Nguyen Cong Dilu vd Dig Tap chi KHOA HQC & CONG NGHE 95(07)' 107- 113
NHOM QUAN HE MO PHU THUOC THOI GIAN
VA iTNG DUNG TRONG MO HINH CHUOl THOI GIAN MO CO TRONG Nguyen Cong Dieu' , Pham Thi Ngan^
'\'ii)i Cong nghe Thong tin Vien Kil A CNVN 'Tviednfi IX" hQc Kmh li' A Quan iri Kinh doanh - DII Thdi Nguyen TOM TAT
Md hinh chuoi thdi gian md dang cd nhilu irn^ d^ing irong cong lic du bio, nhdt 1^ trong cic dy bao kinh te. Trong nhiing nim gan ddy kha nhieu cdng Irinh di dupc hoin thinh theo hudng nang cao dg chinh xic va giim khdi Iirpng tinh loin trong md hinh chudi thdi gian md nhu cic bii bio ciia Chen vi Hsu, Huarng. Kuo, Wu,.., H^u het nhCfng phumig phip tren deu dya vao ky ihuat lao cic nhdm quan he logic md cua Chen de lim giim khdi lupng Ilnh toin. Tuy nhien cic nhom quan he logic md niy chua de \ den thii ty \iiit hiijn ciia cic tap md nfin khi du bio cd thl xuit hipn cic thdnh phdn tap md xudt hipn sau thdi diem dy bio. TCr nhgn xcl tren. chiing tdi dua ra khii niem nhdm quan he logic md phu ihupc ihdi gian v;i ket hpp vdi md hinh chudi thdi gian md cd trpng ciia Yu de dua ra md hinh chuoi thdi gian md cd trpng mdi. Su dung md hinh niy chi ddi vdi md hinh chudi thai gian md bgc I. chiing ldi thu dupc ket qui dy bio sd lupng sinh vien nhap hpc lot hon so vdi ket qua cua Chen va Yu,
TCr khda: Chudi th&i gian ma. Mo hinh chuoi ih&i gian m& co trgng. Mdt sd thudt loan trong md hinh chuoi th&i gian ma
MO DAU
Truac da\. phuang phap chu yeu de phdn ti'ch chudi thdi gian Id su dyng cac cdng cu cua thdng ke nhu hdi quy, phan tich Furie va mpt vai cdng cy khdc. Nhung hieu qua nhdt cd le la phuang phap sir dyng md hinh ARIMA ciia Box-Jenkins. Md hinh nay da cho mdt ket qua kha tdt trong phan tich dir lieu vd dang dupc sii dung rat rpng rai trong thyc te. Tuy nhien, sy phirc tgp cua thudt todn da gdy khd khan khi ling dyng trong phan tich chuoi sd lieu, nhdt Id khi chudi sd lieu cd nhirng thay ddi phan anh sy phi tuyen ciia md hinh.
De vupt qua dupc nhiing khd khdn tren. gdn day nhieu tac gid da sii dyng md hinh chudi thdi gian md. Song va Chissom [1-3] da lan dau tien dua ra khai niem chuoi thdi gian md de dy bao. Chen [4] da cai tiln va dua ra phuong phdp mdi dan gian va hiiu hipu han so vdi phuang phdp cua Song vd Chissom.
Trong cdng trinh nay, chiing tdi dua ra khai nipm mdi la nhdm quan he logic md phy thupc thdi gian de ndng cao dp chinh xdc, Nhan thdy rdng khi xdc djnh nhdm quan he md, Chen chi xac djnh cdc cac tgp md cd ciing ve trdi trong mdi quan he md ma khdng de y din Ijch su xuat hien ciia tung thdnh
Tel 0904 288123. Email ncdieu@ioii ac.vi
phdn ciia nhdm quan he trong ve phdi. Trong dinh nghTa nhdm quan he md mdi chiing tdi djnh nghTa chi nhii'ng phan tir trong ve phai nao xuat hien trudc thoi dilm xuat hipn ciia thdnh phan ve trai ciia nhdm quan he thi mdi tham gia nhdm quan he logic md. Nhd cd mdi quan he logic md mdi nay tinh toan de giai md se don gidn hon vd cho ket qua tdt ban so vdi cdch xac dinh nhdm quan he md theo Chen. Trong rat nhieu cac cdng trinh sau ndy ciia cdc tdc gid khdc nhau deu dua tren vipc xac djnh mdi quan he md cua Chen de xdy dung giai thudt dy bao. Nhu vay vdi cdch cai tien mdi nay hy vpng se giiip tdng dp chinh xdc ciia du bdo trong cdc gidi thudt khdc nhau ciia md hinh chudi thdi gian md.
Bao cdo nay cd 4 muc. Sau phdn md ddu se la phiin dua ra cdc khai lien quan den md hinh chudi thdi gian md, dong thdi md ta cac thudt toan ca ban Men quan den dy bao thdng qua md hinh chudi thdi gian md. Dd la cdc thudt toan CO ban ciia Chen, md hinh cd trpng ciia Yu, Muc 3 dua ra mdt cai bien de xac djnh nhdm quan he logic md phu thudc vao qud trinh ljch sir. Md hinh cai bien chudi thdi gian md Muc thd 4 dp dung md hinh cai tien de dy sd sinh vien nhap hpc ciia Dgi hpc Alabama va xet tinh hieu qua cua thuat todn.
Nguyen Cdng Difiu vc; Dig Tgp chf KHOA HQC & CONG NGHI- 95(07): 107- 113 MOTSOKIIAINILM
Trong phan iiii). chimg la sc su' dyng khdi nipm \ii plurang phap dy bao ciia cliudi Ihdi gian md dirpc Song vii Chissoni [11-[3J phat tricn va md hinh Chen H | ciii lien de xay dung thugt lodii dy bdo cho chudi thdi gian, Mpt so dinh nghTa sau lien quan dcri chudi thdi gian md [4],
Dinh nghia I : Yd) (t -.,.0.1.2. ,) la mpt Igp con ciia R'. Y(l) Id tgp nen iren dd xac djnh cac tgp md fft) F(t) la tgp chira cdc tgp fft) (i = 1,2,..,). Khi dd ta gpi F(l) la chuoi th&i gum ni& xac dpih iron lap nen Y(t), Djnh nghia 2: Tgi cac thdi diem / vd /-/ cd ton lgi mpl mdi quan he md giiia l-'(i/ va F(l- 1) sao cho F(i) = F(i-l) * R(t-1. I) Irong dd * Id k\' hipu ciia mpt toan tii xdc djnh tren tap md. R(t-I. I) Id mdi quan h4 md. Ta ciing cd the k\' hipu mdi quan he md giua F(l) va F(t- l}hin%F(l-l) ->F<ti
NIU ddt F(t-!) = A, va F(t) = A, thi ta ky hipu mdi quan he logic ma giira chimg nhu sau: A,
—> Al Viet nhu the nay co the hieu la tap md A, dupc suy ra tir A,.
Dinh nghia'3: Nhdm cac mdi quan he logic md.
Cac mdi quan he logic cd the gpp Igi thanh mpt nhdm neu trong ky hieu tren, ciing mpt ve trdi se cd nhieu mdi quan he tgi ve phdi.
Thi dy neu ta cd cac moi quan he: A, -*-Ai,, A, -*-A.„
thi ta cd the gpp chimg thanh nhom cdc moi quan he logic ma sau: A, -^Ak.A,,, Binh nghia 4: Gia sd F(t) suy ra tir F(t-l) vd F(l) = F(l-I) * R(i-}, I) cho mpi / Ndu R(t-1.
I) khdng phu thupc vdo / thi F(i) dupc gpi la chudi thdi gian md dirng, cdn ngupc lai ta cd chudi thdi gian md khdng dung.
Binh nghia 5: Gia su F(t) suy ddng thdi tir F(t-}}. F(l-2).... F(i-m) m>0 vd Id chudi thdi gian md dimg. Khi dd mdi quan he md cd the viet dupc F(l-!). F(l-2) F(l-m)-^ F(t) va gpi dd la md hinh dy bao bdc m ciia chudi thdi gian md.
MQT SO THUAT TOAN TRONG MO HiNH CHUOI THCJI GIAN MCi
Thugt todn ciia Song vd Chissom khd phiic tgp vi phdi tinh gia trj max-min trong mdi quan hp md. Thugt todn ciia Chen [4] cai tiln lluigt loan ciia Song-Chissom do da su dyng khai iiipni nhdm cac moi quan hp logic md, Yu [16] dd xay dyng md hinh chudi thdi gian md cd Irgng dc xir ly sy Idp Igi cdc tgp mo .\iial hipn trong ve phdi ciia nhom quan hp ««
md. Doi vdi thd tu xual hipn ciia cac tap md trong nhdm quan hp logic md ta gdn chiing vdi trpng sd khdc nhau. Phuang phdp nay trong da so cdc trudng hpp cho dp chinh xdc dy bdo cao ban. Dudi day md ta thudt toan cua Yu trong md hinh chudi thdi gian md bgc nhat.
Budc 1: Xdc djnh tap U bao gom khoang gid trj ciia chudi thdi gian. Khoang nay xac djnh tir gia trj nho nhat den gia trj ldn nhdt c6 the ciia chuoi thdi gian va chia khoang nay thdnh cac dogn de xdc djnh tgp cdc bien ngdn ngir.
Budc 2; Xac djnh cdc tap md xdc djnh tren cac bien ngdn ngir tren va md hod cdc gid trj Ijch sd.
Budc 3: Thiet Idp mdi quan he md va nhdm quan hp md. Trong nhom quan he md thiet Igp todn bp lich sd xudt hipn cdc tgp md cd trong ve phai ciia mdi quan hp logic md theo thu ty xuat hipn. Thi du neu cd cac quan he md sau: A, —> A: A, —* .-Xi. A, -*A, , A, ->A}
, A, -> .-t, thi nhdm quan he logic md cd dgng A, -^A:.A,A,,A3.A,
Budc 4 , Dy bdo nhu thudt todn cua Chen theo cdc lugt khdc nhau.
Budc 5 : Neu \a\' ra cac trudng hop nhu cac Trudng hpp 1 vd 3 ciia thugt toan Chen thi phdn gidi md dupc giu nguyen. Cdn rai vdo Trudng hop 2 cd xudt hien nhdm cdc quan he logic md A, ->A,i.A,2.-. A,p, va m,/, m,2,--f>Jik Id diem giiia ciia cdc dogn tuang ihig vdi cac bien ngdn ngii' «,, u,2,...u,k ta se gdn cdc trpng 1, 2. ...,k khi giai md gia tri dy bao A, theo cdng thdc sau:
Ixm,, •+2xm. . + k>
l + 2 + ... + k 10
Nguyen Cdng Dilu vd Dtg Tap chf KHOA HQC & CONG NGHE 95(07), 107- 113 THUAT T O A N C A I BIEN MO HINH
CHUOI THCJI GIAN MCf CO TRQNG Trudc het ta dinh nghTa lai nhdm quan hp logic md Nhdn thay rdng trong Binh nghia 3 nhdm quan he md khdng tliay xac djnh thdi gian trong mdi phdn tir ciia tap md A,. Chinh vi vdy khi nao cd nhdm quan hp logic md dgng A, -> A,/.A,?... A,p. thi ta xir ly giong nhu khi dy bao gidi md cho phan tir .1, khdng ke phan tu nay ung vdi gid tri / khac nhau trong chudi thdi gian md F(t). Dimg ban ta phai viit rd phy thudc thdi gian Ffi-i) • .), (I). Khi dd trong \c phai ciia nhdm quan hp ma A, ->A,i,.-l,: .1,,, phai viet lai thanh A,(t) -^ A,i(tl).A,:(l2) -Ii/.dp) Khi dd theo md hinh ciia Chen, du bao ciia phan tu Aft) Men quan den cac phan tu A,,(ll),A,;(l2j A,,,(lp) ma khdng chii y den thai diem xudt hien ciia cdc phdn tu ndy. Nhu vgy cd the cd nhung phdn tii trong ve phdi xuat hien sau thdi diem i. tii'c la cd thdi diem chdng hgn t2 > t ma phan tu A,2(t2) cung tham gia vao dy bao, Dieu ndy td ra vd ly nen chi chap nhgn nhiing phan tu nao cd thdi diem xudt hien trudc / ma thdi. Do vay, ta sS xdc djnh Igi nhdm quan he logic md qua djnh nghTa sau.
Dinh nghia 6 (NItdm quan he logic m&phu thupc th&i gian): Mdi quan he md ta deu xdc djnh tir quan he F(t-J)-*-F(t). Neu nhu tren ta ddt F(t) - A,(t) vd F(t-i) = Aj (t'lj thi ta cd mdi quan he Aj (t-lj -> A,(t). Neu tgi thdi diem I ta cd cdc mdi quan he md: A/t-J) ->
Aft). A/tl-J) '->• A,2(l!) A,(tp-l) -*• A,/lp>) vdi cdc gid tri //. t2, ...tp <l (tdc Id cac mdi quan he md tren xdy ra tgi cac thdi diem trudc A/i-1) ->• Aft) ) thi la cd thl nhdm cdc moi quan he logic md thdnh
A/t-I)^Aft).A,,(tl),A,2(l2) A,p(lp) Vd mdi quan he tren dupc goi Id nhdm quan he logic mor phu thupc th&i gian. Thyc chat each ghi A/t) vln la mpt tap md Aj dd xac djnh nhung chi mudn nhdn manh tap md ndy xudt hipn tgi thdi dilm t ma thdi.
Tir dinh nghTa nhdm quan he logic nay, chiing tdi dua ra thugt todn vl ca ban gidng nhu thuat todn chudi thdi gian md cd trpng ciia Yu nhung su dung nhdm quan he md phy thupc
thdi gian thay cho nhdm quan he md chung cua Chen. Thuat toan dd bao gdm cac budc sau:
1. Xdc dinh tap nen. Tap nen U dupc xdc djnh nhu sau: ldy gia trj ldn nhdt fma, va nhd nhdt /„„„ CLia chudi thdi gian va U ^[f„„„-fi, f'l'.iK'^fJ Irong do f 1/2 Id nhdng gia trj duong
nao dd. Chia dogn U thdnh m khoang con bang nhau H/. U2,...U„,.
2 Xdy dyng cac tap md A, tuang iing vdi cac khodng con nhu trong trong budc 2 va sir dung cac hdm thupc tam gidc cho mdi khodng con ciia phep chia va md hod cdc gid trj chudi thdi gian.
3. Xay dyng mdi quan he md vd xdc djnh nhdm cac quan he logic md theo Djnh nghia 6.
4. Dy bdo chudi thdi gian md theo cac luat sau:
Ludt I. Neu nhdm quan he md A, -> 0 thi gia trj dy bao md tai thdi diem t se la A, Lugt 2: Neu nhdm quan he logic mo cd dang A,
—>Af, gid tri dy bao md tgi thdi diem I se la Ak Lugl3: Neu mdi quan he md bgc cao cd dang A, -> Aii,A,2... A,p, thi gia tri du bao se la:
A,,.A,2... A,p
5. Gidi md dua vao cac luat dy bao tren, Ludt 1: NIU nhdm quan he md ciia la rdng vd gia su m,i va m,2 la diem gitia cua khoang u,i va u,2 khi dd gia tri dy bdo ciia F(l) Id gid trj trung binh ciia hai diem giiia tren, tuc Id:
forecast = (m,i + m,2)/2 Lugt 2: Neu nhdm quan he logic md cd dang A, -^ Ak vd neu diem giua ciia khoang «i Id mtthi forecast^ mk
Lugt 3. NIU mdi quan he md bac cao cd dang A,2 -> A,,,A,2.. A,p, thi gid tri du bdo se Id:
forecast Ixm^i -i-2x m,, -l-....-(-t X m,^
~ l + 2 + ... + k vdi m,i m,2,...m,p la diem gida cua cac doan tuong dng.
DU BAO SO LLTONG SINH VIEN NHAP HOC
De xem xet tinh hieu qud cua djnh nghTa mdi vl nhdm quan he logic md, chung tdi sii dyng dii lieu ciia bai bao Chen[4] vl sd luong hpc 109
Nguyen Cong.Dicu n) Dig Tap chl KHOA HQC & CONG NGHJ 95(07): 107-113 sinh nhap 'ipc c u a Trircmg dai
theo bang sau Rdng 1 Nam S<
/ C " / 19'2 irs
; 9 ' j 1975 19~(, 19- l9-.f 1979 19S0 1981
:
. So lirgng!
i sini) vien 13055
•13563 13867 14696 15460 15311 15603 15861 16807 16919 .16388
ligc Alabama
ilnh vli}n nhqp HQC N9m 19X2 I9SS 19,14 19H5 19m 19,1"
19,111 1989 1990 1991 1992
So sinh vien 15433 15497 15145 15163 15984 16859 18150 18970 19328 19337 18876 Thuat todn cdi licn cho chudi thdi gian md bao gdm cac budc sau day vd dp dyng cho so lieu tai bang 1.
Bir&c I. Xay dung tap nen U, Xdc djnh gid tri Idn nhal va nho nhat cua chudi thdi gian tren Id 19337 vd 13055 sinh vien. Do vdy tap nen Bang 2, Cdc nhom
U dupc xac djnh la gia trj trong khoang [13000,20000], Ta se chia U thdnh 7 khoang Ul, U2, ..„ U7 vdi dp rpng la 1000 nhu trong [4], nhu vgy cac khodng se Id; U| = [13000,14000], U2 = [14000,15000], , . . , u-, = [19000,20000].
Budc 3: Xdy dyng cdc lap md xac djnh tren cdc bicn ngdn ngd Id cdc khoang dd chia.
Trong budc ndy ta xdc djnh lai cdc tap mb A, tuang ling vdi tirng khoang va cd the gdn lai cac gia trj ngdn ngCr cho tdng tgp md ndy, Cac tap md A. I 1,2. .7 dupc djnh nghTa thdng qua cdc ham thupc de dan gian cd dgng hinh ndn nhan 3 gid iri 0, 0.5 va 1 va dupc viet nhu sau:
A, = l/u, + 0.5/U2 + 0/ui +....+ 0/U(. + O/uj A2 = 0.5/u, + J/U2 + O.5/U3 +...+ 0/u^
+ 0/ii~
A- = 0/ui + 0/u: + ,. + 0/Ui + 0.5/Uf. + l/ii- moi quan he m&
Gia T r i 13055 13563 13867 14696 15460 15311 15603 15861 16807 16919 16388 15433 15497 15145 15163 15984 16859 18150 18970 19328 19337 18876
Thiri diem t=l 1-2 1=3 t=4.
t=5 t=6 t - 7 t ' 8 1-9 t=IO t = l l t-12 1-13- t=14 1=15 t=16 1=17 t=l8 t=l9 P20 t-21.
t-22' G [ a T r i mir A l A l A l A2 A3 A3 A3 A3 A4 A4 A4 A3 A3 A3 A3 A3 A4 A6 A6 A7 A7 A6
Nh6m QH mo- Chen
AI,A2 A1,A2 AI,A2 A3 A3,A4 A3,A4 A3,A4 A3,A4 A3,A4,A6 A3,A4,A6 A3,A4,A6 A3,A4 A3,A4 A3,A4 A3,A4 A3,A4 A3,A6 A6,A7 A6,A7 A6,A7 A6,A7
N h 6 m Q H L G m6 Yu
A1,A1,A2 AI,A1,A2 A1,A1,A2 A3
A3,A3,A3.A4,A3,A3,A3,A3.A4 A3,A3,A3.A4.A3,A3,A3,A3,A4 A3,A3,A3,A4.A3,A3,A3.A3,A4 A3,A3,A3.A4.A3.A3,A3.A3,A4 A4,A4,A3,A6
A4,A4,A3,A6 A4,A4,A3,A6
A3,A3,A3.A4,A3,A3,A3,A3,A4 A3,A3,A3,A4,A3,A3,A3,A3,A4 A3,A3,A3,A4.A3,A3,A3,A3,A4 A3,A3,A3,A4.A3,A3,A3,A3,A4 A3,A3,A3,A4,A3,A3,A3,A3,A4 A4,A4,A3,A6
A6,A7 A6,A7 A7,A6 A7,A6
Nh6m Q H logic mcr m6i
A l A l . A l A1,A1.A2 A3 A3 A3,A3 A3.A3,A3 A3,A3,A3,A4 A4 A4,A4 A4.A4,A3 A3.A3,A3,A4,A3 A3,A3,A3,A4,A3,A3 A3,A3,A3,A4,A3,A3,A3 A3,A3.A3,A4,A3,A3,A3,A3 A3,A3,A3,A4,A3,A3,A3,A3,A4 A4,A4,A3,A6
A6 A6,A7 A7 A7,A6
Nguyen Cong Dieu vt
Nam 1971 1972 W73 1974 1975 1976 1977 1978 1979 1980 1981 1-982 1983 1984 1985 1986 1987 1988 1989 1990 1-991 1992 MSE
Algorithms/MSE MSE
iBig Tap chi KHOA HOC & CONG NGH$
Bang 3. Kel qua du bdo cua cdc plnmng phdp khdc nhau S6 lu-Q-ng S V Chen Method Y u Method
13055 13563 13867 14696 15460 15311 15603 15861 16807 16919 16388 15433 15497 15145 15163 15984 16859 18150 18970 19328 19337 18876
14000 14000 14000 15500 16000 16000 16000 16000 16833 16833 16833 16000 16000.
16000 16000 16000 16833 19000 19000 19000 19000 407507 Bang 4. So sdnh hieu qud Thuat toan Chen
407507,3
14000 14000 14000 15500 15789 15789 15789 15789 17000 17000 17000 15789 15789 15789 15789 15789 17000 19167 19167 18833 18833 407322 IhudI lodn Thuat toan Y u
407321.5
95(07): 107- 113
Cdi tien 13500 13500 14000 15500 15500 15500 15500 15900 16500 16500 16000 15767 15690.5
15643 15611 15789 17000 18500 19167 19500 18833 267438
Thuat toan cai bien 267438.4 Budc 4. Xdc djnh mdi quan hp md vd nhdm
quan he md bdc cao
Theo djnh nghTa phan tren ta lap chudi thdi gian md tuang ung vdi cdc tap md d tren vd xdc djnh mdi quan he md tai thdi diem /
=/,2, ...22. Cd the thay ngay dupc cdc mdi quan he ddu tien nhu sau: As-> A), A/-* A/, A,^A:, .A—^A,,.
Til' day xdc dinh nhdm cdc mdi quan hp md theo Djnh nghTa 6 d phan tren. Thi dy ta cd the nhgn dupc mpt nhdm quan he md Men quan den ve trdi A} nhung tai thai diem khdc nhau 1=7, t=8, 1=9 ta lai cd nhdm quan hp logic md khac nhau: Ai(7)-> Ai, Aj, Ai(8)-^Ai.A3.A3:Ai(9)-*-A},A,,Ai,A4 Todn the cac nhdm quan he md se dupc the hien dudi Bdng 2.
Nhin vdo bdng tren, ta thay nhdm cdc quan he md ctia phuang phdp cdi tiln phy thudc vdo tirng thdi dilm chd khdng cd djnh nhu cdc phuang phdp ciia Chen hay cua Yu,
Budc 5. Du bao vd gidi md theo cdc lugt da md td d tren cd tinh den trpng sd, Ket qua tinh todn ciia phuang phap cdi tien vd cdc phuang phap khac duoc dua ra trong bdng 3.
De so sanh cdc ket qua du bdo theo cac phuang phap khac nhau, ta sir dyng sai sd trung binh binh phuang MSE theo cdng thirc;
t^fi'gif
MSE = -^
n
trong d d / la gid trj thyc cdn g, Id gia tri du bao.
Ket qud sai sd theo cac phuang phap dupc dua ra trong bdng 4.
Kit qua tinh toan cho thay trong trudng hpp rdt don gidn chiing ta da thu dupc sai sd chi bdng nua so vdi thudt todn ca bdn trong khi thugt toan cd trpng cua Yu khdng khd han thudt toan Chen la bao.
Nguyen Cong Dicu rd Dig Tap chl KHOA HQC & CONG NaH$ 95(07): 107-113
a i l m e n t F o r o c a s t l n
-^^- ^
5 8 i
i l
J 8 9 9 8 & e 9 SHinh 1: Dd thj kil qua dir Hinh ve 1 sp sanh ket qua tinh toan theo phuang phdp cdi tien vd phuang phap ciia Chen vd Yu. Cd the nhdn thay dd thj ciia phuang phap cai tien phdn dnh xu thl tdt han so vdi hai phuang phap Chen vd Yu, KET LUAN
Ban bdo cdo ndy dua ra mpt cdi bien mdi de sd dung dupc trong md hinh chudi thdi gian md Tuang ty nhu cdi bien ciia Yu khi xdy dyng nhdm quan he logic md dd tinh den su lap lgi ciia cdc gia trj triing nhau ben ve phdi vd gdn trpng khac nhau cho tung vi tri ciia gid tri dd, chiing tdi xet thdi diem xudt hipn ctia tung gia tri ve phai mdi quan he logic md.
Nhu vgy tgi tdng thdi diem, nhdm quan he logic md ddi vdi ve trai gidng nhau nhung Igi khdc nhau d ve phdi. Vdi djnh nghTa mdi ndy ve nhdm quan hp logic md phy thupc thdi gian, chua can sii dyng cdc phuang phdp ndng cao dp chinh xdc khdc nhau nhu phdn doan Igi, sir dung chudi thdi gian md bgc cao hay md hinh hai nhan td [5-9], ket qua da tdt han rat nhieu so vdi thugt todn ca bdn ciia Chen.
Nhdm cac qugn hp logic md Id khai nipm ca bdn de cai tien cac thuat todn trong md hinh chudi thdi gian md. Chimg dupc su dyng trong hdu hit cdc cdng trinh sau nay ciia cac tac gia khac nhau, Chinh vi vdy, sir dyng nhdm quan he md mdi ndy trong cdc phuang 112
hdo kel qud Iheo cdc thugt lodn
phap cai lien khdc nhau hi vpng se Idm tdng hipu qua ctia cac thudt todn ndy.
TAI LIEU THAM KHAO [1], Q. Song. B.S. Chissom, •Fuzzy Time Series and its Model", Fuzzy set and system, vol. 54. pp.
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[2]. Q. Song, B.S. Chissom. "Forecasting Enrollments with Fuzzy Time Series - Part I,"
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[3]. Q. Song. B.S Chissom, "Forecasting Enrollments with Fuzzy Time Series - Part !I,"
Fuzzy set and system, vol, 62, pp. 1-8, 1994, [4]. S.M. Chen. "Forecasting Enrollments based on Fuzzy Time Series," Fuzzy set and system, vol.
81. pp. 311-319. 1996.
[5]. S. M. Chen, '"Forecasting Enrollments based on hight-order Fuzzy Time Series", Int. Journal:
Cybernetic and Systems, N.33. pp. 1-16, 2002.
[6], K.Huamg. "Heuristic models of fiizzy time series forecasting". Fuzzy sets and Systems, V.123.PP 369-386. 2001.
[7]. I,H. Kuo, el al, "An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization". Expert systems with applications, 36(2009)6108-6117.
[8]. LW. Lee, L.H. Wang, S.M, Chen, H.C. Uu
"Handling forecasting problem based on two-factors hight-order fuz:^' time series", IEEE Transactions on Fuzzy Systems, (2006) 14(3)468^77.
[9]. Nguyin Cdng Dieu "Mpl thugt loan mdi cho md hinh chuoi thai gian md heuristic trong dy bao chdng khoan", Bdo cdo tai Dgi hpi Toan hpc loan
Nguyin Cdng Dilu vd Dig Tgp chi KHOA HQC & CONG NGHE 95(07): 107 - 113 qudc nam 8-2008 lai Quy Nhan. Bdi giii dang [10]. H.K., Yu "Weighted fuzzy time series t^i lap chi Khoa hpc \h. Cdng nghp, Vipn models for TAIEX forecasting ", Physica A, 349 KH&CN VN. (2005) 609-624.
S U M M A R Y
T I M E - D E P E N D E N T F U Z Z Y L O G I C A L R E L A T I O N S H I P G R O U P S A N D A P P L I C A T I O N IN W E I G H T E D F U Z Z Y T I M E S E R I E S M O D E L S
Nguyen Cong Dieu'", Pham Thi Ngan^
Imtiiuie (if Information Technology - VAST College of Economics and Business Adminislraiion - TNU Fuzzy time series models have m:iii\ applications in forecasting, especially in ihe economic forecast In recent years many works have been completed towards improving accuracy and reducing the amount calculated in fuzzy lime series models such as the article by Chen and Hsu, Huamg, Kuo, Wu..., Most methods are based on the technique of fuzzy logical relationship groups (Chen [4]) to reduce the amount of computation However, the fuzzy logical relationship groups are used without attention to their order of appearance and the occurrences of the components in the right side of the fuzzy logical relationship groups. From this remark, we propose fiizzy logical relationship groups depends on temporal order. Thanks lo the concept of time dependent fiizzy logical relationship groups and using the weighted fuzzy lime series model, we have established an effective algorithm for predicting time series. The new model is applied for enrollments' forecasting of the University of Alabama. The obtained peforments shows that the proposed method give better accuracy than Chen and Yu models.
Keywords: Fuzzy lime series. Weighted fuzzy time series. Time-dependent Fuzzy Logical Relationship Group. Some algorithms m fuzzy lime series models.
Ngdy nhdn bdi. 25/6/2012,, ngdy phdn bi4n: 4/7/2012, ngdy duyit ddng:27/7/2012
Tel: 0904 288123, Emad ncdieu@ioil ac.v,
