Nguyen Cong Dieu vd cs Tap chi KHOA HOC & CONG NGHE 72(10): 59-65
CAI BIEN THUAT TOAN BAC CAO CUA SINGH VA iTNG DUNG TRONG Dir BAO CHUOI T H O I GIAN
Nguyin Cong Dilu', Tran Thanh Thuong'
'Vien Cong nghe thong tin - \ AST, 'Dgi hoc TImi Nguyen
TOM T A T
Mo hinh chudi thoi gian mo dang c6 nhiSu ling dung trong cong tac du bao. Tuy nhien ket qua du bao ciia cac phuong phap dl xuSt con chua cao. Do do viec tim toi cac mo hinh co do chinh xac cao hon va thuat toan don gian hon dang la mgt uu tien. Trong nhung nam gan day mgt so cong trinh da dugc hoan thanh theo huong nang cao do chinh xac va giam khoi lugng tinh toan trong mo hinh chu6i thai gian mo nhu cac cong trinh cua Chen va Hsu, Huarng, Singh,... Mgt each tiep can khac cho mo hinh chu6i thai gian mo la su dung nhung ky thuat khac trong khai pha du' lieu nhu phan cum, mang no ron,... dl xay dung mo hinh. Ngoai ra con co thi sir dung cac thuat toan bac cao du bao. Singh [10] da de xuat mgt thuat toan nhu vay.
Trong bai bao nay, chiing toi cai tiln thuat toan bac cao ciia Singh cho mo hinh chuoi thoi gian mo.
Cai tiln nay da cho thSy hieu qua dugc tang len ro ret thong qua cac tinh toan so cho chuoi thai gian.
Til' khoa: Chuoi thdi gian md. bien ngon ngit. moi quan he md
MCSDAU • Chuoi thai gian ma va mo hinh chuoi thai
gian ma bac nhat do Song va Chissom [4]-[6]
phat trien tu nam 1993. Sau cong trinh nay, mot loat cac bai bao ciia nhieu tac gia khac nhau tiep tuc dua tren y tuang nay de du bao chuoi thai gian va ung dung trong nhieu Ihih vuc khac nhau nhir du bao dan so, tai chinh, nhiet do, nhu cau dien, vv... Gan day co rat nhieu tac gia lien tuc cai tien mo hinh chuoi thai gian mo de dir bao dat ket qua chinh xac hon.
Chen [7] da dua ra phuang phap moi dan gian va huu hieu hon so voi phuong phap ciia Song va Chissom bang each sii dung cac phep tinh so hoc thay vi cac phep tinh hgp max- min phiic tap trong xu ly moi quan he ma.
Phuong phap ciia Chen cho hieu qua cao hon ve mat sai so du bao va do phiic tap ciia thuat toan.
Nhieu cong trinh tiep theo da sir dung each tiep can nay de du bao cho chuoi thoi gian.
Mot trong cac huong dugc phat trien la su diing moi quan he ma bac cao trong mo hinh chuoi thai gian mo. Singh [10] da dua ra mgt thuat toan moi kha don gian de du bao so lugng sinh vien nhap hgc va san lugng miia
Tel: 0944550008: Email: lhuong.cym(aj,gmail.com
mang trong nong nghiep bang each su dung sai phan cac thong so nhu la moi quan he ma de du bao. Phat trien tiep tiic theo huong sir dung cac thuat toan don gian de du bao, trong [10] Singh da sir dung thuat toan nay cho mo hinh chuoi thai gian ma bac cao.
Trong bai bao nay, chiing toi cai tien thuat toan bac cao ciia Singh nham tang mire do chinh xac ciia du bao.
M O T SO KHAI NIEM
Trong phan nay, chiing ta se su dung khai niem va phuong phap du bao ciia chuoi thai gian ma dugc Song va Chissom [4]-[6] phat trien va dugc Chen [7] cai tien de xay dung thuat toan dir bao cho chuoi thai gian.
Gia sir U la khong gian nen: U = i U|,U2,....,u,„r.
Tap A la ma tren khong gian nen U neu A dugc xac dinh boi ham: |.IA : U —> [0.1]
I^A dugc ggi la ham thugc (Membership function). Con voi bat ky mgt phan tir u nao CLia A thi ham |J.A (U) dugc ggi la do thugc ciia u vao tap mo A.
Tap mo A tren khong gian nen U dugc viet nhu sau:
^ ^ / M i l i l + ILil}iA +
M ,1 ill,,)Nguyen Cong Dilu va cs Tap chi KHOA HOC & CONG NGHE 72(10): 59-65 Mgt so djnh nghTa sau lien quan den chuoi
thai gian ma [5].
Binh nghia 1: Y(t) ({ =...0,1,2,...) la mgt tap con ciia R'. Y(t) la tap nen tren do xac dinh cac tap mo f,(t). F(t) la tap chua cac tap fft) (i = 1.2....). Khi do ta ggi F(t) la chudi thdi gian mdxac dinh tren tap nen Y(t).
Binh nghia 2: Tai cac thoi diem / va /-/ co ton tai mgt moi quan he mo giu'a F(tJ va F(t-l) sao cho F(t) = F(t-l) * R(t-1. t) trong do * la ky hieu cua mgt toan tir xac dinh tren tap mo.
R(t-1. t) la mdi quan he md. Ta cung co the ky hieu moi quan he mo giua F(l) va F(t-l) bang F(t-l) -^ F(t).m\i dat F(t-l) = A, va F(t) = A, thi ta ky hieu mdi quan he logic md giua chiing nhu sau: A, —>-A,
Binh nghia 3:
Gia SLi- F(t) suy ra tir F(t-l) va F(t) = F(t-l) * R(t-1. t) cho mgi t. Neu R(t-1, t) khong phu thugc vao / thi F(t) dugc ggi la chu6i thai gian mo diing, con ngugc lai ta co chuoi thai gian mo khong diing.
Binh nghia 4:
Gia sir Fit) suy d6ng thoi tir F(t-l). F(t-2) F(t-m) m>0 va la chuoi thai gian mo dirng.
Khi do moi quan he ma co the vi^t dugc F(t-l).
F(t-2) F(t-mj-^ F(t) va ggi do la mo hinh du bao bac m ciia chuoi thai gian ma.
THUAT TOAN BAC CAO CUA SINGH Singh da phat trien cac phuang thuc tinh toan de tim ra mgt phuong phap tilp can t6t hon nham khac phue nhung nhugc diSm ciia hien tai ciia mo hinh chuoi thai gian ma bac cao.
Su don gian ciia phuang phap nay n§iTi a ch6 su dung su sai phan de thay thi cho su tinh toan phue tap trong quan he logic ma.
Phuong phap ciia Singh nhu sau:
Budc 1: Xac dinh tap nen. Tap nen U dugc xac djnh nhu sau: lay gia tri Ion nhit f,„a^ va nho nhat f,„i„ cua chuoi thoi gian va U =[f,„,„- f|- f^nax+f":] trong do f.fi la nhung gia tn duong nao do.
Budc 2: Chia doan U thanh m khoang con bang nhau Ui. U:....u„,.
Bir&c 3: Xay dung cac tap mo A, tuong irng voi cac khoang con nhu trong trong buoc 2 va
sii' dung cac ham thugc tam giac cho moi khoang con cua phep chia.
Bw&c 4: Mo hoa cac gia tri cua chuoi thai gian va thiet lap moi quan he ma theo quy tac: neu A, la gia tri mo hoa tai thai diem / va A, la gia trj mo hoa tai thoi diem tiep theo t~l thi ta CO moi quan he mo A, —> Aj nhu tai Dinh nghTa 2. A, la trang thai hien thai con A, la trang thai tiep theo.
Bir&c 5: Tinh toan va dy bao dua tren cac moi quan he mo dugc thiet lap
Thiet lap mdi quan he md cua cdc bgc khdc nhau nhir dua ra dudi day:
(i) Neu cho thoi diem t - 2, t - 1 va t , gia tri chuoi thai gian dugc mo hoa tuong irng la A,I, Aj va Aj, khi do c6 moi quan he ma bac 2 nhu sau: A,i, A, —* A,.
(ii) Neu cho thoi diem t - 3, t - 2, t - I va t, gia tri chuoi thai gian dugc ma hoa tuong img la Ai2, A,i, A, va Aj, khi do co moi quan he mo bac 3 nhu sau: A|2, A,i, A, -^ Aj.
(iii) Tuong ty nhu vay neu cho thoi diem t - 4, t - 3, t - 2, t - I va t, gia trj chuoi thai gian dugc mo hoa tuong ung la A,,, A,2, A,i, A, va AJ, khi do CO moi quan he ma bac 3 nhu sau:
A,3, A,2, Ail, A, - ^ AJ.
Theo each tuong ty chiing ta co the xac dinh dugc cac cao hon nhieu nhu: bac nam, bac sau, bac bay, bac tam va cac moi quan he mo tuong irng.
Tinh todn cdc tham sd d\ n = 2, 3. 4,. . . cua cdc bgc khdc nhau:
(i) khao sat mgt toan tii' khac d" yi = j Vyi | va dugc dinh nghTa la
d-E,= I E i - E i - l | d^E,= |d^Ei-d-Ei-l|
d^Ei = | d ' E i - d - ' E i - l | d ' E i = | d ' E i - d ' E i - l | d ' E i = | d ' E i - d - E i - l | d ' E i = !d''Ei-d''Ei-l|
d"Ei=id"-'Ei-d"-'Ei-l|
Dodo, d ' E i = | | E i - E i - l | - | E i - l - Ei-2 || and d'Ei=|||Ei - E i - l | -I Ei -I - E i - 2 || - ||Ei-1 - Ei -2| - |Ei -2 - Ei -3 III and d'Ei = ||||Ei- Ei-I|
- | E i - l - E i - 2 | | - j j E i - l - Ei-2 I - | E i - 2 - Ei-3 III - | | | E i - l - Ei-2 I - | E i - 2 - Ei-3 jj - ||Ei-2-
Nguyen Cong Dieu va cs Tap chi KHOA HOC & CONG NGHE 72(10): 5 9 - 6 5
Ei-3| - | E i - 3 - Ei-4 |||| va cu' tiep tuc nhu vay.
(ii) So buoc w cua du bao mo = int (so lugng khoang / 2) thu dugc la: int (7/2) = 3.
Tinh todn vd du bdo:
Mgt so ky hieu dugc sii' dung dugc dinh nghTa nhu sau:
[*Aj ] la khoang tuong irng Uj ma ham thugc trong Aj dat gia trj Supremum
L[*Aj ]la gioi han duoi ciia khoang Uj U[*Aj ] la gioi han tren ciia khoang Uj l[*Aj]la do dai khoang Uj trong do ham thugc ciia Aj dat Supremum
M[*Aj ] la gia tri trung binh ciia khoang Uj trong do ham thugc cua Aj dat Supremum Doi voi mgt moi quan he ma Ai ^ Aj:
Ai la gia trj ma tai thai diem t-l Aj la gia tri ma tai thai diem t
Ei la gia tri ciia chuoi thai gian tai thai diem t-l Ei-1 la gia tri ciia chuoi thai gian tai thai diem t-2 Ei-2 la gia tri ciia chuoi thai gian tai thai diem t-3 Ei-3 la gia tri ciia chuoi thai gian tai thai diem t-4 Ei-4 la gia tri ciia chuoi thai gian tai thai diem t-5 Fj la gia tri du bao ciia chuoi thai gian tai thai
diem t
O day, sir dung mo hinh bac 2 voi cac gia tri ciia chuoi thai gian tai thai diem t - 2, t - 1 cho khung quy tac de thuc hien ve moi quan he logic ma, Ai —» Aj, voi Ai, trang thai hien hanh, la ma hoa so lieu tai thai diem t - 1 va Aj, trang thai ke tiep, la ma hoa so lieu tai thai diem t.
Thuat todn tinh toan:
Doi voi du bao chuoi thai gian ma ciia mo hinh bac hai, co the dy bao tir nam thir ba ciia dii' lieu chuoi thai gian va do do can phai dat n = 2 va t = 3.
Dat n = 2, t = 3
For t = 3 den T (ket thiic dir lieu chuoi thai gian) Thu dugc ma quan he tii' thai diem t - l(Ai) den t (Aj): Ai —• Aj
R = 0 v a S = 0 Tinh toan
d"E,= |d"-'E,-d"-'E,_,|
X,= E, + d"E,/2 ' XX,= E, - d"E,/2
Y,= E, + d"E, YY,= E, - d"E, P, = E, + d"E,/4 PP, = E, - rf'E,/4 0,= E, + 2*d"E, C)C), = E, - 2*d"E, G,= E, + d"E,/6 GG, = E, - d"E,/6 H,= E,+ 3*d"E, HH, = E,-3*d"E,
lfX,> L [ * Ajjand X, < U [*Aj]
Then R = R + X, and S = S + I If XXi> L [* Aj] and XX, < U [* Aj]
Then R = R + XX, and S = S + 1 IfY, > L [ * Ajjand Y , < U [*Aj]
Then R = R + Y, and S = S + 1 If YY, > L [* Aj] and YY, < U [* Aj]
Then R = R + YY, and S = S + 1 If P, > L [* AJ] and P, < U [*A,]
Then R = R + P, and S = S + 1 If PP, > L [* AJ] and PP, < U [* Aj]
Then R = R + PP, and S = S + 1 IfO, > L [ * A j ] a n d 0 , < U [* A,]
Then R = R + Q, and S = S + 1 If QQ, > L [* AJ] and QQ, < U [* Aj]
Then R = R + 0 0 , and S = S + 1 IfG, > L [*Aj] and G, < U [* Aj]
Then R = R + G, and S = S + 1 If GG,> L [*Aj] and GG, < U [*Aj]
Then R = R + GG, and S = S + I If H, > L [ * A j ] a n d H, < U [* A,]
Then R = R + H, and S = S + 1 If HH, > L [* AJ] and HH, < U [* A,]
Then R = R + HH, and S = S + I Fj=(R + M(*Aj))=(S + I) Next t
Tuong ty nhu vay, thiet lap n = 3 va t = 4, ta CO the nhan dugc du doan boi mo hinh bac ba va n = 4, t = 5 de co dugc du doan bai mo hinh bac 4 va cir tiep tuc nhu vay. Nhu vay gia tri du bao co the thu dugc bing cac mo hinh bac cao khac nhau.
Nsuven Cona Dieu Tap chi KHOA HOC & CONG NGHE 72(10): 5 9 - 6 5 Be .xuat cdi bien cho thuat todn ciia Singh
Chimg toi de xuat mgt cai bien don gian cho thuat toan bac cao ciia Singh a buoc 2 ciia thuat toan. Chiing toi thuc hien mgt thay doi nho trong buoc 2 cua thuat toan tren de phan bo cac diem roi vao tirng khoang dugc deu hon. Cac buoc con lai dugc giir nguyen nhu thuat toan ciia Singh. Cu the: sau khi chia U thanh m doan con bang nhau, co mgt van de dat ra la so lieu chuoi thai gian se phan bo khong deu trong cac khoang da chia. Co the CO nhting khoang khong co gia tri chuoi thai gian dang xet roi vao nhung cung co the co nhung khoang co rat nhieu gia tri se quy tap tai do. Nhu vay du bao se co nhieu sai so do sy phan bo khong deu nay. Vi vay se nay sinh ra van de can chia lai khoang sao cho phan bo ciia chuoi thai gian roi vao cac khoang da chia se dugc deu hon. Van de nay da dugc quan tam trong [6]. Noi dung chii yeu cua lap luan la tinh toan phan bo cua gia tri chuoi thai gian trong tiing khoang con.Gia sir so lugng cac gia tri chuoi thai gian la p diem. So lugng khoang can chia la m. Khi do trung binh moi khoang chira n=p/m gia tri chuoi thai gian.
Neu khoang nao co so lugng gia tri chuoi thai gian roi vao nho hon hoac bang n thi khong chia nho ra. con so lugng diem roi vao khoang nay Ion hon n bao nhieu lan thi se chia nho khoang do ra lam tirng do lan. Ket qua. sau buoc nay viec chia khoang se khong thanli cac khoang deu nhau nua nhung gia trj chuoi thai gian lai dugc phan bo dong deu ho'n trong tirng khoang con.
UNG DUNG TRONG DU BAO CHI SO CHUNG KHOAN DAI LOAN
Xet bai toan dy bao cho chuoi diT lieu chi so thi truong chirng khoan Dai Loan TAIFEX [2,3], Cu the nhu sau:
Ap dung thuat toan cai bien cho so lieu nay nhir sau:
Bif&c 1. Xay dyng tap nen U. Xac dinh gia tri Ion nhat va nho nhat ciia chuoi thai gian tren la 6200 va 7560 diem. Do vay tap nen U dugc xac dinh la gia tri trong khoang [6200,7600].
Bir&c 2. Chia khoang. Ta se chia U thanh 14 khoang U], u,, ..., uu voi do rgng la 100, nhu vay cac khoang se la: U| = [6200,6300], Ui = [6300,6400], ..., u,4 = [7500.7600].
Chia lgi khoang
Tinh phan bo cua cac gia tri chuoi thoi gian roi vao cac khoang da chia. Dieu nay thuc hien dg biet cac khoang nao co nhieu gia tri roi vao de co the phan khoang tiep lam tang do chinh xac khi dy bao.
Bang sau day se cho thay sy phan bo cac gia tri ciia chuoi thoi gian roi vao tiing khoang:
Bang 2. Phdn bd gid tri trong tirng khoang Khoang
6200-6300 6300-6400 6400-6500 6500-6600 6600-6700 6700-6800 6800-6900
So lu'ong
1 0 3 1 2 9 9
Khoang 6900-7000 7000-7100 7100-7200 7200-7300 7300-7400 7400-7500 7500-7600
So luong
5 1 0 6 5 2 3 Xem xet bang tren thay sy phan bo cac gia tri tai cac khoang khac nhau la khong deu nhau.
Co 47 gia trj trong 14 khoang nen so lugng trung binh roi vao moi khoang la hon 3. Vi vay nhting khoang nao co 5, 6 gia tri roi vao ta chia tiep lam 2 khoang con. con nhung doan nao co 8, 9 gia tri roi vao ta tiep tuc chia thanh 3 khoang de sao cho moi khoang con do CO xap xi 3 gia tri roi vao. Ket qua se hinh thanh 21 khoang sau:
Bang 3. Phdn khoang
u,=[6200-6300]
u:=[6300-6400]
u,=[6400-6500]
u,=[6500-6600]
U8=[6766-6800]
u<,=[6800-68331 u,u=[6833-6866]
u, ,=[6866-6900]
u,5=|7100-72001 u ,,=[7200-7250]
u,7=[7250-7300|
u,s=|7300-735U|
u,=[6600-6700] u,:=[6900-6950] u,<,=[735()-740()l U(,=[6700-6733] u,5=[6950-7000] u,o=[7400-7500]
U7=[6733-6766] u,j=| 7000-7100] U:,=[7500-76001
Nguyen Cong Di
Nam 3/8/1998 4/8/1998 5/8/1998 6/8/1998 7/8/1998 10/8/1998 11/8/1998 12/8/1998 13/08/1998 14/08/1998 15/08/1998 17/08/1998 18/08/1998 19/08/1998 20/08/1998 21/08/1998
ieu va cs
Bang Gia trj thuc
7552 7560 7487 7462 7515 7365 7360 7330 7291 7320 7300 7219 7220 7283 7274 7225
Tap chi K H O A HOC & CONG N G H E
1. Gid tri chi so chirng khodn Ddi Loan Nam Gia trj thuc 24/08/1998 6955 25/08/1998 6949 26/08/1998 6790 27/08/1998 6835 28/08/1998 6695 29/08/1998 6728 31/08/1998 6566 1/9/1998 6409 2/9/1998 6430 3/9/1998 6200 4/9/1998 6403.2 5/9/1998 6697.5 7/9/1998 6722.3 8/9/1998 6859.4 9/9/1998 6769.6 10/9/1998 6709.75
Nam 11/9/1998 14/09/1998 15/09/1998 16/09/1998 17/09/1998 18/09/1998 19/08/1998 21/09/1998 22/09/1998 23/09/1998 24/09/1998 25/09/1998 28/09/1998 29/09/1998 30/09/1998
72(10): 5 9 - 6 5
Gia trj thuc 6726.5 6774.55
6762 6952.75
6906 6842 7039 6861 6926 6852 6890 6871 6840 6806 6787
Budc 3. Xay d u n g cac ham m a tren khoang da chia:
Trong b u o c nay ta xac dinh lai cac tap mo A, t u o n g irng vai tirng khoang va co the gan lai cac gia trj ngon ngu cho tirng tap m a nay. Cac tap m a A, i=l,2,...,21 d u g c djnh nghTa thong qua cac ham thugc de don gian co dang hinh non nhan 3 gia trj 0, 0.5 va I d u g c viet nhu sau:
A, = l/ui + 0.5/U2 + 0/u, +....+ 0/u:o + O/uji A J = 0.5/u, + l/u: + 0.5/u, +...+ O/ibo + O/uji Al = O/u, + 0.5/U2 + I/U3 + 0.5/iu +...+ O/U20 +
0/u,| . . .
Ai9 = 0/U| + O./u, +... + O.5/U18 + l/u,g + O.5/U20+ O/u, I
Bang 4. Moi quan he ma
A20 = 0/u| + O./U2 + ...+ 0.5/u|9 + 1/U2() + O.5/1121
A21 = 0/U| + O/U2 + ...+ 0/U|<; + O.5/U20 + I/U21 Buoc 4. M o hoa cac gia trj ciia chuoi thai gian va thiet lap moi quan he m o :
Ket qua m o hoa cac gia trj cua chuoi thai gian the hien trong Bang 4.
Theo djnh nghTa phan tren la lap chuoi thai gian m a t u o n g irng voi cac tap m a a tren va xac djnh moi quan he m a tai thai diem t
= 1,2,...,47. Co the thay ngay d u g c cac moi quan he dau tien nhu sau: A21—> A21 , A j i ^ - A20, A 2 0 ^ A21 ,..., A g ^ As.
Bu&c 5. Tinh toan va d y bao dya tren cac moi quan he m a d u g c thiet lap:
Nam Gia trj thuc Quan he ma Nam Gia tri thuc Quan he mo 3/8/1998
4/8/1998 5/8/1998 6/8/1998
7552 7560 7487 7462
A22 A22 A21 A21
2/9/1998 3/9/1998 4/9/1998 5/9/1998
6430 6200 6403.2 6697.5
A4
Al
A 4
m
Nguyen Cong D 7/8/1998 10/8/1998 11/8/1998 12/8/1998 13/08/1998 14/08/1998 15/08/1998 17/08/1998 18/08/1998 19/08/1998 20/08/1998 21/08/1998 24/08/1998 25/08/1998 26/08/1998 27/08/1998 28/08/1998 29/08/1998 31/08/1998 1/9/1998
ieu va cs 7515 7365 7360 7330 7291 7320 7300 7219 7220 7283 7274 7225 6955 6949 6790 6835 6695 6728 6566 6409
Tap chi KHOA HOC & CONG NGHE
All
A20 A20 A19 A18 A19 A19 A17 A17 A18 A18 A17 A14 A13 A9 A l l A6 A7 A5 A4
7/9/1998 8/9/1998 9/9/1998 10/9/1998 11/9/1998 14/09/1998 15/09/1998 16/09/1998 17/09/1998 18/09/1998 19/08/1998 21/09/1998 22/09/1998 23/09/1998 24/09/1998 25/09/1998 28/09/1998 29/09/1998 30/09/1998
6722.3 6859.4 6769.6 6709.75
6726.5 6774.55
6762 6952.75
6906 6842 7039 6861 6926 6852 6890 6871 6840 6806 6787
72(10): 5 9 - 6 5 A7 A l l A9 A7 A7 A9 A8 A14 A13 A l l A15 A l l A13 A l l A12 A12 A l l AlO
A9 Trong buoc nay, chi u'ng dung tinh toan voi
mo hinh bac 2 (nghTa la n=2 va t=3). Ket qua tinh toan va dy bao theo thuat toan bieu dien 6 Bang 5. Sai so trung binh binh phuang MSE dugc tinh theo cong thirc:
I(f,
MSE = 416
Ta CO the thay rang ket qua dy bao voi thuat toan Singh la rat tot, nhat la khi so sanh voi cac ket qua ciia Chen hay ciia Huarng. Ket qua khi sii' dung thuat toan cai bien con tot hon nhieu, sai so MSE ciia phuong phap chi bang 1/2 sai so theo phuong phap ban dau Singh dua ra. Trong do thj a Hinh 1, ta c6 thi nhan thay gia trj dy bao gan nhu triing khap hoan toan voi gia trj thyc.
KET LUAN
Bai bao nay dua ra mgt cai bien cho thuat toan bac cao ciia Singh. Tuy chi la mgt cai bien nho nhung hieu qua dat dugc la kha tot. Dieu nay the hien thong qua sai so trung binh binh phuong (MSE) ciia phuong phap chi bang VJ
sai so theo phuong phap nguyen thuy cua Singh. So sanh voi ket qua ciia Huarng va cac phuong phap khac co the xem trong [l]-[3].
Duong dy bao cua chung toi dua ra bam kha sat voi gia tri thyc te nen c6 the sir dung phuong phap cai tien nay cho dy bao cho mot so chuoi thoi gian trong thyc tien.
TAI LIEU THAM KHAO
[1]. Nguyen Cong Dilu (2008), Mot thugt todn mdi cho md hinh chudi thdi gian md heuristic trong du bdo chirng khodn, Bao cao tai Dai hoi Toan hgc toan tai Quy Nhon. Bai giii dang tai Tap chi Todn hoc Ung dung.
[2]. Nguyen Cong Dieu (2009), ''Cdi bien cho mot thugt todn dan gian trong mo hinh chudi thai gian md'\ Bao cao khoa hgc tai Vien Cong nghe thong tin.
[3]. Q. Song, B.S. Chissom (1993), "Fuzzy Time Series and its Model", Fuzzy set and system, vol.
54, pp. 269-277.
[4]. Q.Song, B.S. Chissom (1993), "Forecasting Enrollments with Fuzzy Time Series - Part 1," Fuzzy set and system, vol. 54, pp. 1-9.
[5]. Q.Song, B.S. Chissom (1994), "Forecasting Enrollments with Fuzzy Time Series - Part II,"
Fuzzy set and .system, vol. 62, pp. 1-8.
Nguyen Cong Dieu va cs Tap chi KHOA HOC & CONG NGHE 72(10): 59-65 [6]. S.M.Chen (1996), "Forecasting Enrollments
based on Fuzzy Time Series," Fuzzy set and system, vol. 81, pp. 311 -319.
[7]. S.M.Chen (2002), "Forecasting Enrollments based on hight-order Fuzzy Time Series", Inter.
Jurnal: Cybernetic and Systems, N.33, pp. 1-16.
[9]. S.R. Singh (2007), "A simple method of forecasdng based on fuzzy time series". Applied Mathematics and Computation, 186, pp. 330-339.
[10]. S.R. Singh (2009), "A computational method of forecasting based on high-order fuzzy time series", Expert Systems with Applications, 36 pp.10551-10559.
Algorithms/
MSE MSE
Bang 5. Ket qud khi sir dung Heuristic cai tien Chen
1700 9737
thugt todn cdi bien
Huamg Singh 5437 884
Singh cai tien 416
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Hinh L Do thi so sdnh ket qud du bdo bdng thugt todn Singh cdi bien vdi gid tri thuc vd gid tri dir bdo ,, . bdng thugt todn nguyen thuy ciia Singh
SUMMARY
MODIFICATION O F SINGH'S HIGH ORDER
A P P L I C A T I O N IN FORECASTING TIME SERIES
ALGORITHM AND ITS Nguyen Cong Dieu', Tran Thanh Thuong^*
Institute of Information Technology - VAST. Thai Nguyen University
Fuzzy time series models have many applications in forecastings. However, the predictive resuks of the proposed method were not very accurate. Thus the search for the more accurate models and simpler algorithm is in a priority. In recent years, a number of works have been completed under the direction of improving the accuracy and reducing the amount calculated in fuzzy time series models such as the works of Chen and Hsu, Huamg, Singh, ... A different approach for frizzy time series model is to use these techniques in data mining such as clustering, Neural networking, ... to build the models. There is also possible to use high-order prediction algorithm. Singh [10] has proposed such an algorithm. In this paper, we modified the algorithm of Singh for high order fuzzy time series model. The modification method has showed a very good efficiency.
Key words: Fuzzy time series. Linguistic variables. Fuzzy logical relations
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