Luận án tiến sỹ Xây dựng, phát triển, ứng dụng một số mô hình kết hợp giữa mạng nơron (NN), logic mờ và thuật giải di truyền (GA)

B~I HQCQu6c GIATHANHPH6 He, CHI MINH
TRUC1NGB~I HQCKHOAHQCTV NHIEN
LE HOANGTHAI
xA Y DVNG, PHAT TRIEN, UNG DT,JNGMOT s6 MO
H1NH KET H<lP GIUA M~NG NORON(NN), LOGIC
MO(FL) VA THU~T GIAI DI TRUYEN(GA)
Chuyen nganh: Barn bao tmin hQCcho may tinh
va cac M th6ng tinh toaD.
Mil 56: 1.0LlO
T6MTAT
A' '" - ,
LU~N AN TIEN SI TOAN HQC
Tp. H6 chiminh-2004
-
Cong trlnh nay du'~choan thanh t~i:
Khoa Cong ngh~ thong tin
Tru'i'1ngD~i hQckhoa hQc tl! nhien Tp. H6 chi minh
Ngu'i'1ihu'ang d1inkhoa hQc:
TS. Tru'dng My Dung - DH KHTN TP.HCM
GS.TS. Bili Doan Khanh - DH PARIS VI
Phcin bi~n 1:
GS.TS. Nguyen Lam - DH DL Van Lang TP.HCM
Phan bi~n 2:
PGS.TS. Tr~n Van H~o - DH Su' ph~m TP.HCM
Phcin bi~n 3:
PGS.TS. Nguyen Thanh Thuy - DH Bach khoa Ha ni)i
Lu~n an se du'<1cbao v~ t~i hi)i d&ngcha'm lu~n an dip nha nu'ac hQp
t~i:

vao h6i

gii'1.ngay tMng
flam 2004
Co the Hmhieu lu~n an t~i cac thu'vi~n Khoa hQc:
Thu' vi~n cao hQc tru'ong D~i hQc khoa hQc tl! nhien Tp. H6
Chi Minh.
Thu' vi~n khoa hQct6ng h~p Tp. H&Chi Minh.
A. GIdITHI~U LuAN AN
Vi~c sit d\lng kj thuq.t t{nh roan mim trong tr{ rue nhdn t{lOb~t d~u
du'<;1ckhai thac trong th~p men 90 vdi m\lc tieD giiH quye't nhfi'ng bai
tmin xilp xi, g~n dung. Ky thuQt t(nh todn mim (soft computing) khac
vdi cac ky thu~t truy~n th6ng va ky thu~t tinh tmin cung C1cM: no
chdp nMn tfnh grin dung, kMng chdc chdn. V~ cd ban, mo hlnh m~u
cho kj thuQt t(nh todn mim la tll duy clla con nglliii. No khai thac kha
dng d~c bi~t trong tu'duy cua con ngu'<1ikhi giai quye't hi~u qui cac
viln d~ trong nhii'ng moi tru'(JngkhOng cMc cMn va khong chinh dc,
dl!a tren nhfi'ngphu'dng phap tinh loan va I~p lu~n logic truy~n th6ng.
Kj thul)t t(nh loan mim khOng phii la phu'dng phap ddn Ie. No la sl!
chung phh hay noi cach khac la sl/ kIt h?p qua l{li cua nhi~u phu'dng
phap, trong do cac phu'dng phap cd ban la: Thul)t gidi di truyin
(Genetic Algorithms- GA), m{lng Ndron (Neural Networks- NN) va
Logic mo (Fuzzy Logic- FL). Trong bQ ba GA, NN, va FL; GA la
phu'dng phap tlm kie'm bie'n giup cho vi~c giii cac bai loan t6i u'u;NN
la phu'dng phap hi~u chlnh, sU'ad6i tham s6 sao cho phil h<;1pvoi bai
loan dn giai quye't, no giUp h~ th6ng co kha Dang hQCva nh~n bie't;
FL t~p trung vao vi~c xU'19cac tinh loan g~n dung.
Nhfi'ng tie'n bQ khoa hQc ky thu~t d~t du'<;1ctrong nhfi'ng Dam g~n
day d:i khing dinh vi tri cua t{nh loan thong minh (Computing
Inteligellce- CI) vdi n~n bing la kj ITluQttfnTl tOOIl11/2111.f>~ng th<1i,
xac dinh raub gidi gifi'a no vdi Tr{ rue nluln t{lo clf truyln (nin tang IiI
kj thuQt tfnh loan cling).

Vi~c nghien cuu cua lu~n an vdi m\lc lieu: hy vQng ap d\lng'mo
hlnh kIt h?p cac kj thuQt t{nh loan mlm cho vi~c giii quye't cac bai
loan trong thl!c te'sao cho thu du'<;1chi~u guilt thl!c hi~n cao nhilt.
Lu~n an nay t~p trung nghien CUuhai viln d~ chinh:
(1) T6ng ke't mQt s6 phu'dng phap ke't h<;1pqua l~i gifi'a Thul)t gidi
di truy€n, m{lng Naron va Logic mo eua cae nha nghien CUlltrong va
ngoai nu'de: trlnh bay t(nh cOnthie't cua vi~c ke't h<;1p,cae phll(/f1gthdc
ket h?p, mQt s6 vi d\l minh hQa va dlla ra lup hili roan thich ung Mi
vdi tt'tngmo hlnh ke't h<;1p.
(2) f>~ xuilt mQt s6 mo hmh ke't h<;1prieng: Cae h~ th6ng Di
truyin- Mii, Naron- Mo, Di truyln- Naron, Vi truyln- Naron- Mii.
f>6ng thCJi,chi ra Hnh khd thi eua chUng trong vi~e giai quye't ung
d\lng, d6 la hiliJoan pMn loq.imdu t6ng quat. Lu~n an d~ c~p hai lop
bai toan cua ung d\lng nay: phdn logi mdu khOng mitt mat thOng tin:
Chung thlfc m~u, phan lOpm~u va phlln [oq.imJu hi ml1'tmat thOng tin.
Giiii 100bai toaD vhan loai m~u khong:ma't mat thong: tin:
Giiii lop bai loan chung thlfc m~u (phan bi~t THATI GIA) b?ing
mo hlnh ke'th<;1pgiii'aThuqtgiditienhod (EA)voi Logic mG(FL) (mo
hlnh FL_EA).
Giiii lOp bai loan phan lopm~u b?ing mQt s6 mo hlnh ke't h<;1p:
giii'a mq.ng Naron va Logic miJ (m\\ng Ndron mCl (Fuzzy Neural
Network- FNN»); giii'a mgng Naron va ThUQtgidi di tl'uy€n (mo hlnh
NN_GA); giii'a m(Jng Naron, Logic mil va Thuqt gidi di truy€n (mo
hlnh NN_FL_GA).
Giiii 100 bai toaD phiin loai m~u bi ma't mat thong tin:
Ph\lc h5i m~u bi ma't mat thong tin v~ tr\\ng thai ban dilu b~ng Bi)
nho ke't h<;1p(AssociativeMemory- AM). Sau khi m~u du'<;1cph\lc hM,
quay trCll\\i bili loan phan lo\\i mh khong ma't mat thOng tin: chang
thl,lcmdu ho~c phdn lop mdu. E>~chu~n bi bi) dii'li~u hua'n luy~n clIo
mq.ng plu,lc hai: BI} nhO ktt lu;tpva mqng phdn lrJp:FNN va NN, lu~n

an d~ xua't mi)t ky thu~t tlf di)ng phat sinh bi) dii'li~u hua'n luy~n thay
the' phu'dng phap chQn milu thu congo Ky thu~t nay hlnh thanh tli mo
hinh ktt h</pgiii'a Thuqt gigi di tl'uyin, m\\ng Kohonen va Logic mG
t\\m gQila mo hlnh GA_Kohonen_FL.
Cac ung d\lng thlfc te' trong lu~n an minh hQa clIo vi~c sit d\lng
nhii'ng mo hinh ktt h</pdii xiiy dlfng: Chang thl,lcdnh; Nhqn dq.ng chil
viet tay; Phdn [oq.idnh van tay mift mat thOng tin.
B6 C1,1Ccua lu~n an
Lu~n an dai 155 trang, 53 hlnh ve va d5 thi, 19 bang s6li~u va
ke't quii. Lu~n an g5m Dam philn:
Chu'dng 1: Ke't h<;1pcac mo hlnh Hnh loan thong minh.
Chu'dng 2: Mi)t s6 mo hlnh ke't h<;1pc~p doi: Di tl'uy€n- MG, N(!I'O/l-
MG, Di truy€n- Naron.
Chu'dng 3: Ke't h<;1pba ky thu~t: ThUlJtgidi di truyin, mgng Naron
va Logic mG.
Chu'dng 4: Cac ung ch,mgthlfc te'.
PhVl\lc: g5m lOphvlvc ttt A-J. Tli phVl\!c A de'n plw l\lc G: cac
va'n d~ 19 thuyC't cd biin ma lu~n an sit d\lng. Tli ph\! l\lc H Mn phv
l\lc J: phan Hch cac ung d\lng thit nghi~m.
2
B. NQI DUNG LU~N AN
Chu'dng 1
KET HQP cAc MO H1NH TfNH ToAN THONG MINH
1.1 ThuQt giai di truyin k~t help vui Logic mu
Thuqt giai di truyin va Logic m?1c.omQt vai diem chung va rieng.
Ca hai ky thu~t d~u thich hQp vdi vi~c xu 19bQ du li~u dung cho cac
h~ tM/ng dOngphi tuytn. Su d\Jng hai ky thu~t nay giup cai tie'n hi~u
su[t cua M tho'ng: t6i lIu ktt qua va t6e dO thlfe hi~n. H~ t/1(5ng11/()
du'Qcdung de lu'u tru tri thuc cua chuyen gia vdi dIu truc thich h<;1p,
ti~n l<;1icho vi~c mo phong hay chinh sua tri thuc. Trong khi do, Thu(j.t

gidi di truy€n hu'dng tdi quy trlnh tlm kie'm loan cvc, giam bdt cac
tru'ong h<;1pc1fclieu cvc bQ bhng vi~c gidi h~n t~p giai phap chuifn.
Vi~c ke't h<;1pgiua Logic ma va Thw# gidi di truyin ra dai ti't'Dam
1989 vdi mvc tieuj khai thac u'u diem cua hai ky thu~t rieng Ie. Phh
nhi~u cac ho~t dQngnghien CUud~u t~p tIling vao vi~c su dvng Thu(j.t
gidi di truy€n de tang cu'ang hi~u su[t cua H~ tM/ng ma: trong tru'ong
h<;1pthie'u hvt mQt vai d~c tru'ng cua h~ tho'ng m?1,Thu(j.tgidi di truyin
vh cho phep to'i u'uham thanh VieDva th~m chi lQCcac lu~t m?1.Tuy
nhien, mQt so' nghien CUlldii chI ra phu'dng phap hi~u qua cho phep
cai tie'n cac he tM/ng di truyin bhng bQ d;€u khiin ma ho~c su dvng
t~p lu~t m<1tlm ham thich nghi cho Thuqt gidi di truy€n.
H~ tho'ng ktt h(/p Di truyin- M?1du'a ra mQt phu'dng cach t1fnhien
M giai quye't h~u he't cac bai loan kh6 trong th1fc te', d~ng thai no
ding Dang cao hi~u su[t th1fchi~n cho cac phu'dng phap truy~n tho'ng
khi giai quye't bai loan.
1.2 M{lllg Ndron k~t help vOiLogic mu
Phu'dng phap ke't h<;1pgiua mr;mgNaron vdi Logic ma ra doi ti't'dftu
th~p DieD 1990. Mr;mgNaron va Logic m?1co mQt vai diem chung:
Chung d~u la nhung ham tinh loan dQng, co kha Dang t1fdi~u cWnh
vdi mvc lieu tang hi~u su[t ho~t dQng. Ca hai d~u du'<;1cth1fc hi~n
thee nguyen 19 xu 19 song song. Mq.ng Naron baa g6m t~p h<;1pcac
lien ke't qua l~i hen trong giua cac nut (Naron) tren nguyen t~c: dftu
ra cua m6i Naron du'<;1clien ke't thong qua cac trQng so' de'n cac Naron
khac ho~c tdi chinh no. H~ th{/ng "m?1"xu 19 cac lu~t, nhung lu~t nay
se lien ke't t~p cac dftu ra "m?1"vdi t~p cac dftu vao "m?1".Nhu'Qc
diem chinh cua cac h~ tM/ng "m?1"Ia: r[t kho thie't ke' cd so lu~t ma
3
khi t6n ti;limQt.s6 ht<;1ngIOncae d~u vao va d~u ra eua h~ th6ng. Cae
lu~t mo du'<;1ebi€u dieD nhu' mQt anh Xi;lttt t~p cae bie'n ligon ngii'd~u
vao Mn t~p cae bie'n ligon ngii'd~u ra eua h~ th6ng. Tuy Dillen, d~ co

au'<;1ebQ lu~t mo phai phang va'n ttt cae ehuyen gia, eong vi~e nay
thu'ong ra't kho khan va va't va. Hdn filla, vi~e tlm ra ham thanh VieD
ehinh xae dam baa h~ th6ng di;ltdu'<;1ehi~u sua't t6t cling ra't kho khan.
Mgng Nuron mang li;limQt s6 thu~n l<;1i:kha Dang hQe ttt du li~u qua
khli va t\1'thich ling voi mOl tru'ong khi ni;lpdii'li~u moi vao h~ th6ng.
Mgng Nuron sau khi du'<;1ehua'nluy~n Mi cae ThUll-tgidi h(Jc se co
kha Dang phan,IOi;lidu li~u va nh~n di;lngcac m~u phlic ti;lP.M~t hi;ln
che' eua mgng la: s\1'thie'u h\Jt cae Nuron trong mgng ho~e du li~u
hua'n luy~n khong baa dam: bi nhieu hay khong d~y duo
Vi~c ke't h<;1pLogic m?1voi mgng Nuron du'<;1cthlfc hi~n theo nhi€u
caeh: trong mQt s6 ling dvng, mgng Nuron du'<;1esit dvng eho vi~e thie't
ke'va tinh chlnh cae M thting ma. (j mQt val ling dvng khae, ky thu~t
m?1se hi~u ehlnh cae Nuron trong mgng, ho~e sita d6i ThUll-tgidi huei'n
luy~n mgng sao eho hi~u sua't th\1'ehi~n eua mgng la eao nha't.
1.3 Ke't blip giiia Tlm4t gidi di truyin va m~ng Ndroll
Phu'dng phap ke't h<;1pgiua ThUll-tgidi di truyin voi mi;lngNuron ra
dol ttt Dam 1980. Thurl-tgidi di truyin co kha Dang tlm kie'm hi~u qua
lOr giai teen mien khOng glaD cae 10i giai rQng IOn va phlie ti;lP,no
eho pbep tlm ra lOi giai t6i u'u voi chi phi nha so voi cae phu'dng phap
truy€n th6ng khae. Mi;lng Nuron du'<;1ehi€u nhu' m9t h~ th6ng quye't
dinh pilau lop. Mo hlnh ke'th<;1pDi truyin- Nuron ra dOlvoi mve lieu
Dang eao hi~u sua't phiin ldp cua mi;lng Nuron. Nhu'vh, trong ph~n
ldn cae ling dvng, val tro eua Thurl-tgidi di truyin la h6 tr<;1eho mi;lng
Nuron hay h~ ehuyen gia.
Trong mo hlnh ke't h<;1p,Thurl-tgidi di truyin du'<;1ethie't ke' duoi
di;lng m9t mo dun d9C l~p ghep e~p voi mi;lng Nuron ho~e nhii'ng mo
dun Hnh loan khae, no se hi~p l\1'e cling VOl cae mo dun nay M giiii
quye't bai loan (thu'ong no du'<;1eap d\lug d€ tlm ra lOigiai t6i u'u).
f 1.4 Ke't blip Tlm4t gididi truyill, m(lllgNdrollva Logicmu
f)~ giai quye't hi~u qua nhi€u bai loan phUe ti;lPtrong thlfc te', dol

khi pilaf thie't ke' nbung mo hlnh lien ke't ca ba phudng pilar: Thurl-t
gidi di truyin, m(fng Nuron va Logic m?1.Ba thanh ph~n cd ban cua ky
thu~t Hnh loan m€m nay se h6 tr<;1b6 sung cho nhau trong qua trlnh
giiii quye't m9t ung dvug ev th€.
4
1.5 M6 blnb ke't hqp ba ky tbu~t Di truyhr, Ndro", Mu giai bai
toaD phlin lo~i mdu t6ng quat
Be chi ra Hnh kha thi cua vi~c ke't h<;1pba ky thu~t ThuQt gidi di
truyln, Logic mil va mgng NrJron. Lu~n an dIng d~ xua't mQt s6 ma
hinh Mt hf/p rieng. Nhii'ng ma hinh ktt hf/p nay du'<;1ckiem chung
thOng qua mQt ling dl,lng, do la bai toan pMn logi mliu tdng quat voi
hai lop bai loan: pMn logi mliu khang mlft mat thOng tin: chung th\fc
mall, phan lOpmall va phdn logi mliu bi mat mat thOng tin.
1.5.1 Blii toaD phlin lo~i mdu
Cho nj, i e {l,2, ,n}, nj;t0; va 12 la mQt phan ho1,lchcac nj. Bai
loan phan IO1,limall tang quat la bai loan xac djnh anh x1,l:
p :n~{1,2, ,n}:VX en, p(X)=i(nghia laX en,).
T6n t1,lihai nnh hu6ng voi mall X
- nnh hu6ng 1: KhOng ma't mat thOng tin <:>xen.
- nnh huo'n~ 2: Bj ma't mat thong tin <:>Xmmlt~n.
Voi nnh hu6ng I chlnh la bai loan dii trlnh bay.
Voi tlnh hu6ng 2 phai phl,lc h6i Xmmllv~ Xph~c_Mjsao rho
Xph~c_Mjen,r6i moi phan lo1,liXphKMjv~ nj, ie {1,2, , It}.
Lu~n an xem xet hai d1,lngcua bai loan phan IO1,lim§u:
(I) Bai loan chung th\fc m§u (phan bi~t THATI GIA):
Tru'ong h<;1pn=2=> Q = QTH,4.T U QGlA .
(2) Bai loan phan lOpmall:
Xel de'n hai lru'ong h<;1p:
- Tntllng hqp 1: M§u X la mQt vec td: rho 12la mQl pIlau ho1,lch
cac nj, ie {1,2, ,n} va X=(X" X2, ,XJeO. Xac djnh ie {I, n}: XeOj.

- Truong hqp 2: M§u X Ia M vec ld:
rho 0 la mQt phan ho1,lch cac {OJ, ie{l,2, ,n}} va m§u
X ={xJ=(x(, xi ",.,xI):xJ en, J ={1",.,M}}.Xac djnh i sao rho XeOj.
1.5.2 Ke't hqp Vi truyt". Mu: Ma /ri,,/r FL_EA giai bai toaD
. c/runK t/r!te mliu (phftn bi~t TH~ TI GIA)
Xua't pIlat tit bai toan phon loqi mliu tdng quat (ml,lc 1.5.1). Xet
tru'ong h<;1pn=2 => 0= °TII,4.Tv °GlA : bai lOan cllling thlfC mlil1
(pMn birt THA T/GIA.)- Xac dinh "mliu' dang xem xer co phdi ld
"mliu' gaG cho trllek khOng? Be giai quye't bai loan, lu~n an de xua't
mo hlllh ke'l h<;1pThuQl gidi titn hoa (bie'n the cua ThuQt gidi di
truyln) va Logic mil. Xem d~y du ve phu'dng phap t1,liml,lc 2.1
5
(chu'dng 2). Dng d\mg thlfc te'cua phu'dng phap: Cht1ngthlfe Anh trlnh
bay trong chu'dng 4 (ung d\mg 1).
1.5.3 Ke't hQ'p Di truyin- Ndron- Mll giiii bai loan phlln lup
mau (XeQ)
Xet bdi tadn pMn laf,limdu tdng qudt (m\lc 1.5.1) voi tnf(Jng hl;1pn
nguyen dl/ung ba't ky. Tuy nhien, m\lc nay chi quaD Him de'n noh
hu6og 1 (m\lc 1.5.1): PMn laf,limdu kltong mdt mdt thOng tin: X day
drl d(ie trllng ~ XED. De giai quye't bai toaD, lu~n an d~ xua't b6n mo
kink: mf,lngNdran truyin thling biz lOp; mf,lngNdran miYtruy€n thling
b6n tang (xem m\lc 2.2 thuQc chu'dng 2); Thu~t gidi di truyin kit h{1p
ede 1/u;mgNClrantruy€n thllng ba lOp (xem m\lc 2.3 thuQc chu'dng 2);
Thu~t gidi di truyin lien kit ede mf,lng Ndran miY (xem m\lc 3.1.6
thuQc chu'dng 3). Vi~c so sanh de chQn IQc mo kink ktt h{1plo't nhdl
trong b6n mo hlnh tren du'l;1cminh hol.!trong ung d\lng thlfc te': Nh~n
df,lngk:YIlf viti lay (ung d\lng 2, chu'dng 4).
1.5.4 M6 hloh ke't hQ'p Vi truyin- Ndron- Mll giiii bai loan
philo lo~i mftu co m{(t mat th6ng tin (Xmnrtt~O)
La bai loan phIlOlol.!im§u t6ng quat voi nnh hu6ng 2: PhIlo lol.!i

m§u bi milt mat thOng tin <=>Xmmtt~O.De giai quye't bai tmin, d~u
tieD, phai ph\lC h6i Xmmttv~ XphKh&isao cho XphKh&ieO,r6i moi pMn
lo~i Xph¥cj,&iv~ 0;, ie {I, 2, , n}. De ph\lC h6i m§u X, lu~n an d~ xua't
mo kink ke't hl;1pThUf)tgic1idi Iruyin- mf,lng Kahanen- Logic miY- bQ
nhcJ kit h{1p(AM). M\lc 3.2.2 thuQc chu'dng 3 trlnh bay chi tie't mo
hlnh d~ xua't nay. Sau khi ph\lc h6i, thu du'l;1cXphKM;eO. De phIlO
lo~i XphK!1&iv~ Oi, ie {I, 2, , n}, chQn llfa tit b6n ky thu~t phIlo lo~i
nhu' trong m\lc 3.2.2 thuQc chu'dng 3. Dng d\lng thlfc te' cua bai tmin:
PMn laf,limdu van lay mdt md.t thOng tin (ung d\lng 3, chu'dng 4).
1.6 Tom t~t chu'dng 1
TEnhtadn thOng mink vdi n~n tang la cac ky thu~t Hnh tOaDm~m:
ThutJ.tgidi di truyin, mf,lng Ndran nhan tf,la va Logic miY dii titng h}
cM d€ nghien CUuva Om hieu tit kill Mt d4u chuyen nganh khoa hQc
may tinh (tit Dam 1940). Chu'dng nay dii t6ng ke't mQt s6 nghien CUll
dii co v€ vi~c ke't hc;lpqua l~i giii'a ba ky thu~t cua tfnh tadn thOng
mink: Thu(1tgidi di lmy!n, mf,lngNdran va Logic miY.D6ng tMi, gidi
thi~u mQt s6 mo hini, ket h{1prieng (d~y du xin xem trong cac chu'dng
2,3 va 4 cua lu~n an).
6
Chu'dng 2
MQT so MO HINH KET H<;1PcAp BOI: DI TRUYEN-MeJ,
NdRON-MeJ. DI TRUYEN-NdRON
2.1 Thu4t gidi tit" h6a ke't hllp Logic mil: InOhin" FL_EA giai bai
tmin chung tht1c miD (phan bi~t TB~ T/GIA.)
2.1.1 Md d~u
CMng th(lc mllu (phlln bi~f TH~ T/GL.\): tnt(Jng h<;1pn=2 trong
nnh hu6ng mdu khOng mdt mdt thOng tin cua bai loan phan lo{li mdu
tOng qudt (mvc 1.5.1). Hai loan du'<;1cphat bi~u nhu'sau:
ClIo tru'dc !1TH~T:KhOng gian cac m~u TH~ T;
nc.IA: Khong gian cae m~u GlA.

Vdi !1=!1TH~TU!1mA;!1TH~T'!1mA'~0 va !1TH~T('\!1mA=0.
Hie't: M~u dang ky Ae!1TH~T;M~u dn chU'ngnh~n Xe!1.
It
{
~ .
}
Canxacdinh: p:.!1~ TH~T.GlA saocho
VX!eO, 3ie{TH'; T,GIA}:p(X) = i(nghia [aX eO,).
Th1,J'cch~t. day la bai loan chU'ng th1,J'cm~u X: Tim phu'dng phap
phan loai m~u X Ia THAT hay GlA mot cach nhanh nh~t. Qua trlnh
gild quye't bai loan du'<;1ccilia thanh hai giai do!;!n:Bang ky m~u d!;!i
di~n Ae !1TH~Tva chU'ngnh~n m~u X la TH~ T (X=A) hay GlA (X;tA).
. Giai do{ln 1: Dang IcY
(1) Nh~n mQtm~u Ae !1TH~T'
(2) Hie'n d8i A v~ vec td h
(3) Tim cay nhQn dr,zng_nM.p tM t(l duy~t) d1,J'atren A va TA.
. Giaido(ln2: CII/ingnlz(m .
(4) Nh~n m~u dn chU'ngnh~n X
(5) Hie'n d8i bi8u di~n l!;!iX du'di d!;!ngyec td Tx.
(6) Sit d\lng cay lIMn d(lng_n de chU'ngnh~n Tx ==TA?
Ntu dung ke't lu~n: Xe!1TH~T"grl(lc [{Iike't lu~n: Xe!1mA.
Mo hlnh ke't h<;1pLogic mil va ThUlJtgidi titn hod (EA- Bien thl!
clia ThuQt gidi di truy~n) du'<;1csit dvng d8 thlfc hi~n cac giai do!;!n
ghH quye't bai loan.
2.1.2 Bie'n d6i m(f biiu di~n l~i miD
Dinh nghia 2.1 (ma trQnthObi!u di€n mllu)
ClIo tru'dc mQt anh con G cua mQt m~u. Dung t byte (t nguyen;
t~l) bi8u di~n mU'cxam cua G. Gia Ui E(G)e{O, ,(2/x8-1)) la gicitq
mU'cxam cua G.
7

M6i m§u du<;lcphiin thanh LxK anh con G;J(i=D" ,L-l;j=O, ,K-l;
gici trj L va K tuy thuQc vao ph~n m~m quet anh), thu du<;lCma tr4n
thObitu diln mduALxK sao cho: A;J=E(G;J) (i=D L-l;j=D K-l).
Djnh nghia 2.2
(bienddi mil)
Cho trudc gici trj d~u vao ae{D, ,(2,x8_1»). Biln ddi mu CURa Ia
phep bie'n d8i su dl}ng ky thu~t "mil" (chi tie't v~ ky thu~t m(j xem
trong phI} ll}c G) d~ pban ldp l~i ghi trj CUR a v~ mi~n
BD~r~""~O~C«2x1~ X., X
(I"'" 1 +1))., I""" ( +1)"., I""'" ( +I))>o(~') (""" ( +1)>« "'.1
Hlnh 2.4 Bi8u di6n "mo" bien d5i giil tri a v~ mi~n (0,
"" d.
3vte {D, ,e) ta c6 BDM(a)=vt: JL",(a) = Max fIL,(a)}.
1.0
. Djnh nghia 2.3 (ma tr4n rut g(Jn)
Cho trudc ma tr~n thO bi~u di€n m§u LALXKJ,Cho trudc kfch thudc
hang M va kich thudc cQtN. Ma tr4n rut g(Jnbi~u di€n m~u LA'MXNJIa
mQtRG trunKbinh (Rut gQn trung blnh) CURma tr~n LALxKJsao cho:
{
A;.J(,.O M-I.J.O N-I)=RGtrungbinh(A".){t = O L-I,k = 0 K-I
A;,Je{O, ,(2'" -I)}
(Xem thu~t giai rut gQn trung blnh (Jdudi).
Djnh nghia 2.4 (ma trq.nrut g(Jn nmiln)
Cho trudc' ma tr~n nit gQn LA'MxNJ.Ma trq.n rut g(Jn "miln LBMxNJ
la mQt "bien adi mu"(djnh nghia 2.2) CURph~n tu A'iJCi=O"M-/;i=O"N-/)sao
cho:
{
(
,
)(

)
B',J(':O M-I,J=O N-I) =BDM',J A',J i =D M-I,} =D N-I
B',JE{O, ,e} !
Djnh nghia 2.5 (vee td a{le tr/ing)
Cho trudc ma tr~n rut gQn "ma" LBMxNJ,We id d{ie trunK F CUR
m§u la: F=(fO,fI,fZ, ,fMxN-l); trong d6, /;=B;div N,; modN;(;=O.,}.{xN-I)'
Rutgon trung blnh(RGtrum!binh)
Tinh
trung
blnhA'ij
i=1 L
J
L=L/2
LALxK
l
K=KI2
T. T<'
L=M
vAK=N?
Y"'
thOil ~ LA'A(XNJ
8
Miu dang ky (A) va mill c!n chUng nh~n (X) d~u du'l;Icbi€u di~n
l~i du'oi dillJ;lghai vec td d~c tru'ng TAMxNva TXMxNthong qua cac bie'n
d6i tit cac djnh nghia dii trlnh bay CIteen. Viln d~ con I~i la: xet xem
XEnTH~T7Hay n6i dch khac phiHso khdp xem:TXMxN=TAMxN7
Luc nay, cdy nMn d{mg_n du'l;Icxay d1!ng vdi tieu chi xac djnh
cay 1ft"PIlat hi~n GIA.nhanh nhilt". Ghi djnh tieu chi du'<;1cbie't tru'oc
va du'l;Ic56 boa thanh ham l/./{1ngKia, su d\lng Thu(it gidi tie'n hod
M

gi.H quye't bai loan nay (Th1!chi~n hai bu'oc (3) va (6».
HiBu Quacua bie'nd6i mil trOnl!viac bilu diln lai delit/./um!
Dinh nghia 2.6 (sai s5 bie'nddi ())
Sai s5 bie'n d6i ()li't sai 56 thu du'<;1ckhi anh x~ ma tr~n tho bi€u
di~n mill LALxKJ;A;,jE(O, ,(2'X8-1)},t~l(t nguyen), i=l L; j=l K v~
ma tr~n rut gQn "mo" LBMxNJ;Bm,nE{O, ,c}, O<c«2'X8-1), m=l M;
n=l N vdi l<M ,;,aM 1ftu'oc 56 cua L; l<N va N 1ftu'oc 56 cua K.
Dinh nghia 2.7 (~g/./{ingsai s5 E)
Ng/./iJngsai s5 E1ftngu'6ng sai 56 cho phep d€ anh x~ ma tr~n tho
LALxKJv~ ma tr~n rut gQn "mo" LBMxNJ.
Dinh If 2.1 (xac djnhsai s5 bitn ddi ())
Cho tru'ocma tr~n tho bi€u di~n mill LALxKJ;A;jE{O, ,(2'X8-1)},
t~l(t nguyen), i=l L;j=l K va cho tru'dckich thu'dcM, N cua ma
tr~n rut gQn "mo" LBMxNJ;Bm,nE{O, ,c}. O<C«2,x8_1),m=l M; n=l N.
Luc nay, ,rai,r5bie'nd6i ()du'l;Icxac djnh theo cong thac sau:
(}:(}.x£Jz (2.1)
trong d6, ().lit 5ai 56 thu du'l;Ickhi anh x~ ma tr~n tho LA, xKJ
v~ ma
tr~n rut gQn LA'MXN
(
~dj~h nghia 2.3). ~6 du'l;Icxac djnh theo cong
thac: L L tilech R "
)
6, = R-I ' /'i £ K (2.2)
({; ~I A',J)
£Jzlit 5ai 56 thu du'l;Ickill chuy€n gia trj cua cac pIlAu tu ma tr~n rut
L
'
J
'Ix8 '

gQn AMxN; Am,nE{O, ,(2 -I)}, m=l M; n=l N ve mIen {O ,c}
cho tru'oc d€ co du'l;Ic ma tr~n rut gQn "mo" LBMxNJ. £Jzdu'<;1cxac djnh
theo cong thac: 9 - l/,
2 - /(c + 1) (2.3)
H~ qmi 2.1
Cho tru'dc ma tr~n tho LALxKJvit ng/./{ingsai s{l E . Ch~c eh~n xae
djnh du'<;1ekieh thu'dc cua ma tr~n rut gQn "mo" LBMxNJne'u co t8n t~i
gia trj u'oe 56 M, N cua L, K 5ao eho ,rai,rt;'bien ddi ()(djnh Iy 2.1) ~ E.
9
2.13 Thu~t gi:~itie-n hmi'Hm cliy nMn dll-ng_n t6i tfu
Blnh ngbia 2.8 (cily nhQndr,mg_n)
Cho tru'de hai s5 nguyen du'dng n, L va P={O, ,e,v}L; P={*}uP.
Cay nh~n dr,mgco dil rilng n teen P Ia bQ 4: A=:(V,E, e, 8). Trong d6:
V Ia t~p dinh; E Ia t~p nba,nh; T Ia t~p cae d5i tu'Qngdn kiem tea (t~p
n nut dich (g6m n nut hi », T~V; anh x<}.E :(V\ T)x{+,-)~E; anh x~
8 :V~
PsaD cho 8 -l(*)=T. Ta gQi E(v,+),E(v,-)Ih Iu'QtIa nhanh the'
tnii hay nMnh the' phiii cua ve Vva (V, E) gQiIa diy n~n.
Bai loan d~t ra Ia vdi t~p P i::hotru'dc, ta tlm cay nh~n d<}.ngt5t
nha't theo mQt lieu chi cho tru'de. Vdi gi<\dinh Ia lieu chi du'Qc bie't
tru'dc va du'QCs5 hoa thanh ham lll(fng gia, su d\lng Thugt gidi tie'n
hoa (mQt bie'n the cua Thu~t gidi di truyln) giiii bai loan tlm kie'm t5i
u'u nay, B~t d~u tit quh the A eua cac ca the (cac diy) co dQrQng n,
giii dinh ham lll(fng gia f cho tru'dc, m6i ca the AeA du'QCdaub gia
b<'Jigia triftA)eR+, ta dinh nghla cac phep loan di truy~n nhu'sau:
Blnh nghla 2.9 (cae phep di truyln roan elte)
NhOm eae phep di truyln roan elte lac dQng Ien loan diu truc diy
~
gom:
Tait{Zo:cho phep chQn IQcnhung diy nh~n d<}.ngtrong A vdi mQt xae

sua't tu'dng ung vdi ghi tri Iu'<;1ngghi cua ehung (tu'dng tv nhu' loan tu
tai t<}.othong thu'ong),
wi: Cho hai diy nh~n dc,lOg:A=(V, E, e, 8) va A'=(V', E', e', 8'), ChQn
ngiiu nhien e:w~v, vdi e~ E va v'l.T (t~p cac nut Ia), Phep "Lai"
khong thvc hi~n ne'u: nA.(v')#:nA(v),V'v'eV', Trong tru'ong hQp khac,
phep "Lai" du'<;1cthvc hi~n nhu'sau: ChQn v' eE' saG cho nA,(v')=nA(v).
Thay the' e:w~v b~ng f:w~v' va Av b~ng A' v ~ t<}.ora cay mdi
B=(W,F,)1,v) tit A va A', Tu'dng tv, chUng Wi cling t<}.odu'<;1cdiy mdi:
B'=(W',F',ji',v') tit A va A'.
Phep loan nay dam bao khOng Him anh hu'<'JngMn diu truc ngu
canh trong diy, no chi cho phep traG d5i diy con Av va A',. ne'u
nA(v)=nA'(v') va 8(v)=8'(v'),
Switch: Dng d\lng teen diy nhi pilau cling tu'dng tv nhu' phep loan "dilt
bie'n" ung d\mg tren chu6i. Phep loan "dilt bie'n" cho phep bie'n d5i
mQt bit tit 0 v~ 1 ho~c tit 1 v~ O.
Phep loan switch du'Qcung d\lng ph\l thuQc vao mQt dinh v trong
cay nh~n d<}.ngdQ rQng n: Cho A=(V, E, e, 8) vdi dQ rQng n, Phep
10
switch thOng ho<,ltdQng ne'u: l' e T (t~p cac nut hi). Trong cac tru'ong
hQp khac, phep "switch~ cho phep t<,lodiy mdi c6 dIng dQ rQng
n:A:=(V,E,e:,c51 trong d6 e::(V\T)x{+,-}~E trilng khdp
vdi E, ngo<,litrU'dinh v. T<,Iidinh v,
e:(v,+)=e(v,-)du'Qc thay the'
b~ng e:(v, -)=e(v,+).
Translocation (chuytn dich): Cho diy nMn d<,lngco dQ rQng n:
A=(V,E,E,O). ChQn mQt vai dlnh ve V va mQt vai nut la te T. Phep
"chuy6n dich~ cho phep thay the' A boi mQt diy nh~n d<,lngmdi:
Av,t=(V",t=V,Ev",tv",o",t=O).T~p nhanh Ev,tchua cac nhanh con ev,t, vdi
m6i nhanh e:Vl~V2 trong E, ev,tdu'<;1cdjnh nghia nhu' sau: Ne'u v2#,t,
thl ev,t=e; ne'u V2=V,thl xay dl!ng mQt nhanh mdi ev,t:vl~t; ne'u v2=t,

thl xay dl!ng mQt nMnh mdi ev,l:vl~W, vdi w='t"(dlnh cua A) ho~c
w=v, ph\! thuQc vao teAv hay khOng. Anh X<,Itv,l du'<;1cxac djnh theo
cach sau: B~t Ev,,(!"',+)=E{w,+)v,1thay the' Ev,,(W,-)=E{w,-)v,tcha bllt cu
weV\ Tnao.
Djnh nghia 2,10 (cdc phep di truyin vi m6)
Nh6m cdc phep
di truyin vim6 lac dQngten cac thanh ph~n cd so
cua cay:
VUai: Ph\! thuQc vao anh X<,lX :PxPxJ~PxP, trong do J =[0,1],
Trong ph~n ldn cac ung d\!ng, P se tro thanh t~p (O, "C,V}L
ho~c{O, "c'vrXJ, va vdi mQi jeJ, anh X<,lPxP~PxP se tro thanh
phep "lai" cua mQt nhom ho~c t<,limQt vj trl du'<;1cxac djnh boi j. Xua't
phat tir c~p cay nh~n d<,lngdQrQng n: A=(V,E,E,O)va A'=(V',E',E',8'),
chQn ra mQtdinh khong phiii la nut hi ve V va v' e V'. Ne'u co mQt bie'n
ng~u nhien randel, thl "VUai" se thay the' 8(v) va 8'(v') b<'liq va q',
xac dinh b<'li(q,q')= x[8(v),8'(v'),randj. Trang phien ban tho, v va v'
du<;1cchQn ng~u nhien. Trong phien ban dii tinh chinh, loan tit se xem
xet P c6 phil h<;1pvdi (ki€u, gia trn khong, va chi cho phep .VUai"
giiYacac c~p vdi cilng thanh ph~n ki6u.
VCdQt bitn: Du<;1cxac djnh b<'limQt anh x<,l:}1:PxJ~J vdi J nhu' <'I
teen. Ne'u P={O, ,C,V}L,co th6 xem }1nhu s1/thay d6i cua mQt ph~n
tit t<,livj tei du<;1cxac djnh boi j, thong qua anh X<,l
P -+ P . Trong
tru'ong h<;1pt6ng quat. vdi ba't cu veV\ T, gill trj 8(v) cling co th6 du<;1c
thay the' b~ng }1[8(v),randj;t8(v) (randeJ la mQt gill trj ngh nhien).
Vdi cac phep di truyin djnh nghla nhu' teen, ta co th6 ling d\!ng
Thugt gidi titn hOaEA M xac djnh cay nMn d<,lngt6i Uu.
11
Thuat Iliai titn hoa xav dune mi2n cav nhtin dam: n to'i rtu
(1) t:=O;

(2) Khi'1it'!-oA(t)=(Ah Az, , AM);
(3) Trong khi (I>i~u ki~n ket thuc l~p 1(A(t»*True)
- LU'<jnggill A(t)={j{A,),j(Az), ,j(AM»);
- t:=t+1;
- ChQn:A'(t)=(A'h A'z, , A'NrcA(t-1);
- Lai: R(t)=R(A'(t»; vdi xac sua'tlai Pc
- DQtbien: M(t)=M(R(A'(t»); vdi dc sua't dQt bienp,"
- Chuyen djch:T(t)=T(M(t»; vdi dc sua't chuy~n djch P,
- Vi 1ai:J1c(t)=J1c(T(t»; vdi xac sua't vi 1ai p 11.
- Vi dQt bien:/1m(t)=J1,.(J1c(t»; vdi xac sua't dQt bien PPM
- ChQn:A(t)=A(A(t-1)uR(t)uM(I)uT(t)UJ1c(I)UJ1,.(I»;
Het HiD
Thuat Iliaititn hoa chrlnllt11UCnuiu{vhtinbUt THAT/ GIAI
Cho trU'dcP=(O, "C,V')Ldang ky, dn chUngth1,J'cF=(O, ,C)L.Neu
F tri1ngvdi P thl ket 1u~n:F 1aTH~T ngU'dclai ket lu~n: F la GIA.
PhU'dngphIlp truy~n th5ng ghii quyet bai loan la vet c'!-n:duy~t, so
sanh I~nIU'<jtcac ph~ntu cua hai vec td F va P theo t~ptht1t1,J'tit l L,
neu g~p mQtphh tu sai khac thl ket lu~n: F la GIA, trU'ongh<jpmQi
ph~n tu cua hai vec td d~u gi5ng nhau thl ket lu~n: F la TH~T. Vdi
phU'dngphap'nay, c6 h,!-nche: neu phan tusaikhacn~mi'1cu5ivec td
thl chi2u dai cay clllinglhlfc_n =L (phi 16nthUQlgiai /Un).V~y dn
thiet phciitlm ra mQttQPt/llitlf duy~tt5i U'u(cay clllingthlfc_nt5i U'u)
giup cho vi~c so sanh vdi lieu chi la: phat hi~n GIA nhanh nha't.Su
dl,mgThuQtgidi tie'nhod (EA)cho bai tOllnnay.
2.2 Ke't hc;tpm~ng Ndron vOiLogicmil: m~ngNdron mo (FNN) giiii
bai tOilnphIlo lUpmiu (miu la 1vec td)
2.2.1 Md dllu
Quay tri'1I,!-ibizitodnphtin lo{limdu t6ng qudt (trU'ongh<jpphtin
tap mdu khOngmat mat thOngtin). Luc nay, m~udn pMn Idp (X)c6
th~ dU'<jcdanh gia theo'mQtho~c nhi2u lieu cM khac nhau. M6i lieu

chi daub gia x se dU'~csO'hOav~ mQtvec t(jtu(jngI1ng.NhU'v~y, bai
loan phan Idp m~uXchia thanh hai bai loan con:
12
Mallx g6m 1 vec td (MQt lieu cM duy nhdt dank Kid X).
MJu X g6m M vec td (X dll(/cdank Kid bifi M tieu cM).
M\1cnay t~p trung tlm hi~u va giai quye't Ba.iloan phan lOpmJu X
g6m 1 vec rd. Bai tmin d11'<;Icdinh nghia nh11'sau:
Cho ala mQt phan ho<;1chcac {O;,i E{t, 2 , n}, 0; *0} va miiu
X=(XIoX2 Xt.)E 0. Xac dinh i E{t, II}:X EO;.
2.2.2 M~og Naron mu philo lOp m~u
A. Cd cIte'ho<;ltdQng, diu truc cua m<;lngNdron ma (FNN)
Cd elle' hoar donf: khi mQt miiu d~u vao d11'Qccung c1lp. ailu tien
m<;1ngse mClh6a miiu nay va Hnh loan dQ thuQC(muc dQgi6ng Mall)
gifi'a miiu vai H(tca cac miiu dii hQc, tie'p theo, m<;1ngse d<;1td11'<;IcmOt
ke't lu~n bi'1ivi~c chQn ra mQt miiu dii hQc c6 dQ thuQc cao nh1ltso vdi
mliu d~u vao, cuol cung tie'n hanh khu mCl,r6i gtti n6 Mn mQt d~u fa.
Cdu truc cua man$!:g6m 4 t~ng.
- Tilng tM nhat (lIMp): Nh~n mliu nh~p vao m<;1ng.G6m N1xN2
INPUT-FN trong tr11'Clngh<;1pmAllnh~p c6 kich th11'deN,xN2 ph~n ttt.
- TOngtlll1hai (ma h6a): M<1h6a cae mAll nh~p thOng q\Ja ham trQng
so' w[m,n]. G6m N(xN2 MAX-FN hiSn thi theo hai ehi~u. M6i MAX-
FN co M d~u ra
=s6l11'<;1ngFN trong t~ng thu ba. Trong d6, y~im la
d~u ra thum cua MAX-FN th\1'(p,q) co gia triE[O.I] d11'Qclien ke't vdi
MIN-FN th\1'm trong thg th\1'ba, no philo anh dQ thuQc gifi'a phh ttt
(Jvi tei (p,q) cua miiu nh~p vdi phh ttt t11'dng\1'ngcua miiu hQc th\1'/11.
- TOngtM ba (bilu diln dQthuQc vao /1IJuhQc): G6m M M/N-FN, m6i
M/N-FN trong t~ng nay bi~u dieD dQ thuQc cua mAlldang xct vai mQt
miiu dii hQc(M la s61u'<;1ngcae miiu dii hQc).
- TOng tM tll (TOng xudt - khil mal: ChUng t6i dung M COMP-FN

trong thg nay t11'dng\1'ngvai M mliu dii hQc, cho phcp eung c1lpcac
d~u ra dii khtt mCl(1 ho~c 0). M\1c lieu cua t~ng nay Ia: xac dinh mliu
nh~p thuQc v~ miiu nao trong M miiu dii hQc. Tim dQ thuQc Ian nh1lt.
Ne'u tho.1 ngu'ong T cho phcp d~t la I, cae gia tri con l<;1icho v~ O.
Trong tru'i'1ngh<;1pkh6ng thoa ng11'ongT eho tru'dc th1 M COMP-FN
nh~n gia tri 0: kh6ng thuQc v~ b1ltc\1'miiu nao trong cac mliu dii hQc.
B. Thu~t gidi hQc tlf t5 chllc cua I1I<;lngNdron /1Ia
Cac tham ,wi cein thie't: Cac tham so' cua ham ra d6i vdi cac Naron
MAX-FN trong t~ng th\1'hai: dQ rQng cua ham thanh VieD a, h~ so'
mClhoa f3va 9pqm(cho tung t~p p, q va m). so' 1u'<;Ingcae FN trong
13
t~ng thU'ba va thU' t\1'(M). Tf la ng\1'ong 16i eua m(,lng Ndron roo
(FNN) (O<=Tf<=I) va Kia t6ng 56 cae m~u hua'n luy~n (k=1 K).
Cae bll(Jceila thuat ~?idihoc:
BlI(Jc 1: T<,tocae m~u INPUT-FN kieb eo NIx N2 trong t~ng tM nha't
va cac mftu MAX-FN kieb co NIx N2 trong t~ng thU'hai. ChQn mi?t
gia tricbo a (ex>=0) va mi?tgia leithichh<;lpcho{3. .
BlIae 2: f)~t: M=Ova k=l.
BlIae 3: f)~t M=M+l. T<,tora Ndron MIN-FN thU'M trongthg tbU'ba
va Naron COMP-FN thU'M trong t~ng thU't\1'.Xac djnh:
[2J N, N, ,.
e
pq
M =S
pq
M =max (max (W[p-l,q-j]Xljk»
1=1 /=1
p=I,N1;q=I,N2
(2.13 )
Trong d6, epqMla diSm teQngHim cua ham ra M eho Naron MAX-

FN thU'(p,q) trong t~ng iliU'hai. Xk=(xijd la m~u hua'n luy~n thU'k.
BlIcJc4: f)~t: k=k+l.
Ne'u k > K th'i thu t\lc hQc5e ke't thuc,
Ngu'qc l<,li
- Nh~p mftu hua'n luy~n thU'k vao m<,tngva tinh loan d~u ra cua m<,tng
Ndron mo hi~n t<,ti(vdi M Ndron mo trong t~ng thU'ba va thU't\1').
- X:icdinh: M
. (j =1- max(iJI)
I" Ik
trong d6 y~;1 Ia d~u ra cua MIN-FN thU'j trong t~ng thU'ba U'ngvdi
mftu hua'n Iuy~n thU'k (Xk).
-Ne'u 8 <=Tfth'i quay I<,tiBlIae 4.
- Ne'u 8>Tfth'i quay I<,tiBlIac 3.
c. Hi~u qua eila Thu(it gidi hQc H!t6 chile
Dinh Iy 2.2 (Thu(lt gidi hQc elft6 chuG tlm cdu truc nlgng)
rho tr\1'ocmQt mh hua'n luy~n
l
XNxN.
r
va T mftu dich (56 Naron
I 2
l J
'
d~u fa (t~ng thU'hi» vdi ma tr~n tr<,tngthai tu'dng U'ng (JNI,N2.t =I,T.
Cho d9 rQng ham tbiinh VieD a ~ 0, M 56 mo boa (3va ng\1'ong16i
Tf' Luc nay, 56 lu'<;IngNaron trong t~ng thU'ba va thg iliU'tu' cua
m<,tngmo (M) du'<;Icxac dinh I<,tinhu'5au:
M
=T+ f;(5,Tf)
.

[
0 neu8-Tf~O
trongd6. f.(8,Tf)= I ntu8-Tf>O
(2.14)
(2.15)
T [3]
8 = 1- ~ax (Y
j
' k)
J=I ,
va
14
y~l :Ia d~u ra t~ng tha ba cua m~ng roo: daub gia d(}thu(}ccua
miu hua'nluy~nk vao miu dichthaj.
H~ qua 2.2
Cho K miu hua'n luy~n va T miu dich ban d~u. sfi Naron tfii da
dlt<1cb6 sung trong t~ng tha ba va t~ng tha tit cua m~ng mo 1£1K
Naron.
Luc nay,
H~ qmi 2.3-
Cho K miu hua'n luy~n va T m1iudich ban d~u. Trong trltong hQp
tfii thicgu,se khong c6 ba't ca m(}tNaron mo nao dltQc b6 sung cho
t~ng tha ba, ding nhlt t~ng tha tit cua m~ng.
Luc nay, M=T (2.17)
2.2.3 So sanh m{lng Ndron mu yoi m{lng Ndron trllyill tTrang
Bang 2.1 So sanh thoi glaD hua'n luy~n giil'a thu~t giai hQc tlf t6
chUc FN va thu4t il1iIan tru ~n n l.iqc (NN)
Phltdng phap sfi chii'hua'n T~p miu ThiJi glaD
lu ~n man dich hua'n lu ~n
FNN 5460 26 273 ( hut)

NN 5460 26 9555 ( hUt
Bang 2.2 So sanh ty I~ nMn d~ng (%) giil'aFNN va NN (kicgmtea
M=T+K
(2.16)
FNN ili xu{{t illlf/c so sdnh va; NN trang biti todn Nhq.n dr;mg chi]
viet tay.Vi mvc 2.2 t~p trung giai quye't bai loan phan lop m1iu x
(tru'ong hQp miu x 1£1m(}t vec td), Den cac chii' vie't lay dltQc thti'
nghi~m voi m(}tlieu chi daub gia duy nha'1:vec ta il{ic trlfllg foa" qtC
8x8. Bang 2.1 va bang 2.2 phan anh ke't qua so sanh giil'a mr;lIIg
NaronmiJbOntting(FNN) va nu;l1IgNarollba tting(NN)khi dung voi
cac chil' thti' nghi~m (bicgudi~n bdi vec ta il{ic trlmg toan C!lC8x8)
thlfc hi~n teen may Pentiumll-PC 266 MHz. Nh~n tha'y, FNN hi~u
qua hdn NN ca v~ thiJi gian hua'n luy~n cling nhlt ty I~ nMn d~ng:
FNN Ia kha thi va c6 thcgap dvng n6 cho bat loan phan lOpmiu.
15
2340 chii'
Phltdng sfi chii'dung
sfi chii'
Ty I nhn
Ty 1 16i
phap
sai
dang
FNN 2122 218 90.68% 9.32%
NN 2068 272
88.38%
11.62%
2.3 Thu4t gidi di truyill li@nk@'toh!~u m(lllg N(frOIfa:Ull1gdQog eho
bai tmlo pMn lOp m4u (m4u g~m M vee td)
2.3.1 M6 hlnh bai tmlo

Nhu mQc 2.2.1 dii trlnh b~y. bai tmio philo Idp m~u X khong ma't
mat thOng tin duQc chia thanh hai ba.i loan con: Bai toall phan lop
mdu X g6m 1 Vt1ctd (MQt tieu chEduy nhdt danh Kia X) va Bai roan
phan lop mdu X g6m M vec td (X dlt{1cdanh Kia biJiM tieu ch£). MQc
nay se t~p trung tlm hieu va giai quye't Bai roan phiin LOpmdu X g6m
Mvec(d. Bai loan nay duQCdjnhrighlanhusau:
Cho!1 la mQt phan ho~ch cac {!1;, i Ell, 2, , nl. !1; *O) va
m~u X = {xl = (x(, x;, ,xI}:xJ en, J = {I, ,M}}
Xacdjnhie{l,n):Xe!1;.
2.3.2 Cae phu'dng philp li@ok@'tnhi~u m(l1JgN(froll
Co hai phudng phap t5ng quat cho vi~c ke't hQp cua cac mr;mg
Ndron: cach thU nha't d(ta VaGkj thu~t tuyln ch{Jn(p"ltl1ng phdp dem
Borda), con cach thu hai d(ta VaGkj thuQt lien h{1p.Lu~n an tlm hieu
phlt<1l1gphdp d(ta vao kj thu~( lien h{1p, vdi phlt<1l1gphdp nay, vi~c
phan lo~i mQt m~u nh~p X dtla vao t~p cac gia trj thl,l'c:P(!1;IX), I S;i
S;11,cho bie't xac sua't de X thuQc mQt trong n Idp ban d~u. Sd d6 lien
ke't m~ng bao g6m M nl{lng Ndron, I phep tinh tren m6i m~ng se t~o
ra mQt t~p cac gia trj xac sua't dung nhu sau : PI (!1; I X), IS;IS; M,
IS; is; n. MQt m~ng ddn gian ke't hQp cac ke't qua teen m~u X tu ta't ca
M m~ng ca the bhg vi~c su dQng gia trj trung blob dum day nhumQt
Hnh loan mdi cua lien ke't m~ng:
Nhu v~y, co the hieu trj s6 ke't hQp ohu mQt phan ldp trung blob
P(o,lX)=lfp.,(o,lX), l:~i:S;11 (220
MJ-I
cua phudng phap Bayes. Tinh loan nay se duQc cai tie'n ne'u daub gia
kha Dang djnh hudng cua cac d~u ra dl,l'ateen cd si'1cac tri thuc tho
duQc v~ muc dQ tin,5h cua tung .m~ng :
P(!1, IX)
=Lr;PJ(!1, IX), 1:S;i:S;n
. M J-t

0 day Lr;=1.
1-1
(2.22)
(2.23 )
16
2.3.3 Thu~t gbli di truy~n xac djnh h~ s6 tin c~y cho cae dilu ra
CURtung m{lllg Ndron
Trong qua trlnh tinh loan, ThUQtgidi di truyJn anh x~ khBng giRD
giiii phap bai loan len t~p hl;1pcae chu6i, m6i chu6i biEu di€n mQt
giiii phap ti~m Dang.
Trong bai loan nay, mQt chu6i phiii ma bOa nxM thRill 56 gia trj
thlfc (r/) trong bi~u thU'c(2.22), bhg each nay mdi thu du'l;1cnhung
h~ 58 ke't hl;1pt8i u'u cho vi~c lien ke't cae m{lng Nuron ca th~. M6i h~
58 du'l;1cma h6a thanh 2Lbit va du'l;1cdi~u chlnh trong khming tir [0,1].
Sau d6, ThuQt gidi di truyin se thao tac tren cae chulli ma h6a M tlm
kie'm nhung giiii phap t8t hdn U'ngvdi mlli Mn t~o sinh.
Phu'dng phap d~ nghj 5e Ia'y t~p hl;1pcae h~ 58 (r/) CURcae m{lng
Nuron cd tM dB hlnh thanh nhfi'ng chulli ma tu'dng U'ng.
2.3.4 Chung minh Hnh hQi tQ CURThllQ.tgiai di trllyin trong qua
trlnh xac djnh M s6 tin c4Y
Bjnh Iy (djnh Iy v~ Hnh hQi tQ CUREA trong [KTN2000])
Cho EA=(I, cp Q, 1/1.s. 1;J1,A)
Giii thuye't:
(i) KhOng giRDWi giiii /la t~p hUuh~n.
(ii) T6n t~i 1i'1igiiii a* e I
Khi d6, vdi mQi quaIl tM khiJi t{lOprO), EA se thod cdc diJu ki~1Isou:
(I) Dirng 5au mQtso'bll(Jc l{ip hau h{lll: 'fEA<oova
(2) Ke'tquii thu du'l;1cCUREA kill ap d\mg,len quan tM khiJit{lOprO)
HiICJigiiii t8i u'ua*: <1>(0')= min{<1>(a)laeUvr(P(O))}.
Bjnh nghia 2,11 (Sai 56 E) ,

SRi s6 ECURs6 thlfc la sRi 56 thu du'l;1ckhi anh x~ gia trj CUR58
thlfc d6 v~ mi~n [UmimUmax] ba'tky; Umin<Umax.Umin>-oo. Umax< + 00.
M~nh d~ 2,1
Cho tru'dc vec td nhi philo g6m L bit d~ anh x~ mQt gia trj thlfc x
v~ rni~n [UminoUmaJ.Luc nay, SRis6 E CURx 5e du'l;1cde djnh theo
cBng thU'c5au:
£ -(U U_){y
M~nh d~ 2.2 - 2
Cho tntdc sRi 58 E CURmQt gia trj thlfc x. S8 bit nhj philo L dn
thie't dB anh x~ x v~ mi~n [UmimUmax].du'l;1cde djnh theo cBng iliac:
L=Round_UP(IOg,((Umn-Um:f6xd)
(2.26)
(2.27)
17
M~nh d~ 2.3
Cho vec td nhi phan string2 dQ diUL bit bieu dien ghi tri th1,icx e
[Urni",Urnax]'Luc nay, x se dU'(,1cdc dinh theo cong thl1'c:
x = U + decimal (string 2)X g
g =(U.Q - U -)6 L - 1)
(2.28)
trang do,
H~ qua 2.4
T5n t~i chu6i nhi phan string2bieu clietth~ s6 tin c~y r/e[O,I]
thoa sai s6 e E 91 cho trU'dc. .
HI; qua 2.5 (di!m hQitit ella h~ sr{tin el,iy)
Sau mQt s6 bU'dcl~p hil'u h~n, Thul,itgidi di truy€n se Hm dU'(,1cbQ
h~ s6 tin e~y t6i u'u, r/ (J=1,M , i=I,n), ung vdi sd d5 lien ke't M
n/.{lngNaron thoa sai s6 e E 91 cho trU'dc.
2.3.5 Phan tleh, danh gia mo hinh d~ xua't
A. Bai loan flu]nghi~m

De chI ra tinh kha thi cua mo hlnh ke't h(,1p:Thul,itgidi di truyln
lien ke't nhi~u mgng Naron trong phan lap m~u, chung ta quay trC1l~i
bai loan vi dv C1mvc 2.2.3: liMn dgllg ella viti lay. s6 chu thit nghi~m
la 26 chu cai vje't lay thU'ang vdi: lOx30x26=7800 chu, trong do,
7x30x26=5460 chil hua'n luy~n va 3x30x26=2340 chil kiem tea. Cae
chil vie't lay dU'(,1cdanh gia Mi 3 lieu chi khac nhau (3 d~ng d~c trU'ng
ri~ng bi~t): vee ta 4 dge trllng dja phllcmg 4x4; vee ta dge tr/.lflgloan
cite 8x8 va vee ta d{ie trllng bi!u diln bien ella ehil (mvc 2.2.3).
B. NluJn dgng ehil viti lay
Mgng Naron truyln theine ba tdng(NNi} vdi Thu(1tKid; Ian truy€n
ngll{1ese dU'(,1cdung de hQCva nh~n d~ng cac d~ng vec td d~c trU'ng
nay. Cv the, NNI dung rieng cho vee ta 4 d(ie trllng dja phllcmg 4x4;
NN2 dung cho vec ta dgc trllng loan cite 8x8; NN3 dung cho vee ta
d{ic trllng bi!u diln bien clla chil.
Tung m~ng se dU'(,1chua'n luy~n vai 5460 m~u chil va dU'(,1ckiem
tra tren 2340 m~u chu va ding th1,ichi~n tren may Pentiumll-PC 266
MHz. Vdi phU'dng phap nay, m6i m~ng se hlnh thanh quye't dinh
thong qua tieu chuifn rieng cua no.
Sau khi hua'n luy~n ca ba mgng Naron vdi cac d~c trU'ngrieng
bi~t. GA du(,1cdung .de Hm ra nhilng tham s6 t6i u'u cho vi~c ke't h(,1p
cac m~ng. Quh the ban dh vdi 100 ca the, m6i ca the chl1'a840 bit
(3x35x8). Nhilng tham s6 tie'n hoa dU'(,1cdung trong thit nghi~m nay
18
nhu' sau: xde sudt lai ghep t{li mQt dilm la 0.6 (60%) vii cae xae su{;'t
dQt bitn bang 0.01(1 %). Gid tr; tMeh nghi du'~c gall cho mQt chu6i
b~ng vi~c ki6m tra tY l~ nMn d{lng vOi cae m~u chfi' dii hu1i'nIuy~n.
Chu trlnh xu Iy ti€n Ma ditng Il,Iikhi gia trl thich nghi to't nha't cua
qu~n th6 khong du'(jccai ti€n hdn nii'a trong cae vong I~p tie'p theo.
Cac ke't qua so sanh ty I~ nh~n dl,lngteen bQ dii' Ii~u ki6m tea khi
su d\mg cac m{lngNuron rieng bi~t: NNl, NN2, NN3, NNal1:hulln

luy~n vOi t1i'tca ba bQvee td d~e tru'ng; cac phlicJngphdp ktt h{fp ba
m{lng NN truyen th6ng: phlicJngphdp trung blnh, phu'dng phap Mm
Borda (dlfa viio ky thu~t tuy6n chQn: xe'p h~lng) va mo hlnlt de xu{;'t:
GA lien ktt 3 m{lng NN. Nh~n xet: Bllt ct1 phu'dng pilar ke't h<;1pba
ml,lng Ndron nao ding dl,lthi~u qua cao hdn vi~c su dvng rieng bi~t
titng m{lng Naron. M~t khae, mo hlnh d~ xullt: GA lien kIt 3 m{lng
NN Il,Iitho du'~c hi~u qua eao hdn so vOi vi~c su dvng cac phu'dng
phap k€t h~p khad (93.29%).
Hdn nii'a, phu'dng phap d~ fight cling du'~e so sanh vOi mQt so'ke't
qua cua mQt vai phu'dng phap truy~n th6ng va mdi nhllt. Nh~n thlly:
hi~u qua eua mo hlnh d€ xudt Iii dang quaD tam va co th6 so sanh no
vdi nhfi'ng phu'dng phap nh~n d~lngchfi'vie't lay t6t nhllt hi~n hanh.
Chu'dng 3
Klh HQPBA KY THU';' T: THU';' T GIAI DI TRUYEN, MANG
NaRON v A.LOGIC MC1
3.1 MQt s6ky thu4t kit hr,fpDi truyill- Ndron- Mil
3.1.1 M~ng Kohonen d'n djnh trj s6 thich nghi IDa cho ThuQt gidi
di truyin
Djnh nghia 3.1 (vee ta d{ie trling)
M~u F du'~cdinh nghia Iii mQt vee ta d{ie trling co L phh tu:
F=(jl, 12, ,/L). Trong d6, fie (O,Max); gia tri Max tuy thuQc vao bai
loan cl,lth6; i=1 L.
Dinh nghia 3.2 (mdu trunK blnh)
Vec td d~c tru'ngbi6u di~n mdu trunK blnlt 0 dtt~c dinh nghia:
0=(01. O2., , OL).
Trong d6,
0 I = [ Im'o :1m lImlo = 0 va I max= Max ; i = 1 L.
(3.1)
19
Djnh nghia 3.3JmJu dQidi~n)

Bitt.n = U 11.; 11. ~ 0 ; 11 . (")11 . ~ 0 vui i ~ j.
i= 1 I I I J
Cbo tru'de mQt m~u: p'=(p'J, P'2,'", p'L)e 0,. Lue d6, pi du'cjegQi la
mdu d{li di~n eua khOng gian OJ.
Dinh nghia 3.4 (Khoaog cach rang buQc)
Cho tnidc 2 m§u A, B. Khoang each rang buQc giua A va B du'clc
dinh nghianhu'sau: -' £
d(A,B)=AB=IA-BI= 2:(al-b,)'
Dinh nghia 3.5 (G6c) 1.0
Cho tntdc 2 m§u A, B. G6e giua A va B du'QCdinh nghIa nhu'sau:
( )
-I (A- O)(B- 0) -I (A- O)(B- 0)
a A,B =LAOB =COS COS
ADx BO d(A,0) x d(B,0) (3.3)
(3.2)
M\le nay d~ xua't mQt ky thu~t a'n djnh tr! s6 Wch nghi mo: Xac
dinh muc dQ ddng df;lnggiua hai m§u (vec td) A va B ba't ky. Ba df;li
Iu'Qng: Khoang caeh(d), Goc(a) va L'n tf;losinh thu(g) la cd sfl d~
danh gia mue dQ ddng df;lngnay. Trong do, u'u tieD s6 1 la Khoang
each(d): phan anh stf sai kMc v~ gia tr! giua cae ph'n tit cua hai vec
td A va B. Uu lien s6 2 la G6c(a):phan anh dQ l~ch giua hai vec td
thOng qua m§u trung blnh O. Cu6i cung Ia L'n tf;losinh thu(g) d~
danh gia muc dQ t6i u'u cua Thu~t gicii. Ba df;lilu'clngla d'u vao de
xae dinh muc dQ ddng d1)ngcua hai m§u A va B teen nguyen t~c: (d)
va(a) dng nha thi A va B cang gi6ng nhau va (g) nM thi thu~t gicii
cang t6i u'u. .
A+B
He th6n~ mC!+ man~ Kobonen
r"""""""""""""""-""""'-"""";""""""-"'-"""""'""""""""'j ISm:
I

M
i Ldn(l.O)
I ang ,
I
d
K
.
h
! TB-Ldn(O.7)
.
L
.'
V( ) 0 ODeD I
! a U\ltmo. V V2, ,V27 ;~TB(OA)
I . 'v'VIE[O,I] I TB- Nho(O.I)
i g i Nho(O.O2)
l J
20
3.1.2 (fog d\mg ThuQ-tgitUdi truyin(GA) voi ham thfch nghi mo
ddl/c in djnh trong m\lC3.1.1 di t:Jo ra qudn thi M mftu
- I
F,.,k =I,M ddng d:Jngvoi P Eill
Djnh nghia 3.6 (ngl/iJng tr; sd thEchnghi &)
Cho tntoe mau d<,\idi~n Peni (dinh nghla 3.3) va qu~n th6 N ca
th6 Fj. j = I, N
.Ngl/iJng tr; sd thEch nghi &e[O.I] la ngu'ong qui dinh
dn thie't d6 daub gia mue dQ d6ng d<,\nggiii'a Fj va mau d<,\idi~n pi
(mue dQFjeni).
Ne'u tr; .fd thEchnghi cua FJ>-&tIll ke't lu~n: Fjeni.
Ngu'<;1c I<,\ike't lu~n: F/~nl.

Dill blziloan
Cho tnfoe mau d<,\idi~n
P eni (dinh nghla 3.3) dn xac dinh M
mau Fko k =I,M d6ng d<,\ng voi P.Co nghla Ia tlm ra M mau Fk sac
eho Fk e 0.1; k = 1,M .
Tlmat gidi
T<,\omau d6ng d<,\ng(GA + FS + m<,\ng Kohonen)
pi r""~"~'~~;:~~"""""'~';~'~;~";:-"""""""""'~'~:"'I
I
ho~c sau SVL I
khong I
Tmin ttcdi truy~n
I
I
I (GA)
I " 1
pi + popF[Mj
3.1.3 Hi~u qua CUBroo blnh ktt hrfp Vi tmyin KohOlte11.Mll trong
xac djnh miu ddng d~ng
M~nh d~ 3.1
Cho tru'oc mdu d{li
di~n Peni (dinh nghia 3.3) va quh th6 khoi
t<,\og6m N ca th6 FI'j = I,N; Nnguyen7?l. Cho tnfoe ngl/iJng tr; .f/I
thlch nghi &(dinh nghia 3.6) va sd [I/<lngcac Mn t{lOsinh G. Ghi thie't
qu~n th6 chua cae ea th6 pIlau bi~t va bie't M s6 cua cae loan tti' di
truy~n. Llle nay, s61u'<;1ngm~u d6ng d~ng voi P;enl Iii M(G) du'<;1c
xac dinhthee cong thuc: G
M(G) = Lm(g) (3.4)
Trong do, m(g) Iii s6 1u'<;Ing;;;au d6ng d<,\ngvdi pi (TSTN 7?&)t<,\i
I~n t<,\osinh thu g.

21
B6 d~ 3.1
Ne'u M(G) =0 (Hnh theo m~nh de 3.1) thl ke't lu~n : thOng t6n t;.1i
. m~u d6ng d;.1ngvdi pi sau G l~n t;.10sinh eua ThUf)tgidi di truyln thao
- lac teen mien qu~n th~ khl1it;.10Fl' j = 1,N .
M~nh d~ 3.2
Cho trtfde mdu d(li di~n pieni (djnh nghla 3.4) va qu~n th6 kMi
t;.10g6m N ca th~ Fl' j = I,N . Cho trtfdengllilngtr;.rdthfchnghi EVa
s61tf<1ngt6i thi~u cae mau d6ng d;.1ngvdi pi E n; la (M). Gia thie't,
quh th~ ehua cae ea th~ rieng bi4\t va bie't h~ 56 eua cae loan tli'di
truy~n. .
Lue nay, s61h t;.10sinh G dtf<1Kexae djnh:
G =K ntu Lm(g)? M
1=1
Trong do, m(g) 13s61tf<1ngcae m~u d6ng d;.1ngvdipi t;.1il~n thu g.
B6 d~ 3.2 K
Ne'u thong t6n t;.1igia trj K nguyen dtfdng d~ Lm(g) ~ M(tinh theo
m~nh de 3.2) thl.rd Lant(lO.rinhG thOng de djnlC'
H~ qua 3.1 G
Ne'u tfln t;.1iG l~n t;.10sinh sao eho Lm(g) ~ M (m4\nh de 3.2) thl
ehiic chiinse co t6i thi~u M m~u d6ng d~~g vdi pi eho trude (t6i thi6u
M m~u Fko k = I,M en;).
3.1.4 BQ nM ke't hQ'pph\lc h~i maD ma't mat th6ng tin
Djnh nghia 3.7 (nulu mat mat thOng tin)
Mdu ma't nuN thong tin Xmmllla mQt vee td d~e trtfng co L phh tli'
vdi nhii'ng phh tli'bj thie'u hvt dtf<1equy v~ gia trj D:
ThOngtinbL ~
X/lIltllt=(Xlo X2, , D, D, D, D,. . . . D, D, D, D, Xi).
(3.5)
D~t bai tOiln

Cho trtfdemdu a(lidi~npieni, bie't:
n
Q= U Q.;Q.;t:0;Q.()Q.;t:0vai ;;t:j.
;=1 t t t J
Cho m~u milt mat thong tin Xmmtt(Bjnh nghla 3.7). Bie't Xph~c-,,&;eQ.
ch xae djnh Xph~c_h&itit Xmmttva thOng gian m~u Q.
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Cach ghH quy€t
(1) Xae dinh 0 ttt mau d{li dien pi:
Tir pi en; xae dinh dtic;1eM m~u h k = 1,M d6ng d1,lngvoi p;
M + I k M .
(mve 3.1.2). E>~t: U T
= U Fk U pI
k=l k=I
.n. =
{T
k =
(
'T'k
T
k
)}
(M+I)Xn
:::):!ol: .£1 , , L k=1
(2) Sau khi co b() mau hudn [uyen o. Sri d{lng B() nM kgt IU/p
(Associative Memory- AM) ph{le h6i mau mat mdt thOng tin
3.1.5 GA lien ke't cae lm;l1Igmu: ung dQng cho pMn lo\li mfiu
PIll/dug pluip kef II(/pnhi!u ",(lllg Ndroll mu(FNN).
C6 hai phtidng phap t6ng quat eho vi~e ke't h<;1pcua cae m{lng
Naron: cach thu nha't dl/a vao ky thugt h{1pl1hilt,con cach thu hai d{ta

vao ky thugt tuy/!n;eh(Jn. Mvc nay d~ c~p den PIll/dug pluip d{/a vao
kj thul;t h(fp nMI. .
Cho trtioc m~u X ={Xl = (X.k, X: "",X~IXNJXk eO, k = {I, ,n}}
M
(chtiabie'tthuQclop nao) va khong giancae lOp0 =Uo" 0; *0,
0;" nj =0 , i * j. 1=1
E>6phan lOp m~u X v~ khong gian 0;, i = I, M eho trude, d~u lien
phai phan lop cac tr1,lngthai xt, k = 1,n v~ mQt trong M lop ban d~u.
S\t dvng n m1,lngmo cho m~u X, m1,lngmo k se dung cho tr1,lngthai xt,
n6 danh gia gia tri xac sua't dung d6 Xk e OJ' k = 1,n; i = 1,M nhti
san:
l{(~ IXk)=y,~], l~k~n, I~i~M. (3.6)
Trong do, YikI3].I~ i~ M, I~ k~ n, chinh Ia d~u ra cua thg thu 3
trong m{lng Naron mif (FNN) thu k (ehtidng 2- mve 2.2.2). Nhti v~y,
khOng dn th\fc hi~n t~ng thu 4, cac ke't qua cua thg thu 3 se la d~u
vao d6 th\fc hi~n ky thu~t ke't h<;1p.
Lue nay, sd d6 ke't h<;1pbao g6m n m1,lng,m6i m1,lngk se danh gia
gicilei xac sua't dung Pk(OJ IXk}k
= I,n; i = I,M.
Quay Ira [{Iim{le 2.3: Thugt gidi di truyin xde dinh he sa tin et;1y
clIo cdc dilu ra eila tung 11I{lngNaron se dttQc ap dvng cho cac mr,ll/g
Naron mo.
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