T^p chi Tin hQc va Di4u khiSn hpc, T27, 54 (2011), 329-340
CAU TRA L 6 | G A N DUNG CHO TRUY VAN NULL TREN MO HINH Cd s d OUT LIEU Hl/dNG DOI Tl/dNG M6 THIEU THONG TIN
D O A N VAN BAN^ TRUONG C O N G T U A N ^ , D O A N VAN T H A N G ^
^ Vien Cdng ngh? Thdng tm, Vien Khoa Hoc vd Cong Ngh$ Vi?t Nam
^Dai HQC Khoa HQC - D^i HQC Hui
^Cao Ddng CNTT Hau Nghj Vm Hdn
Tom t a t . L^p lu^n tuong tu la mOt c5ng cy suy diln quan trpng trong nghien citu tri tue nhan tao.
Truy v^n Null la nhiing truy vin md nd nh^n mOt cau trk ldi Null tit hf thong co sd dQ lieu, thudng la vi thong tin khOng day du trong co sd dfl li?u (CSDL) Ldp ludn tUOng tU thdt sU rit Id hflu ich dl tao ra mot cdu tra ldi gin dung cho truy v§ji Null. Ldp ludn tuong tu sii dung phu thuOc hkm md de tra ldi cac truy v4n Null tren cO sd dfl lieu quan he md da dUdc nghign cflu. Bai bao de xuat mot cdch tilp c&n dl cd dfldc mot cdu trd lpi g^n dung cho truy vin Null tren mo hinh CSDL hudng doi tfldng (HDT) vdi thong tin md vd khOng ch^c ch^n dfla tren dai s6 gia tfl (DSGT). PhflOng phdp tiep cdn d day dfla tren Ikn can ngu: nghta cua DSGT dl xay dflng cdc xdc dinh md thu5c tinh va xdc dinh md phfldng thflc.
A b s t r a c t . Reasoning by analogy is an important inference tool in the study of artificial intelligence Null queries are queries that Find an answer to Null from the database system, often because of the imcompleteness of information in the database. Analogical reasoning are really useful to generate an approximate answers for Null queries. Analogical reasoning using fuzzy functional dependencies to answer null queries on fuzzy relational databases have been studied In this paper, we present an approach to obtain an approximate answer for Null queries on Object-oriented database model with fuzzy information and uncertainty based on hedge algebra. Our approach was based on the concept semantic neighborhood of hedge algebra to build attribute fuzzy determination and method fuzzy determination.
1. M 6 DAU
Md hinh CSDL quan hg va hUdng d6i tupng md chita thong tin khong diy dii, khdng chinh xdc hodc khong chic chin da dUdc nghien cflu rdng rai trong nhfmg ndm gan dky [l-U]. Dl bilu dien nhflng thdng tin md trong md hinh d\i ligu, cd nhilu hUdng tilp can cp ban' mo hinh dua tren quan hg tUPng tU [5] vk md hinh phan b6 khd nkng [1], . . .
Mdt can truy van ditpc xem Ik truy van Null khi nd nhkn dUOc cau trk Idi Null ti( CSDL.
Cau tra ldi Null cd thg dupc sinh ra do nhieu nguygn nhan khdc nhau. Nguyen nhkn thd nhit, Ik khi dfl lieu trong CSDL khdng thoa man dilu kign cua cau truy vin. M6t nguyen nhan tiep theo, hokc la do dfl lieu khdng ton tgi trong CSDL, ching han ta truy vin cdc bp (tuple) dfl ligu t'i quan hg R, nhitng chiing khPng ton tai trong CSDL. Mpt nguyen nhkn nfla, dd Ik do thdng tin khdng diy du trong CSDL, nguyen nhkn nky thudng Ik do gid tri thudc tinh cua
330 D O A N VAN nAN, T R U O N G C O N G TUAN, D O A N VAN T H A N G
mdt s6 d6i tupng bi tliilii Vii ngodi ra cbn c6 lut nhilu nguygn nhkn khdc nhau Bki bdo se tap trung nghien cflu liuy \'aii Null dUpc Hinh ra do iiguyfin nhdn thdng tin kliPng diy du trong CSDL. Iliu hit Irong cdc CSDL tniyeii th6iig khi truy vin dfl Ugu trong trudng hpp nay thi cdu trd ldi Null ludn dupc tgo rn. Tuy iiliiOn, vigc cd difpc cku t r i Idi gin dung thi bao gid Cling t6t hdn khi nhkn ditpc mol cau iid 16i Null,
C'ac lar gii trong [5] dn ditn rn md hinh ly thuylt sfl dung Idp lukn tfldng ti,t d l t r i ldi cdc truy vmi Null cho md hinh CSDL quan h? md ditn vko phdn b6 k h i ndng. Tuy nhien, trong md hinh nky. Duftn khdng xem xel dfl ligu vdi cdc mien ttfdng tU rdi rac. ndi dfl hgu c6 till dupc md hinh hda llidng qua cdc m6i qunn lig titdng tif,
Difa \-ao nhflng ifu (li(''in ciia cmi tnic dgi s6 gia fu (DSGT) [7], cdc tdc gik da nghien cflu mp hinh CSDL quan hO [8-10] vk hitdng d6i tifpiig [2, 3] md difa trgn cdch tilp ckn cua DSGT. trpng dd ngfl ngliTn ngdn ngfl ditpc lifpiig li6a bing cdc dnh xa dinh lupng ciia DSGT.
Theo cdch tilp can cua DSGT. ngfl iigliia ngdn ngfl cd thi difpc bilu thi bing mpt ldn can cdc khoang difpc xdc dinh bdi do do tinh md ciin cdc gid tri ngPn ngfl ciia mdt thudc tinh vdi
\-ai trd Ik bicn ngdn ngfl Bdi bdo sfl dung ly thuylt lap ludn tifOng tu [5] d l trd ldi cdc truy vin Null cho inP hinh CSDL HDT md difa theo cdch tilp ckn DSGT.
Bai bdo difOc trinli bky nhu sau, Muc 2 trinh bky mdt s6 khdi nigm cP bdn lign quan den DSGT 1km cd sd cho cdc muc tiep theo. Muc 3 trinh bky cdc dinh nghia vl xdc dinh md thupc tinh. xdc dinh md phifpng thflc vk cP chi lap ludn tfldng tu cho viec tra ldi nhflng truy vdn Null Muc 4 trinh bay cac qui trinh sfl dung xdc dinh md thudc tinh, xdc dinh md phitong thi'tc vk mdt s6 vi du minh hoa cho y tifdng ciia hfldng tiep ckn nky, va cuoi ciing Ik kit ludn.
2. M O T S 6 K H A I N I E M C O B A N
Sau daj' Ik mot sd khai niem ve dnh xa dinh htpng [7] vd cdch thflc xdc dinh cdc he lan ckn ngfl nghia dinh htpng [8, 10]
2.1. Dai so gia tvt
Cho mdt DSGT X = {X. G. H. <), trong dd X - LDom{20, G = {1. c". W . c+. 0} la tdp cdc phan tfl sinh, H Ik tap cdc gia tfl ditpc xem nlnt Id cdc phep todn mdt ngdi va < Ik quan hg thfl tif ngfl nghia trgn X. T^p X dflpc sinh ra tfl tdp G bdi cdc phep toan trong H. Nhit vky. mdi phin tfl ciia X se cd dang bilu dien x ^ /(n'^n-i hix.x G G Tkp t i t ca cdc phdn tfl dupc sinh ra tfl mpt plian tu x dfldc ky higu Ik H(x). Cho tkp cdc gia tfl H ^ H" U H""", trong dd //"'' = {hi...., hp} va H~ = {/i_i...., h-q], deu Ik tuyln tinh vdi thfl tif nlnt sau:
hi < ... < hp vk h-i < ... < h-q, trong d6 p.q > 1. Khi dd, ta cd cdc dinh nghia hen quan nhif sau'
D i n h nghia 2 . 1 . Hkm fm:X-> [0.1] dUpc gpi Ik dp do tinh md tren X neu thoa man cdc dieu kien sau:
1. fm Ik dp do md day dii tren X, tflc Ik YI fm{hiu) - fm{u).
-Q<i<P. i / o
2. Nlu x Ik khdi nigm ro. tflc Ik H(x)={x} thi fm(x)=0, do dd / m ( 0 ) - fm{W) fm{l) - 0.
CAU TRA Ldi CAN DUNG <.'lIO TRUY VAN NULL... 331 3. VPi VT. y e X. V/i e J / . ta cd ^f^ = T S ' " S ^ a Id ti s6 nky khdng phu thuQc vko
X vk y. dUdc ki higu Ik ^^('0 gpi Ik dd do tinh md (fuzzincss measure) cua gia tfl h.
D i n h n g h i a 2.2. (Hkm dinh htdng ngfl nghia v)
Cho fm Ik dd do tinh md tren X. hkm dinh lUdng ngfl nghia v trgn X ditPc dinh nghia nhu sau:
1. v(W)^O^fm{c-).v{c-) = 0-a.fm{r-) vhv{c+) =0 + a.fm{c^)
2. N e u l < J < p t h i : i'(/)j.r) = T(,r) -I- Sign{hjX) x k ] / m ( / t , . T ) ~ u{hjx)fm{hjx)\,
'\~' 1
Neu - ( / < j < - 1 thi: i'{hj.i:) = v{.r) H- Sign{hjx) X ^ fm(htx) - ui(hjx)fm{hjx) .
['=' J trong d6;
uj{hjx) = 111 + Sign[hjx)Sign(h,,hjx){;3 - a)] e {a.p}.
Phan hoach dUa tren dd do tinh md cua cac gid tn ngon ngii trong dai so gia tiC VI do do tinh nid cua cac tft la mot Uhoang cua doan [U. 1] va ho cac khoang nhif vay cua cac ti"f CO cuiig do dai .sii tao thanh phSn hoach ciia [U. 1]. Phan hoacli i'tng vdi do dai ttf Idn hdn se min hon va khi do dai ldn v6 han thi do diii ciia cac khoang phan hoach giam diln ve 0.
D i n h nghia 2.3. Gpi fm la dO do ti'nh md tren DSGT X. Vdi mdi x G X. ta ky hieu 7(x) c [0.1| vk \I(x)\ la do diii ciia I{x).
Mot ho J = {/(.T) : X e A'} difdc goi l?i phan hoach ciia [0, 1| g?in vdi x neu:
1. /(c+ ). / ( c ~ ) la phan hoach cua |0, 1] sao cho \I[c)\ = /m{c), vdi c 6 {c+.c'}.
2. Neu doan I(x) da difdc dinh nghia va \I(x)\ = Jm{x) thi {/(ft,x) : ! = l...p + 7} difdc dinh nghia la phRn hoach ciia 7(.T) sao cho thoa man dieu kien: |/(ft,x)| = fm(h,x) va {I(h,x) : i = 1...P+ 17} 1& tap s4p thil tif tuyln tmh, tifc \k: hoac I(hix) < I(h2x) <
I{h3x] < . < Hhp+qx). hoac I(hix) > I(h2x) > I{h3x) > ... > I{hp+,x).
P+Q
Tkp {I(h,x)} difdo goi 1& ph.xn hoach giin vdi phan tif I . Ta cd Y, \i(h,x)\ = |/(.T)1 = fm{x).
D i n h n g h i a 2.4. Cho P ' = {/(x) : X € Xt] vdi Xt = {x € X : \x\ = k} \k mOt phan hoach ciia [0, 1|. Ta ndi rang 11 biing v theo miSc k trong f', difOc ky hiSu u aJt v. khi va chi khi I{u) vk I{v) Cling thudc met khoang trong />'. Cd nghia Vx. j/ e X. u » H ) •!=!• 3 A ' e P ' : I(u) C A ' va I(v) C A ' .
2.2. Lan can mijc k
Xet mdt CSDL {U; Const}, trong doU = {Aj.A2 An} la tap vii tru cac thudc tinh.
Const la mdt tap cac rang buSc dff lieu cua CSDL Mdi thuOc tinh A dildc gan vdi mdt miSn gia tii thugc tinh, ky hieu la Dom(A), trong dd mdt s6 thudc tfnh cho phep nhan cac gia tri ngOn ngi't trong hfu trft trong CSDL hay trong cac can hoi truy van va ditdc goi la thuOc tinh
332 DOAN \AN BAN, TRUtJNc; CONC; TUAN, noAN VAN THANG
ngdn iij;fl Miflng tliiipc tinh cdn Igi difpc gpi Ik tliuPc tinh tliitc hay kinh dicn. Thupc tinli tliitc .1 ditiii gi\n vdi innl mien gid (ri kiiili dii'ii. ky liipn la DA Thudc tinh ngdn ngfl A sc difPc gin mpi niiln gid In kinh dien DA vh mnl miln gid t n ngdn ngfl LDA hay la tap cdc phin tfl Clin mpt DSGT. Dl bi'io dam tinh iiliit quan trong xfl ly ngfl nghia dfl Hgu tren cP sfl thdng iilinl kiOii dfl ligu ciia tliupc tinh ngdn ngfl. mSi tliuOc tfnh ngdn ngfl se difpc gin vdi mdt dnh xg dmh lflpng IM • LDA —' DA dflpc xdc diiili bdi mpt bp tham .s6 dinh lifpng cua A.
Nhu viiv moi t,'i;i tri ngdn ngfl ,r ciia .•\ sc difdc gnn indt nhdn gid t n lliifc VA € DA dflpc xem nhfl gia tn dgi digii cun x. N'ln danh gid dp tfldng tu gifla cdc dfl ligu nin mpt thupc tinh A ditdc dfla ticn kliai nigm Inn i an ini'fc k cun mnl gid tn ngdn ngfl, vdi k Ih s6 nguyen dflpng.
Cac tac gii trong [8. 10] da lay ciic klioi'uig md ciin cac phin tfl dp diii k lain dp titPiig tit gifln cac phan tfl. nghin la cac phin tit niii (ac gid tn dgi dign ciia chung thudc cimg mdt khoang md mite k la tfldng tfl miic k. Tuy nliicii theo ca( li xdy ditng cdc khoang mp mii'c k gid tri (lai tlicn cun rac phin tif J cd dp dai nho hdn k ludn Id dau mut ciin cdc khoaii(j mij miic k Do vi'n'. kin xdc I'liih bin can miic k clntiig ta iiiong inu6n cdc gia tri dai dicn nlnt vay phdi Id dieiii trong cila ldn can miic k.
Cluing tn ludn ludn gid thiet ring in6i tdp / / " \-a IP cln'ta it nhit 2 gin tfl. X6t Xk Id tap tat Cii car phin ti'r dd ddi /.• Difa vko khoniig md miic k vk mite k+1 < .i{ tac gia [8. 1(J] da xay difng mdt phdn honcli ciia inicii |U, 1] iiliit san
(1) Do tiidng tii miic !• Vdi A: = 1, cdc khoang md mflc 1 g6m I{c~) vd /(c"*"). Cac khoang md iiii'tc 2 tren khoang 7(c"*") Ik I{h-,,c^) < /(/i.^+ic''")... < /(/i_2C+) < /(/i- ic+) <
VAic^) < I{hic^) < I{h2C+) < ... < /(/tp_ic+) < /(/ipC+). Khi dd.ta xay ditng phdn hogch ve dp tiidng tU miic 1 gom cac Idp titPiigditdngsau. 6'(0) = I{hpC~), S{c~) = /(c~y\[/(/i_,c")U / ( V " ) l . -^'(W) - I{h.,c-) U /(/i_,c+); 5(c+) = /(c-^)\[/(/i_,c+) U l{hpc^)\ vk 5(1) = Ta thiy. trfl hai digm dau mut i u ( 0 ) = 0 vk VA{^) = 1. cdc gia tri dgi dign IM(C~). i'/i(W).
VA{e'^) dgu la didm trong tifpiig flng ciia cac Idp tiidng t\C miic I S{c~). 5'(W) vk S{c^) (2) Dd tuang tii miic 2- vdi k ^ 2. cdc klionng md mflc 2 g6ni I{htC~) va I{h,c^). Cliiiiig ta se cd cac Idp titdng ditdng sau: 5(0) = I{hphpC-): S{li,c-) = I{h,c-)\[I{h-gh,c-)U I{hph,c-)\. 5 ( W ) = /(/i_,/i_,c-)U/(/i_,/i_,c+): S{h,c+) = /(/t,c+) \[I{h.^h,c+)Ul{hph,c*)\
vd 5(1) = I{hphpC^). vdi -q < i < p.
Bdng each titPiig tit nhif vdy. cd thg xay difng cac phdn hogch cdc Idp tiidng tif miic k bat ky Tuy nhien. trong thuc to flng dung theo [6] thi k < I. tflc cd t6i da 4 gia tfl tdc ddng lien tiep len phin tfl nguyen thuy c" va C^. Cdc gid tri rd vk cdc gid t n md gpi la cd dp tUdng tii mice k neu cdc gid t n dgi dipii ciia chung cimg nim tiong mpt Idp tUdng tif miic k.
Lan can nu'te k ciia khai n i e m mC/: Gia sfl phkn hogch cdc Idp tuang tu miic k la cdc khoang 5(xi). S{x2) 5(.Tn,) Khi dd, moi gid tri ngdn ngxifu chi vk chi thudc ve mot Idp tifPiig tfl, chdng han dd Id S{xi) vk nd gpi Ik ldn cdn miic k cun fu vk ky higu Ik FRNk{fu).
3. LAP LUAN XAP Xl DE TRA L6I TRUY VAN NULL
Cho mdt Idp md C bao gom tkp cdc tliuPc tinh vk phitPng thflc C = {{ai.a2 o„}, {M1.M2 Mr,^}).
Ldp ludn tflong tit Ik nhim nhan ditpc mi'tc dp tifdng tit gifta cac doi titpng nguon vk d6i tifdng dich d6ng thdi suy ra dUpc mpt s6 cdc tmh chit ciia d6i tUpng dich dfla vko cdc tinh
CAU TRA LOI G A N D U N G ClIO TRUY VAN NULL,..
chat titdng tif ciia cac ddi titdng ngudn. TVong CSDL md. thong tin khdng day dO, khdng cliSc ch&i thildng cau tra ldi cho truy van Null la cau tra ldi Null do thieu cic gi<i tri thudc tinh ciia mot s6 doi tiidng Quan h? titdng tit sc rjt phii lidp (16 c6 difdc c4c can tra ldi gar. diing cho cau truy van Null.
Goi S la doi tifdng nguon v& T la doi titdng dich, tap ddi titdng nguon va di'cli cd thih c!mt tuong ti.f nhau la P. Theo lap luan titdng tif, neu S cd tinli cliJt P' tin chiing ta suy ra T cd thg Cling cd P' difa vao tinh chat P cd trong ca 5 va T [11]
Vi d u 3.1. Xet 1116 Ihnh CSDL HDT md bao gdm mdt ta]) cSc doi tifdng ciia ldp NhanVien nhif sau
BoPhan 1
t l e n H g o a i G i o
HhanVien t o n v i T r i t r i n h D o
t 1
Q u a n l y t i e n T h u a n g
Hinh 3.1. Cd sd dfl liOu hitdng ddi titdng
Sau day Ik mot s& thg hien ciia ldp BoPhan, ldp QuanLy de ddn gian ta gidi hgn bang dfl lieu chi gdm nhflng thudc tinh
Bdng 1. Thg hien cua Idp BoPhan vk QuanLy
(a) The hien cua ldp BoPhan (b) T h i hi^n ciia ldp QuanLy BoPhon
iDBP i D l I D J
i D 3 i D 4
t e n A r . Binh H o a H u e
VI Tn k.to.n ketoan vanhanh vanhaah
trinhDo C D C D T C T H
t.enNeoa.Gm 3D 27 24 23
luong 9 0 8 0 70 65
QuanLy iDQL
i D l i D 2 i D 3 i D 4
t e n H a i M.nh T a m N a m
viTri C d Qlvh Qlap Qlht
tnnh Do C D T C C D C H
lien Thuong 3 0 2 7 1 5 2 2
luong 9 0
2 5 3 0
Vi du. xet cdc doi titdng difpc cho trong Vi du 3 1. Gia sfl ring gid tri thudc tinh luong cua doi tUdng Binh Ik thieu vk cau truy vin nhu sau: "Cho hiit lUdng cua Binh"
(luong(Binh)?}. Khi dd cku tra ldi la Null ditpc tao ra. Ta cd the gid thiet rkng c6 mpt cku tra ldi gdn dung cho cau tra Idi Null dd Ik hfdng cua Binh vko khodng 90. Bdi vi cdng vigc cua Binh Ik ke todn vk cd thg tim thky lUdng cua cdng viec ke todn tfl tap cdc doi titpng trong Vi du 3.1 la 90. dky chinh la Ifldng cua d6i tflpng An {Binh vk An cd thupc tinh giong nhau Ik ki todn. thupc tinh nay la mpt yeu to xdc dinh htdng) T^t nhien. cau tra ldi xkp xi cd thg khdng dung vi do nhilu yeu t6 dnh hudng d^n litPng cua nhkn vign. Tuy nhien. viec cd ditac trd ldi xkp xi cd thg t6t hdn Ik khPng cd cau trd ldi khi truy vkn dft ligu. Ngoki ra. trong mP hinh CSDL HDT md ta gia thiet r^ng cdc gid tri thudc tinh d6i titpng la day du vh khong rdng. Ngu cdc gia tri thupc tinh doi titpng bi thieu (hodc rong) thi trong tntdng hpp nky se khdng cd cku tra ldi khi truy van.
33-1 DOAN VAN BAN. TRi'ON(; c;ONf; TUAN, DOAN VAN TIIANG
Co hai van dv se difdr gidi cpn'cl troug qud Iriiili Miy difin nky; Thfl iihfit dd Ik xdc diiik tinh chnt tflpng tfl nhan P gifln ta]) dni tifpug iign6n vh dich, cliAiig iiaii thudc tinh viTn tioiig \'i dll 3 1. \aii dc thfl hni rln Id thiidi tinh Q linuf; ca S vk T cd Ilic' xac dinh thupc tinh khdng rd Q'. chdng Iigii Q \h viTn vh Q' Ik luong. \'an dh nky hen quan den phu thupc ham md (xdc dinh md) gifln cac thiinc tinh.
Ti-oiig md hinh CSDL IIDT md. gid trj tliiioc tinh ciin d6i tifpng lat phflc tgp. TVong [3], da Irhih ba\ gid In thunc linii c6'1 trfldng hp]): gid tn rd, gid tij md, tham chieu d6n d6i tifdng (d6i lflpng ndv co thg md) vd tuyOn lap (collection). Muc tifiu ciin bki bdo Ik difa ra gidi phdp dg cd rmi tia Idi gnn dung, vi va\ se tnp tmng .xem xet gid tri tlindc tinh trong trfldng IiOp thfl nliAt vd hai. dd ik: gid In chinh xdc (gid tri rd) va gid trj khdng chinh xkc (gid tri nid).
tren cd hd xem gin tii id la liifdng iipp iirup, ciin gid tri md. Gik tii md thudng rkt phflc tap vk nhnii ngdn ngfl thfldng dupc Mf dung dv liiOii dien cho nhflng logi gid tri nay M'lhu gid tri thudc tinh ind Ik hpp ciia hai thiuili |)haii
Dojn{a,) ^ CDom{a,) U F£>om(a,)(l <i <n) Trong do
- CDoni{a,): Mien gid tri rd ciin thupc tinh a,-.
- FDom{a,) Mien gia In mP ciia thupc tinh a,.
3.1. X a p xi mii^c k
Tren cd .sd khai nigm lan can. chung ta dita ra dinh nghia vc xap xi miic k ciia cdc thupc tinh doi tifpng Xkp xi miic k difdc dinh nghia nhfl sau.
D i n h nghia 3 . 1 . Clio ldp md C xdc dinh tren tdp thudc tinh .1 vk tkp phifdng thflc M.
a, C A{1 < i <n). 0\.02 & C' Ta ndi rdng oi.a, xap xi bac k 02.Q, difdc ky hieu oi-o, =Sfc 02.a, ngu oi.a, vk 02 Qj cimg thudc mdt ve mdt ldp titPng tU FRNk{fu)- Trong dd FRNk{fu) Id mpt khoang phan hoach cdc ldp tUPng tif miic k
Vi du 3.2 Dim tren md hinh CSDL HDT md dd cho d Vi du 3.1. ta xet DSGT cua bien ngon ngfl tienNgoaiCio Ik thudc tinh ciia Idp BoPhan. trong dd D,,enNgoaiGio = [^- 3U]. tap cdc phan tfl .sinli Ik {0. thap. \\'. cao. 1}. tgp cdc gin tfl la {it. khd. liPn. rat}. \'k FDu^nNgoaido
= ^(ienJVffOa.C.o(cao) U /^(itnNgoaiG.oCthkp).
Chon /m(cao) = U 35. /m(thkp) = 0 65. ^(khd) = 0.25. /i(it) = 0.20. ;i(hoii) = 0.15 ^-a
;i(rat) - 0.40 Ta phkn hoach dogn [0. 30] thknh 5 khoang tfldng tfl mflc 1 nhu sau:
/m(rat cao) * 30 = 0 35*0 35*30=3.675. vay S'(1)*3U= (26,325. 30], (/m(kha cao) + /m(Iidn cao))*30 = (0.25*0.35 + U.15*0.35)*30 = 4.2.
vay5(cao)*30 = (22.125. 26.325].
(/m(it thdp) + / m ( i t cao))*30 = (0.25*0.65 + 0.25*0.35)*30 =T 5.
vay S(W)*3U = (11.625. 22.125].
(/m(khd thap) + /m(hPn th&p))*30 = (0.25*0 65 + 0.15*0.65)*30 = 7.8.
vky 5(thkp)*30 = (6 825. M 625]. vk 6'(0)*30 - [0. 6 825).
Tfl dd. ta cd lan can miic 1 cua cdc ldp titdng tu nhit sau: FRNi{0) = [0, 6.825], FHiVi(thap) = (6.825, 14.625]. FRNi{'W) = (14.625, 22 125], FRNi{cao) = (22.125, 26.325]
vkFRNi{\) = (26.325. 30]
Vky ta ndi 01.04 asi 02.a^ vi 01.04 = 30 € FRNi{0) vk 02.04 = 27 G FRNi{0) ; hodc 03.04 =Bi 04.04 vi 03.Q4 = 24 6 FRNi{cao) vk 04.(14 = 23 G FRNi{cao).
CAU TRA LOI G A N DUNG CHO TRUY VAN NULL 335 3.2. X a c d i n h mc* t h u p c t i n h
Trong pliAii nay. sc dc xuat each x.u: dinh iiid thuoc tinh dira tren Ian can ngfl nghia cua DSGT. Khai niem xac dinh ind thuoc tinh nay til sit 1116 r&ng ciia khdi iiieni phu thuoc hhm mcl ciia 1116 hinh CSDL quan lie inft di(a tren DSGT |9| Ta dinli nghia ve x4c dinh ni6 thuOc thih (Attribute Fuzzy Deteiinination. viet t^t Ift AFD) nhif sau
D i n h nghia 3.2. Cho Wp mf) C vdi tUp thuoc tinh U.X.Y Q U vk X \k tap cfc thuOc tinh nhan gift tri dOn (gift tri ro ho?ic md). k \k miic pliftn hoach. Chung ta dinh nghia X
ajd
xftc dinh md thuOc tinh Y theo miic k. kv hieu .V "->;,• Y khi vk chi khi Voi. 02 e C neu o\.X ^k 02.X till o\.Y ^k 02.Y (01..V- gift tri ciia 01 trCn X).
U 1ft tap cac tliuOc tinh eiia Idp C, -V. 1', l l ' C [/. A la miic phan hoach.
Dila vao cac ket qua [4. 8. IU]. ta c6 cftc luat suy dftn AFD nhu sau' aJd
L u a t 1.1: Phan xa Neu 1' C .Y thi A' ~>t Y.
Luat 1.2, T^ng trirdng, Xcu .V ~>i Y vk Y ~>k Z thi XZ ~ > t YZ Luat 1.3 BSe cSu Neu -V ~ > i . Y va Y ~>t Z thi X ~>k Z.
Luat 1.4' Gia t.^ing Neu A' ~>t y va Z C W till XW ~>t YZ.
Vi d u 3.3. TVong Vi du 3 2 da xay di.tng ngfl nghia dmh htdng cho thuOc tinh ngOn ngff tienNgoaiGio Ti'Ong vi du nay. s(5 xay dimg ngft nghia dinh htdng cho thuoc tinh ngon ngfr luong ciia Idp BoPhan. Xet DSGT ciia bien ngOii ngi't Innng. trong dd Dtiumg= [0, 100].
cftc phftn trt sinh 1ft {0. thftp IT. cao. 1}, tap cac gia ti'f la {it. kha. hon. rftt}. FDi^mg - Him„,{cao) U Hi^nglamp)
Chon /m(cao) = 0 60. /m(thap) = 0.40, (i(khft) = 0 15, /i(it) = 0.25. /i(hon) = 0.25 va /i[rat) - 0.35. Ta phan hoach doan ]0, 100] thanh 5 khoang titdng tn mi?c 1 nhu sau
/m{rat cao) * 100 = 0.35*0.60*100=21. vjy S(l)*21= (79. 100].
(/m(kha cao) + /m(IiOn cao))*100 = (0.25*0.60 + 0.15*0 60)*100 = 24.
vfty S(cao)*100 = (55. 79].
(/m(it thap) + / m ( i t cao))*100 = (0.25*0.60 + 0 25*0.40)*100 =25.
vav S(H')*100 = (30. 55].
(/m(kha thap) + /m{hon thap))'100 = (0.25*0 40 + 0.15*0.40)*100 = 16.
vay S(tliap)*100 = (1-1. 30]. va S(0)*100 = ]0. 14].
Tft dd. ta c6 Ian can mv:c 1 cua cftc Mp titdng tit nhit sau' FflA'i(O) = ]0, 14], i='fiiVi(thap)
= (14. 30]. FRNi{\V) = (30. 55], FflJVi(cao) = (55, 79] va FRNi{l) = (79, 100].
D^ dang nhan thSy r&ng tienNgoaiGio xac dinh md thudc tinh luong theo miic k=l, nghia la tienNgoaiGio ^>k luong
3.3. Xac d i n h m S phifdng thiiTc
Viec xac dinh sit gSn ket gifta phuang thiic d6i tifdng d6i vdi cac thuOc tinh md difdc xac dinh thong qua viec phitdng thi'fc si'l dung cac thuoc tinh dd d l dgc hay si'fa dOi. ViSc xac dinh nhif lay duoc goi 1ft xac dinh md phifdng thrtc (Method Fuzzy Determination, viet tat Ift MFD).
336 DOAN VAN BAN, TRUONC; CONC TUAN, DOAN VAN TIIANG
Dinh nghTa 3.3. C'lio 71/j Ik inPt phifdng thi'fc cua mpt ldp C, X Ik tkp cdc thupc tinh nhdn gid tri ddn (gid iri rd hodc md) (cd tli(? dpi: hodc sfla d6i), k Ik mflc phkn hoach. Ta dinh
mfJ
nghia A' xdc djnn md phifdng thflc Mj tlico miic k. difpc ky hi^u X ~>fc Mj , nSu X dupc sfl dung bdi Mj theo mflc phrui ho^ch k.
Dun vko cdc kk qud (ll. ta vf) ri'w Iual ^uy dftii MFD nhif snu:
Lnkt 2.1 N('u A' - > \ Mj vb Y '^>k Mj tin XY ~>k Mj- mf,l mfd mfd Luat 2.2 Neu .V '->i. M, vk .V '->fc ;i/^ thi A' ^ > A il/.^/j.
.7././ mfd Luat 2.3 Neu A' - > i yi/^ vii 1' C A tin K - > j t ^ / j .
Vi du 3.4 Gid hfl ldp NhaiiVicii cd phifdng thflc thucLinh() thi vi^c xdc dinh md phifoiig thflc fhucLmh() ditpc thd liipn (.rong hai ldp k6 thfla Id BoPhan vk QuanLy nlnt sau:
D6i vdi ldp BoPhan: (luoiigNgoaiGio, luong} ~>A: thucLinh{).
mfd
D6I vdi ldp QuanLy: {iienThuong, luong} '^>k thucLinh{).
4. T H U A T T O A N T R A L 6 I G A N D U N G T R U Y V A N NULL Trong phkn nay, se neu gidi phdp de trd ldi gan diing cho nhflng truy vkn Null dita tren xdc dinh md thudc tinh vk xdc dinh md phitOiig thflc.
a. Doi vdi t r u y van t h u o c t i n h , t a co 16i giai t h u a t t o d n nhuf sau:
T h u a t t o a n N Q A O (Null Queries for Attributes Objects)
Vao: Mdt Idp C vdi m thuoc tinh vk p phifdng thi'tc; O = {01.02 o„} G C.
TVong dd. (01.02. ....On-i) [0.1.02- •••,aT,i] vk o„.[ai.a2 flni-i] 1^ difdc dinh nghia (cd iigliia Ik gia tri dft lieu ton tai) vk On.a„i Ik chita ditqc dinh nghia (cd nghia Ik gid tri dfl h?u bi thieu).
R a : Tra ve gid tri titdng tu gan dung cho On.tin,.
Phiidng p h a p : / / Khdi tao cdc gid tri (1) For i = 1 t o 111 d o (2) Begin
(3) G«. = {0. C-. W. c+. 1}; Ha, = H+ U H " . Trong dd H+ = {hi. hi}. / / " - {/13. hi}.
vdi hi < hz vk /13 > /14. Chgn dO do tinh md cho cdc ph&n tfl sinh vk gia tfl.
(4) Da, = [miUa^.TnaXa,]// mina,. maXa,:gia tri nho iihAt vk Idn nhkt mi^n tri gid tn a, (5) FDa,=Ha,{cl)^Ha,{c-)
(6) E n d
//Xky dflng cdc khodng tUdng tif miic k =1 (7) For i = 1 t o m d o
(8) For j = 1 t o 8 d o
(9) Xdy difng cdc khodng tUdng tif miic kiS^J^Xj), //Xay dung ldn can mdc k =1 cua o.o;
(10) For i = 1 t o n d o (11) F o r j = 1 t o m d c (12) Begin (13) t =0;
CAU TRA LOI GAN DUNG CHO TRUY VAN NULL... 337 (14) R e p e a t
(15) t = t + 1 .
(16) U n t i l o,.a, e i'J (.r,) or t > 8 (17) FRNl'(o,.a,) = FRNl'(o,.a,) U S j (.T,) (18) E n d
//Xay difng thudc ^ inh chifa dmh nghia On .«„, (19) result = B.
(20) For i = 1 t o n-l d o
(21) If o„.o„,_i = o,.o„,-i t h e n result = result UF/iiV,'(ci,.a„,);
(22) Return result.
Vi d u 4.1 Cho biel iMng cua tat cd nhdn vien qudn Ig
Tff CSDL HDT da cho 6 \'i du 3.1 ta nhan thay Iifong ciia d6i tifdng Mmh la chifa dinll nghia (bi thieu). vi vay ta can tim gia tri titdng tu gan cluing cho hfdng ciia doi tifdng nay Si't dung thuat toan N Q A O . nhif sau,
Bitdc (1)—(6) Chon do do tinh md cho cftc pli^n til: sinh va gia ti'f cho 2 thupc tinh tienThuong vk luong
A.m7-/,TOns = !"• 30] va Di„„„g = ]0. 100] FDi,c„Thmng vk FD,„mg CO ciiug tap xau gi6ng nhau vdi tap cac phan tit shili la {0. thap. U'. cao. 1} va tap cac gia ti'f la {it. kha. han. rat}.
Biidc (7)-(18) Xay difng iinic phan hoach cho 2 thuoc tinh tienThuong vk luong.
Dai vdi thupc tinh tienThuong. Chon /m(cao) ^ 0.35. /m(thap) = 0.65. /z(kha) = 0.25.
/i(it) = 0 20. /i(Iion) = 0.15 va /i(rat) = 0.40. Ta phan hoach doan JO. 30] thanh 5 khoang tifdng tif iniic 1 nhif sau;
/m(rat cao)*30 = 0 35*0.35*30=3.675. ray S(i)*30= (26 325. 30].
(/m(klia cao) + /m(lidii cao))*30 = (0 25*0.35 + 0 15*0.35)*30 = 4.2.
vay S(cao)*30 = (22.125. 26.325],
(/m(it thSp) + / m ( i t cao))*30 = (0.25*0.65 + 0 25*0,35)*30 =7.5.
vay S(W)*30 = (14 625. 22.125].
(/m(klia thap) + /m(hdii thap))*30 = (0.25*0.65 + 0.15*0.65)*30 = 7.8.
vay S(tliap)*30 = (6.825. 14.625]. va S(0)*30 = ]0. 6.825].
Ti'f do ta CO ldn cdn miic 1 ciia cac Up tudng tu nhit sau: FRNi(a) = JO, 6 825], fflJVi(thap) = (6.825. 14.625]. FRNr{W] = (14.625, 22.125], FBiVi(cao) = (22 125, 26.325]
va FRNiil) = (26,325, 30],
DOi vdi thuoc tinh luong- /m(cao) = 0.60, /ni(thap) = 0.40, /i(kha) = 0.15. /^(it) = 0.25.
Ai(hon) = 0.25 va /i(rat) = 0.35, Ta phan hoach doan JO. 100] thanh 5 khoSng titdng tif mrtc 1 nhif sau.
/m(rat cao) * 100 = 0 35*0 60*100=21. vSy S(l)*21= (79. 100].
(/m(kha cao) + /m(hdn cao))*100 = (0.25*0.60 + 0.15*0.60)*100 = 24.
vay S(cao)*100 = (55. 79],
(/m(it thftp) + / m ( i t cao))*iaO = (0.25*0.60 + 0.25*0.40)*100 =25.
vay S(W)*WO = {30. 55].
/m(kha thip) + / m ( h d n thSp))*100 = (0.25*0.40 + 0.15*0.40)*100 = 16.
vay S(thSp)*100 = (14. 30]. va S{0)*100 = JO. 14].
Tft d6 ta CO ISn can miic 1 ciia cac ldp titdng tit nhit sau: FRNi(0) = [0, 14], FiJJVi{thap)
= {14, 30], FRNilW) = (30, 55], FRNi^cao) = (55, 79] vk FflJVi{l) = {79, 100].
338 DOAN V,.\N RAN. TRUdNG CONG TUAN, DOAN VAN TIIANG
Budc (19)-(22) Dua van diuh iigliTn 3.2 xdc djiili md lliiiOc tinh, iilidn thay rkng viec xdc dinll md thudc titili IienThuong '^>\ luong \h tlioa man
\avgid tri titdng tfl dung clio tlindr tinh luong cua d6i titong Minh ^ FRNi{l) = (79.100]
b. Doi vdi t r u y van phiWng thiJc, t a c6 ICli giai t h u a t t o k n n h i i s a u : T h u a t toan N Q M O (Null Queries for Method Objects)
Vao: .Mot ldp C vdi m thuQc tinh va p phitdng thflc, O = O1.O2 «„ G C
Ti'oiig dd' (o].02 On -1)-{oi. 02 n„,] va o„.[a].a2 (in,-i\ Ik dfldc dinh nghia (c6 nghia Id gid tn dfl heu tdn tai) vk 0r,.a„, Id chita ditpc dinh nglna (cd nghia Ik gid tri dfl HQU bi thieu)
R a : TVa ve gid In titdng tfl gan dung cho pliifdng thi'tc Phiidng phdp:
/ / Khdi tao cdc gid fii (1) For i - 1 to m d o (2) Begin
(3) G„, = { 0 . c ; _ . i r . c + . 1): Ha, = / / + U H ^ 'R-ong d d / / + ^{hi.h2}.H- = {/[3./t4}, vdi h\ < /i2 vk /13 > /14. Chpn dd do tinh md cho cnc phkn tu smh vk gia tfl.
(4) Da, ^ [mina,. maxa,[// mina,. maXa,.gid tri nhe nhat vk ldn nhat mien tri gid tri a,.
(5) FDa, -•^Ha,{cl)UHa,{Ca,) (6) End
//Xay dung cdc khodng tiiOng tif miic k ~I (7) For i — 1 t o ill d o
(8) For j - 1 to 8 do
(9) Xdy difng cdc khodng tiidng tif miic k:S^ {-TJ);
//Xay dflng ldn cdn mUc k =1 cua o.a, (10) For i - 1 to 11 d o
(11) For j = 1 to m d o (12) Begin (13) t - 0 ; (14) R e p e a t (15) t = t + l ;
(16) Until o,.aj e 6'i;(,T,) or t.-8 (17) FRN^{o,.aj) = F/?7V,''-(o,.a_,) U SJ^^ix,) (18) E n d
//Xay ditng thudc tinh chua dinh nghia On.Un, (19) For i - 1 t o n-i d o
(20) If On.a„,-i - o^.a„._] t h e n FRNl'{on.u„,) = FflA^f (oi.On,);
(21) Chpn hdm kit nhdp DSGT FHA eho phUdng thiic, (22) result - t);
(23) For i = 1 t o n d o
(24) result = result UFl'!A{FRNA'^{o,.aj))\
(25) Return result;
Vi du 4.2. Cho biet thifc linh cUa tdt cd nhdn viSn gudn ly.
CAU TRA LOI GAN DONG CHO TRUY VAN NULL . 339 Sfl dung thukt toan N Q M O , nhit sau:
- Bii-dc ( l ) - ( 2 0 ) tinh todn gi6ng nhit Vi du 4.1 d tren Ket qud difpc cho 6 Bdng 2(a).
- Bifdc ( 2 1 ) - ( 2 5 ) Hkm tich hop DSGT trong trfldng hpp nky ph^p hpp cua hai DSGT tienThuong vk luong. Ket qud cho d Bang 2(b).
(a) Ket qua thyc hiOii bitac (1) - (20)
Bdng 2. Cdc ket qud thifc hien vi du 4.2
iDQL i D l
• D 2 i D 3
<D4
Q u « ttenThuong 30 (26 335. 30]
J5 (36 325, 30]
IS (14 62S, 22.12SI 22 (14 625, 23 I35|
L y luong 90 (T<(, lOO) (79. 100|
25 (IJ, JO]
30 (14. 30]
IhucLinhO
(b) Ket qua thyc hi?n budc (21) - (25)
iDQL i D l i D 2 . D 3 i D 4
Q u a tienThuong 3U (26 325, 30]
35 (36 325, 30|
15 (14.635, 22 I35{
22 (14 626, 22 135]
n L y luonB 90 [79. 100|
(79, 100]
25 (14, 30]
30 [14, 30]
thucLinhO (79, 130|
(79, 130|
(14, 52.1251 (14, 52 1251
Dinh ly' Thudt todn NQAO vd NQMO luon ditng vd dung ddn.
Chiing minh:
1 Chiing mmh tinh dOng' Tap cdc thudc tinh, phitdng thflc cua ddi tupng Ik hflu han (n, p. m la hflu han) nen thuat toan se dflng sau khi duySt xong tat ca cac doi tUdng.
2. Chiing minh tinh diing dan: Thukt tokn NQAO va N Q M O sfl dung Dinh nghia 6 xac dinh md thudc tinh vk Dinh nghia 7 xdc dinh md phitdng thi'tc. Khai niem xac dinh md thupc tinh vk xdc dinh md phfldng thflc Ik sfl md rong cija khdi niem phu thudc ham md trong CSDL quan he md. Su suy ddn logic nay dfla vko sfl suy dkn ciia phu thupc md trong CSDL quan he md. Tinh dung dSn cua phep suy dan bdi phu thudc ham md
trong CSDL quan he md da dflpc ehflng minh. • Dd phflc tap thuat todn. Thukt todn N Q A O vk N Q M O cd do phflc tap tinh toan Ik
0(n*m). vdi n Ik s6 d6i titpng vk m tkp thudc tinh
^. K f i T L U A N
Bai bdo da de xukt mot cdch ti^p can d^ tra ldi cdc truy vkn Null sfl dung lap lukn tUdng tu trong mo hinh CSDL HDT md dUa tren cdch ti€p can cua DSGT. Dua tren Ikn ckn ngfl nghia cua DSGT, bki bdo da dfla ra cdc dinh nghTa xdc dinh md thudc tinh vk xdc dinh md phitdng thflc. Viec xky cdc bitdc thflc hien trong hai thuat todn N Q A O va N Q M O nh^m tim ra mot cau tra idi g4n dung cho cdc truy van Null doi vdi thudc tinh ldn phitdng thflc ma cd cac gid tri dfl lieu bi thieu tfl mdt CSDL khdng dky dii. Dfla tren cd sd cdc xac dinh md thudc tinh va xac dinh md phfldng thflc, cdc dang chudn ldp md vk phfldng phdp tach ldp vl cdc dang chukn trong ldp doi tifpng md se dflpc trinh bky trong ckc nghien cflu tiep theo.
T A I LIEU T H A M K H A O
[1] V. Biazzo, R. Giugno, T. Lukasiewiez, V.S.Subrahmanian, Temporal probabillistic object bases, IEEE Transaction on Knowledge and Engineering, 2002, (921-939).
340 DOAN VAN nAN, TRI/ONG CONG TUAN, DOAN VAN TIIANC
[2| D.V Tli;inf^. D.V.Ban, Query data with fuzzy information in object-oriented databases an ap- proach the semantic neighborhood of hedge algebras, International Journal of Computer Science and Information Security (IJCS1S),9 {5) (2011) 37-42.
[3] D.V.Thang, D.V Ban, Query data with fuzzy information in object-oriented databases an ap- proach interval values. International Journal of Computer Science and Information Se- curity (IJCSIS), 9 (2) (20n) 1-6.
[4] D.V.Ban, H.C.IIk, V.D.Qukng, Phuong phdp phdt hiCn cdc ldp bO phkn trong ldp d6i tuijng md, Tap chi Tm hqc vd diiu khiin hoc 26 (4) (2010) 321-331.
[5| S. Dutta. Approximate reasoning by analogy to answer null queries, Int. J. of Appr. Reasoning (5) (1991) .37.3-39H
[6] N.C.Ho, Quantifying Hedge Algebras and Interpolation Methods in Approximate Reasoning, Proc. of the 5th Inter. Conf. on Fuzzy Information Processing. Beijing, March 1-4, 2003 (105-112).
[7] N.C.Ho, Ly thuyit t^p md vd cdng ngh$ tinh todn mim, H$ md, mQ,ng ndron vd iing dung, NXB Khoa hpc & Ky thu§it, 2001 (37-74).
[8| Nguyen Cdt H6, Nguyin C6ng Hdo, MOt phUdng phdp xfl ly truy vdn trong co sd dfl li?u mcl tiep ckn ngfl nghia ldn cdn ciia d?i s6 gia tfl, Ta.p chi Tm hgc vd Diiu khien hQC 24 (4) (2008) 281-294.
[9] Nguyen Cong Hdo, M^t s6 dang chudn trong co s6 dfl li§u md theo cdch tilp ckn d?ii so gia til.
Tap chi Tin hgc vd Diiu khiin hgc 17 (2007) 101-107.
[10] PhUdng Minh Nam, Trdn Thdi Son, Vl m^t cd sd dfl lifu md vk flng dyng trong quan ly tiji pham hinh sfl, Tg,p chi Tin hgc vd Dieu khiin hgc 22 (1) (2006) 67-73.
[11) S.L. Wang, and T.J. Huang, Analogical reasoning to answer null queries in fuzzy object-oriented data model, Proc. of the 6th IEEE Inter. Conf. on Fuzzy Systems, Barcelona, Spain, July 1-5, 1997 (31-36).
Nhdn bdi ngdy 16-6- 2011 Nh^n /pi sow siia ngdy 20-10- 2011
