Phụ thuộc đơn điệu trong cơ sở dữ liệu mờ theo cách tiếp cận ngữ nghĩa lân cận của đại số gia tử

0
G7 Thanh 500 3500000
G8 Thieˆ.n 650 4500000
G9 Nhaˆn 700 50000000
Trong quan heˆ. Giangday ta thaˆ´y ra`˘ng neˆ´u SOTIETGIANG cu’a gia´o vieˆn ca`ng lo´
.n
th`ı V UOTGIO ca`ng lo´.n, hay phu. thuoˆ.c do
.n dieˆ.u ta˘ng SOTIETGIANG
+ → V UOTGIO
du´ng trong quan heˆ. Giangday. Thaˆ.t vaˆ.y, ∀t, s ∈ Giangday ta co´ t[SOTIETGIANG] ≤
s[SOTIETGIANG]⇒ t[V UOTGIO] ≤ s[V UOTGIO].
Go.i FA la` ho. ca´c phu. thuoˆ.c do
.n dieˆ.u ta˘ng treˆn lu
.o.. c doˆ` quan heˆ. U. Ta ky´ hieˆ.u FA∗ la` taˆ.p
taˆ´t ca’ ca´c phu. thuoˆ.c do
.n dieˆ.u ta˘ng X
+ → Y ma` du.o.. c suy daˆ˜n tu`
. FA.
Di.nh ly´ 4.1. Trong CSDL vo´
.i taˆ. p vu˜ tru. ca´c thuoˆ. c t´ınh U , ho. FA∗ tho’a ma˜n ca´c tieˆn de`ˆ
sau:
(1) Pha’n xa. : X
+ → X ∈ FA∗ .
(2)Gia ta˘ng: X+ → Y ∈ FA∗ ⇒ XZ
+ → Y Z ∈ FA∗ , vo´
.i Z ⊆ U.
(3) Ba˘´c ca`ˆu: X+ → Y ∈ FA∗ , Y
+ → Z ∈ FA∗ ⇒ X
+ → Z ∈ FA∗ .
Ca´c tieˆn de`ˆ (1) - (3) trong Di.nh ly´ 4.1 la` du´ng da˘´n.
PHU. THUOˆ. C DO
.
N DIEˆ. U TRONG CO
.
SO
.’ DU˜
.
LIEˆ. U MO`
. 25
Chu´.ng minh
(1) Pha’n xa. :
Hieˆ’n nhieˆn v`ı ∀t, s ∈ r, t[X ] ≤ s[X ]⇒ t[X ] ≤ s[X ]. Vaˆ.y X
+ → X ∈ FA∗ .
(2) Theo gia’ thieˆ´t ta co´ X+ → Y ∈ FA∗ neˆn theo di.nh ngh˜ıa ∀t, s ∈ r, t[X ] ≤ s[X ] ⇒
t[Y ] ≤ s[Y ] (1’). Vo´.i Z ⊆ U, tu`. t[X ] ≤ s[X ] ta co´ t[XZ] ≤ s[XZ] (2’). Tu.o.ng tu.. , tu`
.
t[Y ] ≤ s[Y ] ta co´ t[Y Z] ≤ s[Y Z] (3’). Tu`. (1’), (2’), (3’) ta co´ ∀t, s ∈ r, t[XZ] ≤ s[XZ] ⇒
t[Y Z] ≤ s[Y Z]. Vaˆ.y XZ
+ → Y Z ∈ FA∗ .
(3) Theo gia’ thieˆ´t X+ → Y ∈ FA∗ , Y
+ → Z ∈ FA∗ neˆn ta co´ ∀t, s ∈ r, t[X ] ≤ s[X ] ⇒
t[Y ] ≤ s[Y ]va` ∀t, s ∈ r, t[Y ] ≤ s[Y ]⇒ t[Z] ≤ s[Z] hay ∀t, s ∈ r, t[X ] ≤ s[X ]⇒ t[Z] ≤ s[Z].
Vaˆ.y X
+ → Z ∈ FA∗ . 
4.1.2. Phu. thuoˆ. c do
.n dieˆ.u gia’m
Vo´.i X la` moˆ. t taˆ.p con cu’a U va` t, s la` hai boˆ. tu`y y´ treˆn U , ta vieˆ´t t[X ] ≥ s[X ], neˆ´u vo´
.i
mo. i A ∈ X, ta co´ t[A] ≥ s[A].
Di.nh ngh˜ıa 4.2. Cho U la` moˆ. t lu
.o.. c doˆ` quan heˆ., r la` moˆ.t quan heˆ. treˆn U va` X, Y ⊆ U . Ta
no´i ra`˘ng quan heˆ. r tho’a ma˜n phu. thuoˆ. c do
.n dieˆ.u gia’m X xa´c di.nh Y , ky´ hieˆ.u la` X → Y ,
trong quan heˆ. r, neˆ´u ta co´: ∀t, s ∈ r, t[X ] ≤ s[X ]⇒ t[Y ] ≥ s[Y ].
Vı´ du. 4.2. Ta xe´t lu
.o.. c doˆ` quan heˆ. U = {SOBD, TENHS,SOPHUT,DIEMTHI} vo´
.i
y´ ngh˜ıa: Soˆ´ ba´o danh ho.c sinh (SOBD), Teˆn ho.c sinh (TENHS), Soˆ´ phu´t cha.y trong 100m
(SOPHUT), Dieˆ’m thi (DIEMTHI). Quan heˆ. Thihocky xa´c di.nh treˆn U du
.o.. c cho o
.’ Ba’ng 4.2.
Ba’ng 4.2. Quan heˆ. Thihocky
SOBD TENHS SOPHUT DIEMTHI
001 Thu’y 10 8
002 B`ınh 12 6
003 Minh 11 7
004 Nhaˆ. t 9 9
005 Thu.o.ng 13 5
006 Huye`ˆn 12 6
007 Thuaˆ.n 8 10
008 Tha`nh 10 8
009 Ha`˘ng 14 4
Trong quan heˆ. Thihocky ta thaˆ´y ra`˘ng, neˆ´u SOPHUT ma` ho.c sinh cha.y trong 100m ca`ng
lo´.n th`ı DIEMTHI cu’a ho.c sinh ca`ng ke´m. Nhu
. vaˆ.y, trong quan heˆ. Thihocky toˆ`n ta. i phu.
thu oˆ.c do
.n dieˆ.u gia’m SOPHUT
− → DIEMTHI du´ng trong quan heˆ. Thihocky. Thaˆ. t vaˆ.y,
∀t, s ∈ Thihocky ta co´ t[SOPHUT ] ≤ s[SOPHUT ]⇒ t[DIEMTHI ]≤ s[DIEMTHI ].
Go.i FD la` ho. ca´c phu. thuoˆ.c do
.n dieˆ.u gia’m treˆn lu
.o.. c doˆ` quan heˆ. U. Ta ky´ hieˆ.u FD∗ la`
taˆ.p taˆ´t ca’ ca´c phu. thuoˆ.c do
.n dieˆ.u gia’m X
− → Y ma` du.o.. c suy daˆ˜n tu`
. FD.
Di.nh ly´ 4.2. Trong CSDL vo´
.i taˆ. p vu˜ tru. ca´c thuoˆ. c t´ınh U, ho. FD∗ tho’a ma˜n ca´c tieˆn de`ˆ
sau:
(1) Pha’n xa. : X
−→ X ∈ FD∗ .
(2) Gia ta˘ng: X−→ Y ∈ FD∗ ⇒ XZ
− → Y Z ∈ FD∗ , Z ⊆ U.
(3) Hoˆ˜n ho.. p ba˘´c ca`ˆu: X
−→ Y ∈ FD∗, Y
+ → Z ∈ FA∗ ⇒ X
−→ Z ∈ FD∗ .
26 NGUYE˜ˆN CA´T HOˆ`, NGUYE˜ˆN COˆNG HA`O
Chu´.ng minh. Tu.o.ng tu.. nhu
. chu´.ng minh Di.nh ly´ 4.2.
Heˆ. qua’ 4.1. Tu`
. Di.nh ly´ 4.2 ta co´
(4) Hoˆ˜n ho.. p ba˘´c ca`ˆu 1: X
+ → Y ∈ FA∗ , Y
− → Z ∈ FD∗ ⇒ X
−→ Z ∈ FD∗ .
(5) Hoˆ˜n ho.. p ba˘´c ca`ˆu 2: X
−→ Y ∈ FD∗ , Y
− → Z ∈ FD∗ ⇒ X
+ → Z ∈ FA∗ .
4.2. Phu. thuoˆ.c do
.n dieˆ.u trong CSDL mo`
.
4.2.1. Phu. thuoˆ. c do
.n dieˆ.u ta˘ng
Vo´.i X la` moˆ. t taˆ.p con cu’a U va` t, s la` hai boˆ. tu`y y´ treˆn U , ta vieˆ´t t[X ] ≤k s[X ], neˆ´u vo´
.i
mo. i A ∈ X, ta co´ t[A] ≤k s[A].
Di.nh ngh˜ıa 4.3. Cho U la` moˆ. t lu
.o.. c doˆ` quan heˆ., r la` moˆ. t quan heˆ. treˆn U va` X, Y ⊆ U. Ta
no´i ra`˘ng quan heˆ. r tho’a ma˜n phu. thuoˆ.c do
.n dieˆ.u ta˘ng X xa´c di.nh Y vo´
.i mu´.c k, ky´ hieˆ.u la`
X+ k Y trong quan heˆ. r, neˆ´u ta co´: ∀t, s ∈ r, t[X ] ≤k s[X ]⇒ t[Y ] ≤k s[Y ].
Vı´ du. 4.3. Ta xe´t lu
.o.. c doˆ` quan heˆ. U = {MASO, TENCN, SONLV, THUNHAP} vo´
.i y´
ngh˜ıa: Ma˜ soˆ´ coˆng nhaˆn (MASO), Teˆn coˆng nhaˆn (TENCN) la` 2 thuoˆ.c t´ınh kinh dieˆ’n, Soˆ´
nga`y la`m vieˆ. c trong tha´ng (SONLV), Thu nhaˆ. p (THUNHAP) la` 2 thuoˆ. c t´ınh ngoˆn ngu˜
.. Trong
do´ DSONLV = [0, 30] va` DTHUNHAP = [0, 100]. LDSONLV va` LDTHUNHAP co´
cu`ng taˆ.p ca´c xaˆu gioˆ´ng nhau vo´
.i taˆ.p ca´c pha`ˆn tu
.’ sinh la` {0, thaˆ´p, W, cao, 1} va` taˆ.p ca´c gia
tu.’ la` {´ıt, kha’ na˘ng, ho.n, raˆ´t}. Quan heˆ. Luongcb xa´c di.nh treˆn U du
.o.. c cho o
.’ Ba’ng 4.3.
Ba’ng 4.3. Quan heˆ. Luongcb
MASO TENCN SONLV THUNHAP
N1 Anh 27 90
N2 A´nh Cao cao
N3 Lan 28 94
N4 Hu.o.ng 20 52
N5 Ha`˘ng 22 53
N6 Hoˆ`ng 22 54
N7 Thu´y thaˆ´p 10
N8 Thanh 21 52
N9 Hieˆ’n 12 thaˆ´p
Doˆ´i vo´.i thuoˆ. c t´ınh SONLV : fm(cao) = 0, 35, fm (thaˆ´p) = 0,65, µ(kha’ na˘ng) = 0,25,
µ(´ıt) = 0,2, µho.n) = 0.15 va` µraˆ´t) = 0,4. Ta phaˆn hoa.ch doa.n [0, 30] tha`nh 5 khoa’ng tu
.o.ng
tu.. mu´
.c 1 la`:
fm(raˆ´t cao) ×30 = 0, 35× 0, 35× 30 = 3, 675. Vaˆ.y S(1)× 30 = (26, 325, 30].
(fm(kha’ na˘ng cao) + fm(ho.n cao)) ×30 = (0, 25× 0, 35 + 0, 15× 0, 35)× 30 = 4, 2 va`
S(cao)× 30 = (22, 125, 26, 325]; (fm (´ıt thaˆ´p) +fm(´ıt cao)) ×30 = (0, 25× 0, 65 + 0, 25×
0, 35)30 = 7, 5 va` S(W ) × 30 = (14, 625, 22, 125]; (fm (kha’ na˘ng thaˆ´p) + fm(ho.n thaˆ´p))
×30 = (0, 25×0, 65+0, 15×0, 65)×30 = 7, 8 va` S(thaˆ´p)×30 = (6, 825, 14, 625], S(0)×30 =[0,
6,825].
Doˆ´i vo´.i thuoˆ.c t´ınh THUNHAP : fm(cao) = 0, 6, fm(thaˆ´p) = 0,4, µ(kha’ na˘ng) = 0,15,
µ´ıt) = 0,25, µho.n) = 0,25 va` µraˆ´t) = 0,35. Ta phaˆn hoa.ch doa.n [0, 100] tha`nh 5 khoa’ng
tu.o.ng tu.. mu´
.c 1 la`:
PHU. THUOˆ. C DO
.
N DIEˆ. U TRONG CO
.
SO
.’ DU˜
.
LIEˆ. U MO`
. 27
fm(raˆ´t cao) ×100 = 0, 35× 0, 6× 100 = 21. Vaˆ.y S(1)× 100 = (79, 100].
(fm(kha’ na˘ng cao) + fm(ho.n cao)) ×100 = (0, 25× 0, 6 + 0, 15× 0, 6)× 100 = 24 va`
S(cao)×100 = (55, 79]; (fm(´ıt thaˆ´p) +fm(´ıt cao))×100 = (0, 25×0, 6+0, 25×0, 4)×100 = 25
va` S(W )×100 = (30, 55]; (fm(kha’ na˘ng thaˆ´p) + fm(ho.n thaˆ´p))×100 = (0, 25×0, 4+0, 15×
0, 4)× 100 = 16 va` S(thaˆ´p) ×100 = (14, 30], S(0)× 100 = [0, 14].
Chu´ng ta co´ theˆ’ thaˆ´y phu. thuoˆ.c do
.n dieˆ.u ta˘ng SONLV
+
 1 THUNHAP du´ng trong
quan heˆ. Luongcb. Thaˆ.t vaˆ.y, ta co´ ∀t, s ∈ Luongcb, t[SONLV ] ≤1 s[SONLV ]⇒ t[THUNHAP ] ≤1
s[THUNHAP ]. Do do´ theo di.nh ngh˜ıa ta co´ SONLV
+
 1 THUNHAP.
Vı´ du. 4.4. Cho lu
.o.. c doˆ` quan heˆ. U = {TENCTY,NAM,DOANHTHU,LOINHUAN}
vo´.i y´ ngh˜ıa: Teˆn coˆng ty (TENCTY), Na˘m (NAM) la` 2 thuoˆ. c t´ınh kinh dieˆ’n, Doanh thu
trong na˘m (DOANHTHU), Lo.. i nhuaˆ.n (LOINHUAN) la` 2 thuoˆ.c t´ınh ngoˆn ngu˜
.. Trong do´
DDOANHTHU = [500, 3000] va` DLOINHUAN = [50, 500]. LDDOANHTHU va` LDLOINHUAN
co´ cu`ng taˆ.p ca´c xaˆu gioˆ´ng nhau vo´
.i taˆ.p ca´c pha`ˆn tu
.’ sinh la` {0, thaˆ´p,W , cao, 1} va` taˆ.p ca´c
gia tu.’ la` ı´t, kha’ na˘ng, ho.n, raˆ´t. Quan heˆ. Loinhuancty xa´c di.nh treˆn U du
.o.. c cho o
.’ Ba’ng 4.4.
Ba’ng 4.4. Quan heˆ. Loinhuancty
TENCTY NAM DOANHTHU LOINHUAN
Tha˘ng Long 2006 raˆ´t thaˆ´p 135
Thuaˆ. n Tha`nh 2006 872 140
Tra`ng Tie`ˆn 2007 1275 170
Ca`ˆu Giaˆ´y 2007 ho.n thaˆ´p ı´t thaˆ´p
Doˆ´ng Da 2007 1990 260
Da`ˆu kh´ı 2006 ho.n cao ho.n cao
Ha. Long 2007 2575 375
Coˆ´ doˆ 2005 raˆ´t cao raˆ´t cao
Hu.o.ng Giang 2005 2950 490
Doˆ´i vo´.i thuoˆ.c t´ınh DOANHTHU : Cho.n fm(cao) = 0, 35, fm(thaˆ´p) = 0, 65, µ(kha’ na˘ng) =
0, 25, µ(´ıt) = 0, 2, µ(ho.n) = 0, 15 va` µ(raˆ´t) = 0, 4. Ta phaˆn hoa.ch doa.n [500, 3000] tha`nh
ca´c khoa’ng tu.o.ng tu.. mu´
.c 2 la`:
fm(raˆ´t raˆ´t cao)×2500 = 0, 4×0, 4×0, 35×2500 = 140. Vaˆ.y S(1)×2500 = (2860, 3000].
(fm(ho.n raˆ´t cao) + fm(kha’ na˘ng raˆ´t cao))× 2500 = (0, 15× 0, 4× 0, 35+ 0, 25× 0, 4×
0, 35)×2500 = 140 va` S(raˆ´t cao)×2500 = (2720, 2860]; (fm(´ıt raˆ´t cao)+fm(raˆ´t ho.n cao))×
2500 = (0, 2× 0, 4× 0, 35 + 0, 4× 0, 15× 0, 35)× 2500 = 122, 5; (fm(kha’ na˘ng ho.n cao) +
fm(ho.n ho.n cao)) × 2500 = (0, 25× 0, 15× 0, 35 + 0, 15× 0, 15× 0, 35)× 2500 = 52, 5 va`
S(ho.n cao) × 2500 = (2545, 2597, 5]; (fm(´ıt ho.n cao) + fm(raˆ´t kha’ na˘ng cao)) × 2500 =
(0, 2 × 0, 15 × 0, 35 + 0, 4 × 0, 25 × 0, 35) × 2500 = 113, 75; (fm(ho.n kha’ na˘ng cao) +
fm(kha’ na˘ng kha’ na˘ng cao))×2500 = (0, 15×0, 25×0, 35+0, 25×0, 25×0, 35)×2500 = 87, 5
va` S(kha’ na˘ng cao)× 2500 = (2343, 75, 2431, 25].
(fm(´ıt kha’ na˘ng cao)+fm( raˆ´t ı´t cao))×2500 = (0, 2×0, 25×0, 35+0, 4×0, 2×0, 35)×
2500 = 113, 75; (fm(ho.n ı´t cao)+fm(kha’ na˘ng ı´t cao))×2500 = (0, 15×0, 2×0, 35+0, 25×
0, 2× 0, 35)× 2500 = 70 va` S (´ıt cao)× 2500 = (2160, 2230].
(fm(´ıt ı´t cao) + fm(´ıt ı´t thaˆ´p)) × 2500 = (0, 2 × 0, 2 × 0, 35 + 0, 2 × 0, 2 × 0, 65) ×
2500 = 100 va` S(W ) × 2500 = (2060, 2160]; (fm(ho.n ı´t thaˆ´p) + fm(kha’ na˘ng ı´t thaˆ´p)) ×
28 NGUYE˜ˆN CA´T HOˆ`, NGUYE˜ˆN COˆNG HA`O
2500 = (0, 15 × 0, 2 × 0, 65 + 0, 25 × 0, 2 × 0, 65) × 2500 = 130 va` S (´ıt thaˆ´p) × 2500 =
(1930, 2060]; (fm(´ıt kha’ na˘ng thaˆ´p) + fm(raˆ´t ı´t thaˆ´p))× 2500 = (0, 2× 0, 25× 0, 65+0, 4×
0, 2× 0, 65)× 2500 = 211, 25; (fm(ho.n kha’ na˘ng thaˆ´p) + fm(kha’ na˘ng kha’ na˘ng thaˆ´p)) ×
2500 = (0, 15×0, 25×0, 65+0, 25×0, 25×0, 65)×2500 = 162, 5 va` S(kha’ na˘ng thaˆ´p)×2500 =
(1556, 25, 1718, 75]; (fm(´ıt ho.n thaˆ´p)+fm(raˆ´t kha’ na˘ng thaˆ´p))×2500 = (0, 2×0, 15×0, 65+
0, 4× 0, 25× 0, 65)× 2500 = 211, 25.
(fm(ho.n ho.n thaˆ´p) + fm(kha’ na˘ng ho.n thaˆ´p))× 2500 = (0, 15× 0, 15× 0, 65 + 0, 25×
0, 15 × 0, 65)× 2500 = 97, 5 va` S(ho.n thaˆ´p) × 2500 = (1247, 5, 1345]; (fm(´ıt raˆ´t thaˆ´p) +
fm(raˆ´t ho.n thaˆ´p)) × 2500 = (0, 2 × 0, 4 × 0, 65 + 0, 4 × 0, 15 × 0, 65) × 2500 = 227, 5;
(fm(ho.n raˆ´t thaˆ´p) + fm(kha’ na˘ng raˆ´t thaˆ´p))× 2500 = (0, 15× 0, 4× 0, 65 + 0, 25× 0, 4×
0, 65) × 2500 = 260 va` S(raˆ´t thaˆ´p) × 2500 = (857, 5, 1117, 5]; fm(raˆ´t raˆ´t thaˆ´p) × 2500 =
0, 4× 0, 4× 0, 65× 2500 = 260, Vaˆ.y S(0)× 2500 = [500, 857, 5].
Doˆ´i vo´.i thuoˆ.c t´ınh LOINHUAN : Cho.n fm(cao) = 0, 6, fm(thaˆ´p) = 0, 4, µ(kha’ na˘ng) =
0, 15, µ(´ıt) = 0, 25, µ(ho.n) = 0, 25 va` µ(raˆ´t) = 0, 35.
Tu.o.ng tu.. , phaˆn hoa.ch doa.n [50, 500] tha`nh ca´c khoa’ng tu
.o.ng tu.. mu´
.c 2 ta co´ ca´c keˆ´t
qua’ tu.o.ng u´.ng nhu. sau: S(1)×450 = (466, 925, 500], S(raˆ´t cao)×450 = (429, 125, 466, 925],
S(ho.n cao)×450 = (354, 875, 381, 875], S(kha’ na˘ng cao)×450 = (307, 625, 323, 825], S (´ıt cao)×
450 = (246, 875, 273, 875], S(W )×450 = (218, 75, 246, 875], S (´ıt thaˆ´p)×450 = (200, 75, 218, 75],
S(kha’ na˘ng thaˆ´p)× = (167, 45, 178, 25], S(ho.n thaˆ´p)× = (128, 75, 146, 75], S(raˆ´t thaˆ´p)× =
(72, 05, 97, 25], S(0)× = [50, 72, 05].
Chu´ng ta co´ theˆ’ thaˆ´y phu. thuoˆ.c do
.n dieˆ.u ta˘ng DOANHTHU
+
 2 LOINHUAN du´ng
trong quan heˆ. Loinhuancty. Thaˆ. t vaˆ.y, ta co´ ∀t, s ∈ Loinhuancty, t[DOANHTHU ] ≤2
s[DOANHTHU ] ⇒ t[LOINHUAN ] ≤2 s[LOINHUAN ]. Do do´ theo di.nh ngh˜ıa ta co´
DOANHTHU+ 2 LOINHUAN.
Go.i F
k
A la` ho. ca´c phu. thuoˆ.c do
.n dieˆ.u ta˘ng mu´
.c k treˆn lu.o.. c doˆ` quan heˆ. U. Ta ky´ hieˆ.u
FA∗k la` taˆ.p taˆ´t ca’ ca´c phu. thuoˆ.c do
.n dieˆ.u ta˘ng X
+
 k Y mu´.c k ma` du.o.. c suy daˆ˜n tu`
. FkA.
Di.nh ly´ 4.3. Trong CSDL mo`
. vo´.i taˆ. p vu˜ tru. ca´c thuoˆ. c t´ınh U, ho. F
k
A∗ tho’a ma˜n ca´c tieˆn
de`ˆ sau:
(1) Pha’n xa. : X
+
 k X ∈ F
k
A∗ .
(2) Gia ta˘ng: X+ k Y ∈ F
k
A∗ ⇒ XZ
+
 k Y Z ∈ F
k
A∗ , Z ⊆ U.
(3) Ba˘´c ca`ˆu: X+ k Y ∈ F
k
A∗ , Y
+
 k Z ∈ F
k
A∗ ⇒ X
+
 k Z ∈ F
k
A∗ .
Chu´.ng minh
(1) Pha’n xa. : Hieˆ’n nhieˆn v`ı ∀t, s ∈ r, t[X ] ≤k s[X ](t[X ]≤k s[X ]. Vaˆ.y X
+
 k X ∈ F
k
A∗ .
(2) Theo gia’ thieˆ´t ta co´ X+ k Y ∈ F
k
A∗ neˆn theo di.nh ngh˜ıa ∀t, s ∈ r, t[X ] ≤k s[X ]⇒
t[Y ] ≤k s[Y ] (1’). Vo´
.i Z ⊆ U, tu`. t[X ] ≤k s[X ] ta co´ t[XZ] ≤k s[XZ] (2’). Tu
.o.ng tu.. , tu`
.
t[Y ] ≤k s[Y ] ta co´ t[Y Z] ≤k s[Y Z] (3’). Tu`. (1’), (2’), (3’) ta co´ ∀t, s ∈ r, t[XZ] ≤k s[XZ]⇒
t[Y Z] ≤k s[Y Z]. Vaˆ.y XZ
+
 k Y Z ∈ F
k
A∗ .
(3) Theo gia’ thieˆ´t X+ k Y ∈ F
k
A∗ , Y
+
 k Z ∈ F
k
A∗ neˆn ta co´ ∀t, s ∈ r, t[X ] ≤k s[X ]⇒
t[Y ] ≤k s[Y ] va` ∀t, s ∈ r, t[Y ] ≤k s[Y ]⇒ t[Z] ≤k s[Z] hay ∀t, s ∈ r, t[X ] ≤k s[X ]⇒ t[Z] ≤k
s[Z]. Vaˆ.y X
+
 k Z ∈ F
k
A∗ . 
4.2.2. Phu. thuoˆ. c do
.n dieˆ.u gia’m
PHU. THUOˆ. C DO
.
N DIEˆ. U TRONG CO
.
SO
.’ DU˜
.
LIEˆ. U MO`
. 29
Vo´.i X la` moˆ. t taˆ.p con cu’a U va` t, s la` hai boˆ. tu`y y´ treˆn U , ta vieˆ´t t[X ] ≥k s[X ], neˆ´u vo´
.i
mo. i A ∈ X, ta co´ t[A] ≥k s[A].
Di.nh ngh˜ıa 4.4. Cho U la` moˆ. t lu
.o.. c doˆ` quan heˆ., r la` moˆ. t quan heˆ. treˆn U va` X, Y ⊆ U. Ta
no´i ra`˘ng quan heˆ. r tho’a ma˜n phu. thuoˆ.c do
.n dieˆ.u gia’m X xa´c di.nh Y vo´
.i mu´.c k, ky´ hieˆ.u la`
X− k Y, trong quan heˆ. r, neˆ´u ta co´: ∀t, s ∈ r, t[X ] ≤k s[X ]⇒ t[Y ] ≥k s[Y ].
Vı´ du. 4.5. Ta xe´t lu
.o.. c doˆ` quan heˆ. U = {MASO, TENCN, SN NGHILV, THUNHAP}
vo´.i y´ ngh˜ıa: Ma˜ soˆ´ coˆng nhaˆn (MASO), Teˆn coˆng nhaˆn (TENCN ) la` 2 thuoˆ. c t´ınh kinh dieˆ’n,
Soˆ´ nga`y nghı’ la`m vieˆ.c trong tha´ng (SN NGHILV), Thu nhaˆ.p (THUNHAP ) la` 2 thuoˆ. c t´ınh
ngoˆn ngu˜.. Trong do´ DSN NGHILV = [0, 30] va` DTHUNHAP = [0, 100]. LDSN NGHILV va`
LDTHUNHAP co´ cu`ng taˆ.p ca´c xaˆu gioˆ´ng nhau vo´
.i taˆ.p ca´c pha`ˆn tu
.’ sinh la` {0, thaˆ´p,W , cao, 1}
va` taˆ.p ca´c gia tu
.’ la` {´ıt, kha’ na˘ng, ho.n, raˆ´t}. Ma˘.c du` ca´c thuoˆ.c t´ınh ngoˆn ngu˜
. dang xe´t co´
cu`ng taˆ.p ca´c xaˆu, nhu
.ng ngu˜. ngh˜ıa di.nh lu
.o.. ng cu’a chu´ng kha´c nhau. Phaˆn hoa.ch ca´c mie`ˆn
tri. du
.o.. c t´ınh gioˆ´ng nhu
. trong Vı´ du. 4.3. Quan heˆ. Luongcb1 trong v´ı du. na`y du
.o.. c cho trong
Ba’ng 4.5.
Ba’ng 4.5. Quan heˆ. Luongcb1
MASO TENCN SN NGHILV THUNHAP
N1 Anh 3 78
N2 A´nh 5 75
N3 Lan 2 cao
N4 Hu.o.ng thaˆ´p 52
N5 Ha`˘ng 8 53
N6 Hoˆ`ng 8 54
N7 Thu´y cao 10
N8 Thanh 9 52
N9 Hieˆ’n 18 thaˆ´p
Chu´ng ta co´ theˆ’ thaˆ´y ra`˘ng phu. thuoˆ.c do
.n dieˆ.u gia’m SN NGHILV
−
 1 THUNHAP
du´ng trong quan heˆ. Luongcb1. Thaˆ. t vaˆ.y, ta co´ ∀t, s ∈ Luongcb1, t[SN NGHILV ] ≤1
s[SN NGHILV ] ⇒ t[THUNHAP ] ≥1 s[THUNHAP ]. Do do´ theo di.nh ngh˜ıa ta co´
SN NGHILV− 1 THUNHAP.
Go.i F
k
D la` ho. ca´c phu. thuoˆ.c do
.n dieˆ.u gia’m mu´
.c k treˆn lu.o.. c doˆ` quan heˆ. U . Ta ky´ hieˆ.u
FkD∗ la` taˆ.p taˆ´t ca’ ca´c phu. thuoˆ. c do
.n dieˆ.u gia’m X
−
 k Y mu´.c k ma` du.o.. c suy daˆ˜n tu`
. FkD.
Di.nh ly´ 4.4. Trong CSDL mo`
. vo´.i taˆ. p vu˜ tru. ca´c thuoˆ. c t´ınh U, ho. F
k
D∗ tho’a ma˜n ca´c tieˆn
de`ˆ sau:
(1) Pha’n xa. : X
−
 k X ∈ F
k
D∗ .
(2) Gia ta˘ng: X− Y ∈ F
k
D∗ ⇒ XZ
−
 Y Z ∈ F
k
D∗ , Z ⊆ U.
(3) Hoˆ˜n ho.. p ba˘´c ca`ˆu: X
−
 k Y ∈ F
k
D∗ , Y
+
 k Z ∈ F
k
A∗ ∈ X
−
 k Z ∈ F
k
D∗ .
Chu´.ng minh. Tu.o.ng tu.. nhu
. Di.nh ly´ 4.3.
Tu`. Di.nh ly´ 4.4 ta co´ heˆ. qua’ sau.
Heˆ. qua’ 4.2.
(4) Hoˆ˜n ho.. p ba˘´c ca`ˆu 1: X
+
 k Y ∈ F
k
A∗ , Y
−
 k Z ∈ F
k
D∗ ⇒ X
−
 k Z ∈ F
k
D∗ .
30 NGUYE˜ˆN CA´T HOˆ`, NGUYE˜ˆN COˆNG HA`O
(5) Hoˆ˜n ho.. p ba˘´c ca`ˆu 2: X
−
 k Y ∈ F
k
D∗, Y
−
 k Z ∈ F
k
D∗ ⇒ X
+
 k Z ∈ F
k
A∗ .
5. KEˆ´T LUAˆ. N
Vieˆ.c nghieˆn cu´
.u CSDL vo´.i thoˆng tin mo`., khoˆng cha˘´c cha˘´n du.. a treˆn ca´ch tieˆ´p caˆ.n DSGT
cho phe´p chu´ng ta gia’ i quyeˆ´t ba`i toa´n tru.. c quan ho
.n so vo´.i ca´ch tieˆ´p caˆ.n ly´ thuyeˆ´t taˆ.p mo`
.,
ly´ thuyeˆ´t kha’ na˘ng va` co. so.’ tu.o.ng tu.. ... Nho`
. xaˆy du.. ng ca´c khoa’ng laˆn caˆ.n va` su
.’ du.ng a´nh xa.
di.nh lu
.o.. ng vo´
.i tham soˆ´ la` doˆ. do t´ınh mo`
. cu’a ngoˆn ngu˜., ca´c gia´ tri. ngoˆn ngu˜
. co´ gia´ tri. thu
.
. c
trong mie`ˆn tham chieˆ´u la`m da. i dieˆ.n cu`ng vo´
.i heˆ. laˆn caˆ.n ngu˜
. ngh˜ıa cu’a no´ cho phe´p chu´ng ta
chuyeˆ’n ca´c thao ta´c du˜. lieˆ.u trong CSDL mo`
. ve`ˆ ca´c thao ta´c du˜. lieˆ.u kinh dieˆ’n la`m cho vieˆ.c
toˆ’ chu´.c thao ta´c tro.’ neˆn do.n gia’n ho.n. Vo´.i u.u dieˆ’m cu’a DSGT, trong ba`i ba´o na`y chu´ng toˆi
nghieˆn cu´.u phu. thuoˆ.c do
.n dieˆ.u ta˘ng va` do
.n dieˆ.u gia’m trong CSDL mo`
., CSDL kinh dieˆ’n va`
moˆ´i lieˆn heˆ. giu˜
.a chu´ng doˆ´i vo´.i phu. thuoˆ.c ha`m mo`
.. T´ınh da`ˆy du’ cu’a ca´c tieˆn de`ˆ tu`. Di.nh ly´
4.1 deˆ´n Di.nh ly´ 4.4 vaˆ˜n chu
.a du.o.. c kha˘’ ng di.nh bo
.’ i v`ı pha’ i ca`ˆn co´ moˆ.t tieˆn de`ˆ bao ha`m mu´
.c
k pha’ i co´ t´ınh du´ng da˘´n va` da`ˆy du’ .
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.
N DIEˆ. U TRONG CO
.
SO
.’ DU˜
.
LIEˆ. U MO`
. 31
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Nhaˆ. n ba`i nga`y 11 - 7 - 2007
Nhaˆ. n la. i sau su
.’ a nga`y 12 - 5 -2008