Song & Chissom (1993b, 1994) also showed that forecastinginflation rate using
constructedfirst order fuzzy time series for
singular value method had a higher accuracy
time invariant and time variant cases.This thanthatusingWang'smethod.
model needs complex computation for fuzzy
Abadi et al. (2008c) constructed a
relationalequation. Furthermore,to overcome generalizationof table lookup method using
the weakness of the model, Chen (1996) firing strength of rules and applied it in
designedfuzzy time seriesmodel by clustering financial problems. Fuzzy time series model
of fuzzyrelations.
basedon a generalizedWang's method was
Hwang et al. (1998) constructedfuzzy time designedand it was appliedto forecastinterest
series model to forecast the enrollment in
rate of Bank Indonesiacertificate that gave a
Alabama University. Fuzzy time seriesmodei higher prediction accuracythan using Wang's
basedon heuristic model gives more accuracy method (Abadi et al. 2009a). Furthermore,
than its model designed by some previous forecasting interest rate of Bank Indonesia
researchers(Huamg 2001). Forecasting for certificate based on multivariate fuzzy time
enrollment in Alabama University based on seriesdata was done by Abadi et al. (2O09b).
high order fuzzy time series resulted high Kustono et aI. (2O06)applied neural network
prediction accuracy (Chen 2002). First order method to forecast interest rate of Bank
fuzzy titmeseriesmodel is also developedby
Indonesiacertificate.
INTRODUCTION
i
:
I
l
Jurnal ILMU DASAR.Vol. I0 No. 2. Juli 2009 : j,90-198
In this paper, we will design fuzzy time
series model combining table lookup method
and singular value decomposition using
continuous membershipfunctions to improve
the predictionaccuracy.This methodis usedto
forecastinflation rate in Indonesia.
METHODS
are defined.If F(r) is the collectionof/, (r), i = l,
2, 3,..., then F(t)is called fuzzy time serieson
I (t) . Based on this definition, fuzzy time series
F(t) can be consideredas a linguistic variable and
/, (r) as the possiblelinguistic valuesof f. (r) . The
value of F(r) can be different dependingon time t.
Therefore F(r) is function of time r. Let{(r) be
QR factorization and singular value
decomposition
In this section, we will introduce QR factoizatiot
and singular value decompositionof matrix and its
propertiesreferredfrom Scheick(1997). l,et B be m
x n matrix and suppose mSn.
The QR
factorizationof B is given by B =QR, where Q is
m x m orthogonalmatrix and R = [R,, R,r) is m x n
matrix with m x m uppet triangularmatrix R,, . The
QR factorizationof matrix B always exists and can
be computed by Gram-Schmidt orthogonalization.
Any m x n matrixA can be expressedas
( l)
A =USV, ,
where U and V are orthogonal matrices of
dimensionsm x tn, n x /r respectively,and S is n x n
matrix whose entries are 0 except s,; = o,
i =1,2 ,...,r
wit h
6, 2 o, 2. . . > o. > 0,
r
V o l u m e1 0 N o mo r2
J u r n a lI LMUD A S A R V o l .1 0 No.2
Hlm. 109-244
Jem ber
Juli 2009
ISSN
14',11-5735
lssN 1411-57:5
,
Jurnal ILMUDASAR
Volume10 Nomor2 Juli2009
PimpinanEditor
I MadeTirta
Sekretaris
KartikaSenjarini
EditorPelaksana
EvaTyas Utami
EdySupriyanto
DewanEditor
Moh.Hasan
Sujito
WuryantiHandayani
SattyaArimurti
EditorTeknik
Kusbudiono
Adminisffi:'g,,ilfffansan
Nur SyamsiyahHarpanti
JurnalllmuDasarditerbitkan
oleh:
FakultasMatematika
dan llmuPengetahuan
Alam,Universitas
Jember.
TerbitsejakJanqpri2000denganfrekuensi
penerbitan
dua kalisetahun.
Terakreditasi
berdasarkan
SK DirjenDiktiNOMOR:65a/DlKTl/Kep/2008
tanggal15 Desember
2008
AlamatEditor/Penerbit:
Jl. Kajimantan
37 KampusTegalboto,
Jember68'12'l
Telp.(0331)334293;Fax.(0331)330225
E-mail: jid@fmipa.unej.ac.id
ataujurnalilmudasar@gmail.com
http://www.unej.ac.id/fakultaslmipa/
atauhttp:l/r,vww.mipa.unei.ac.id
Keterangan
sampul:
Atas
: Cormelexplantswithshootintiationof threegladiolus
(a) Nabila,
cultivars;
(b) Claraand (c) Kaifain 18 days"afterplantingon MS freehormonemedia.
(a)cv. Nabilaon 2 mgilBAr
Bawah : Plantletperformance
of gladiolus
cultivars:
(b)cv.Claraand (c)cv. Kaifa on 3 mg/lBA supplemented
in MS + 0.5 mg/l
NAA after60 daysculture.
UCAPANTERIMAKASIH
Diucapkan
terimakasihkepadaMITRABESTARIatas kontribusinya
pada penerbitan
Jurnal
ILMUDASARVolume10tahun2009:
1.
2.
Prof.AgusSubekti,
M.Sc.,Ph.D.
ph.D.
Prof.Prof.Dra.SusantiLinuwih,
M.Stats.,
4.
Prof.Dr.rer.nat.
KarnaWijaya,M.Eng.
Prof.Dr.WiwikTriWahyuni,
M.Sc.
5.
Triyanta,
Ph.D.
6.
Prof.Dr.Tejasari,
M.Sc.
7.
Slamin.
Ph.D.
B.
Drs.Moh.Hasan,M.Sc.,Ph.D.
L
Prof.Kusno,DEA.,Ph.D.
3.
10. Prof.Endang
Semiarti,
M.Sc.,Ph.D.
11. Prof.Dr.Mammed
Sagi,M.S.
12. Prof.EndangSoetarto,
M.Sc.,ph.D.
13. PepenArifin,Ph.D.
14.
15.
Prof.Dr.Bambang
Sugiharto,
M.Sc.Agr.
Prof.Dr.I NyomanBudiantara,
M.Si.
16. Drs.Siswoyo,
M.Sc.,Ph.D.
17. Drs.AchmadSjaifullah,
M.Sc.,ph.D
18. Drs.Zulfikar,
Ph.D.
19. Drs.Bambang
Kuswandi,
M.sc.,ph.D.
20. TriAtmojo
Kusmayadi,
M.Sc.,ph.D.
21.
Dr.Sekartedjo
22.
Dr.HidayatTeguhWiyono,M.pd.
23.
Drs.BudiLestari,
M.Si.
24.
Dr.dr. Supangat,
M.Kes.
25.
Dra.HariSulistyowati,
M.Sc.
26.
Dr.WiwikSriWahyuni,
M.Kes.
27.
Dr.M. lsa lrawan,M.T.
Volume10 Nomor2 Juli 2009
lssN 1411-5735
Jurnal ILMU DASAR
DAFTAR ISI
ln Vitro Regeneration
of Three GladiolusCultivarsUsing Cormel Explantsby Kurniawan Budiarto
(109-1
13).
SolusiAnalitikPersamaanSchrddinger
SistemOsilatorHarmonik1 DimensidenganMassaBergantung
Posisimenggunakan
MetodeTransformasi
(AnatyticatSotutionol Schrodinger
Eq-uation
oi tneUarmonic
Oscillator
SystemwithPositionDependent
MassUsingTransformation
Method")ofefr'suiisna
(114-120).
Peningkatan
KualitasMinyakJelantahMenggunakan
AdsorbenHs-NZAdalamReaktorsistem Fluidfixed
bed [he lmprovementof_WasteCookingOil QuatityusingH5-NZAAdsorbentin FtuidFixed Bed Reactor)
olehDonatussetyawanp. Handoko,Triyono,Narsito,tutlr owi (121-1g2).
Konsistensi
dan AsimtotikNormalitas
ModelMultivariale
AdaptiveRegression
Spline(Mars)ResponBiner
(Consistency
and AsymptoticNormatityof MaximumLiketihoodEstimior in MniS ainiry iisponse Model
olehBambangWidjanarko
Otok(133-140).
AnalisisReservoar
DaerahPotensiPanasbumi
GunungRajabasa
Kalianda
denganMetodeTahananJenis
dan Geotermometer(GeothermatReservoir Anatysisof ilount RajabasaKaianda pitency Area using
ResistivityMethod and Geothermometer)
oleh Nandi Haerudin, Vina Jaya parOeOe,'
Syamsurijai
Rasimeng
(141-146).
AplikasiSistemInformasiGeografi(SlG) untuk-Mempelajari-Keragaman
StrukturHabitatLaba-labapada
LansekapPertaniandi DaerahAliranSungai(DI\q).cialJul (AppticZtion
of Geographical
tnfomationSystem
Diyersityof HabitatStructureof Spider i; Ag'ri;itturat Landscapein Cianjur Watershed)oteh
(!-tp) to S_tudy
I WayanSuanadan Yaherwandi(147-152).
ModifiedNewtonKantorovich
problemsby AgungTjahjo
Methodsfor SolvingMicrowave
InverseScattering
Nugroho(153,159).
ldentifikasi
FraksiAktifBakterisida
pada RimpangLempuyang
(ZingiberramineumBlume)
(tdentification
of
TheBactericide
ActiveFractionon Zinqiberqiamineum'8iumdearxio'lehI Madeoira Swairtara(160-170).
Embe.dding
Grat Kz,s,npada Torus (EmbeddingK23,, Graphson Torus)oleh Liliek Susilowati, Nency
RosyidaY, YayukWahyuni(171-180).
Uji Sitotoksisitas
EkstrakMetanolBuahBuni(An.tidesma
bunius(L)Spreng)terhadapSet Hela(Cytotoxicity
Effectof Methanolic
Extract.of.
Buni-'s
Fruits(Anldcsmgbunius1Ly'sjreng)'against
Hiti ceirg otenEndah
Puspitasari
& Evi UmayahUtfa(181-185).
LaserInduced
ThinFilmProduction
(LITFP)
UsingNitrogen
(N2)LaserDeposition
by SyamsirDewang(186189).
ConstructingFuzzy Time Series Model Using Combinationof Table Lookup and Singutarvalue
Decomposition
Methodsgnd lts Application
to Foiecasting
InflationRateby Agus MamanAbadi,Subanar,
Widodo,Samsubar
Sateh(190-i9S).
SimulasiModelJaringanSelularmelaluiPemrogramanInte-ger
(Simutation
of CeilularNetworkModetby
Integer Programming)otehAgustinapradjaningsih (199-206j.
Jurnal ILMU DASAR
DAFTAR ISI
Efek ProtektifPropolisDalamMencegahstres oksidatifAkibatAktifitas
Fisik Berat (swrmming stress)
(PropotisProtectiveEffect to Prevent-oxidarive^
stress cai;;J-oy' itrenous pnyiiiit \iiii,ty (swimming
Sfress))ofeh Hairrudindan DinaHetianti(207-211).
Pusatdari BeberapaGelanggang
PolinomMiring(rhe centreof some skewpotynomialRings)
oleh Amir
Kamaf Amir(212-2181.
EfekKondisiHiperglikemik
terhadapstrukturovariumdan siklusEstrusMencit(Mus musculusL)
(Effectof
Hyperglikemic
conditionson ovarianstructure.andestpui)icte i'ui"r(Mus musculus
L))
oteh
'
Eva
Tyas
Utami,RizkaFitrianti, Mahriani,SusantinFajariyah
tZtg-iiil.
Generalized
ReducedGradientUntukoptimasiAmunisiKaliber57 mm c-60 Het (Generalized
Reduced
Gradientoptimizationfor Ammunitioncaiiber57 mm c-oo ieo-olii Muhammad
ev sjahid
vre"rv Akbar,
Bambang
WidjanarkoOtok,dan LestiAnggraini(225-23s)
^^vr
BeberapasenyawaHasillsolasidari Kulit BatangTumbuhanKedoya(Dysoxylum
gaudichaudianum
(A.
Juss.) Miq.) (Metiaceae)
compoundi tsotatedrroi-'dtem Bark of Kedoya
.(p9v9r7t
erqvlur
oaudichaudianum
(A. JussJ.Miq
oleh ruliran, i"yutr" Hamdani,RosyidMahyudi,
) (Meliaceie))
sri
HidayatiSyariefdan NurutHidayati(296-244i.
I
(AgusM amanAbadi dkk)
ConstructingF uzzyTime.............
190
ConstructingFazzy Time SeriesModel Using Combination of Table Lookup
and Singular Value DecompositionMethods and
Its Application to ForecastingInflation Rate
Agus Maman Abadir),Subanar2),
widodo2),SamsubarSaleh3)
1)Department
andNaturalSciences,
of Mathematics
Education,
Facultyof Mathematics
Yogyakarta Stat e Univ ersity
Student, Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Gadjah Mada University
2)Department
of Mathematics, Faculty of Mathematics and Natural Sciences,
Gadjah Mada University
3)Department
of Economics, Faculty of Economics and Business, Gadjah Mada University
t)Ph.D
ABSTRACT
Modellingfuzzy time sedes
Fuzry time seriesis a dynamicprocesswith linguisticvaluesasits observations.
datadevelo@ by someresearchers
useddiscretemembership
functionsandtablelookupmethodfurm taining
data.Thispaperpresents
a newmettrodto modellingfuzzytime seriesdatacombiningtablelookupandsingular
value decompositionmethodsusing continuousmembershipfunctions.Table lookup methodis used to
of fuing strengthmahix and QR
constuctfuzzy relationsfrom frainingdata.Singularvaluedecomposition
this methodis appliedto forecastinflationratein
factorizationareusedto rcducefuzz] relations.Furthermore,
Indonesiabasedon six-factors
one-orderfuz4r time series.Thisresultis comparedwith neuralnefivorkrnethod
methodgetsa higherforecasting
ratethantheneuralnetworkmethod.
andtheproposed
accuracy
inflationrate.
Keywords:Fuzrytimeseries,tablelookup,singularvaluedecompositioq
(Sah& Degtiarev2004, Chen
someresearchers
& Hsu 2004).
Fuzzy time series is a dynamic processwith
Forecastinginflation rate in Indonesia by
linguistic values as its observations.Many fuzzy model resultedmore accuracythan that
researchershave developedfizzy time series by regression method (Abadi et al. 2006).
model. Song & Chissom (1993a) developed Following the abovepaper,Abadi et al. (2007)
fuzzy time series model based on fuzzy also constructedflzzy time seriesmodel using
relational equation using Mamdani's method. table lookup methodto forecastinterestrate of
In their paper, determination of the fuzzy Bank Indonesiacertificate and the result gave
relation needslarge computation.Meanwhile, high accuracy. Abadi et al. (2OO8a,2008b)
Song & Chissom (1993b, 1994) also showed that forecastinginflation rate using
constructedfirst order fuzzy time series for
singular value method had a higher accuracy
time invariant and time variant cases.This thanthatusingWang'smethod.
model needs complex computation for fuzzy
Abadi et al. (2008c) constructed a
relationalequation. Furthermore,to overcome generalizationof table lookup method using
the weakness of the model, Chen (1996) firing strength of rules and applied it in
designedfuzzy time seriesmodel by clustering financial problems. Fuzzy time series model
of fuzzyrelations.
basedon a generalizedWang's method was
Hwang et al. (1998) constructedfuzzy time designedand it was appliedto forecastinterest
series model to forecast the enrollment in
rate of Bank Indonesiacertificate that gave a
Alabama University. Fuzzy time seriesmodei higher prediction accuracythan using Wang's
basedon heuristic model gives more accuracy method (Abadi et al. 2009a). Furthermore,
than its model designed by some previous forecasting interest rate of Bank Indonesia
researchers(Huamg 2001). Forecasting for certificate based on multivariate fuzzy time
enrollment in Alabama University based on seriesdata was done by Abadi et al. (2O09b).
high order fuzzy time series resulted high Kustono et aI. (2O06)applied neural network
prediction accuracy (Chen 2002). First order method to forecast interest rate of Bank
fuzzy titmeseriesmodel is also developedby
Indonesiacertificate.
INTRODUCTION
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Jurnal ILMU DASAR.Vol. I0 No. 2. Juli 2009 : j,90-198
In this paper, we will design fuzzy time
series model combining table lookup method
and singular value decomposition using
continuous membershipfunctions to improve
the predictionaccuracy.This methodis usedto
forecastinflation rate in Indonesia.
METHODS
are defined.If F(r) is the collectionof/, (r), i = l,
2, 3,..., then F(t)is called fuzzy time serieson
I (t) . Based on this definition, fuzzy time series
F(t) can be consideredas a linguistic variable and
/, (r) as the possiblelinguistic valuesof f. (r) . The
value of F(r) can be different dependingon time t.
Therefore F(r) is function of time r. Let{(r) be
QR factorization and singular value
decomposition
In this section, we will introduce QR factoizatiot
and singular value decompositionof matrix and its
propertiesreferredfrom Scheick(1997). l,et B be m
x n matrix and suppose mSn.
The QR
factorizationof B is given by B =QR, where Q is
m x m orthogonalmatrix and R = [R,, R,r) is m x n
matrix with m x m uppet triangularmatrix R,, . The
QR factorizationof matrix B always exists and can
be computed by Gram-Schmidt orthogonalization.
Any m x n matrixA can be expressedas
( l)
A =USV, ,
where U and V are orthogonal matrices of
dimensionsm x tn, n x /r respectively,and S is n x n
matrix whose entries are 0 except s,; = o,
i =1,2 ,...,r
wit h
6, 2 o, 2. . . > o. > 0,
r