Phụ thuộc dữ liệu trong trong cơ sở dữ liệu quan hệ với thông tin ngôn ngữ

ng mo`. tu.o.ng u´.ng vo´.i
thang da´nh gia´ suaˆ´t sa˘´c la. i tu
.o.ng doˆ´i lo´.n. Vo´.i ly´ do do´ ta cho.n ca´c tham soˆ´ doˆ. do t´ınh mo`
.
ngoˆn ngu˜. nhu. sau:
- Doˆ´i vo´.i thuoˆ.c t´ınh CTTN: fm(lo´
.n) = fm(c+) = 0, 35, fm(nho’) =fm(c−) = 0, 65,
µ(kha´) = 0, 25, µ(´ıt) = 0, 20, µ(ho.n) = 0, 15 va` µ(raˆ´t) = 0, 40. Nhu. vaˆ.y, α = 0, 45 va`
β = 0, 55.
Ta phaˆn hoa.ch doa.n [0, 60] tha`nh 5 khoa’ng tu
.o.ng tu.. mu´
.c 1 la`:
fm(kc+)× 60 = 0, 35× 0, 35× 60 = 7, 35. Vaˆ.y, S(1)× 60 = (52, 65, 60, 00].
(fm(h′c+) + fm(hc+))× 60 = (0, 25× 0, 35 + 0, 15× 0, 35)× 60 = 8, 4 va`
S(c+)× 60 = (44, 25, 52, 65].
(fm(k′c−) + fm(k′c+))× 60 = (0, 25× 0, 65+ 0, 25× 0, 35)× 60 = 15, 0 va`
S(W )× 60 = (29, 25, 44, 25].
(fm(h′c−) + fm(hc−))× 60 = (0, 25× 0, 65 + 0, 15× 0, 65)× 60 = 15, 6 va`
S(c−)× 60 = (13, 65, 29, 25].
Cuoˆ´i cu`ng, S(0)× 60 = [00, 00, 13, 65].
- Doˆ´i vo´.i thuoˆ.c t´ınh CTNN: Do thu
.
. c teˆ´, ca´c nho´m nghiaˆn cu´
.u co`n ı´t coˆng boˆ´ o.’ nu.´o.c
ngoa`i neˆn ta se˜ xa´c di.nh tham soˆ´ theo khuynh hu
.´o.ng “de˜ˆ da˜i” doˆ´i vo´.i tieˆu ch´ı na`y: fm(lo´.n)
PHU. THUOˆ. C DU˜
.
LIEˆ. U TRONG CO
.
SO
.’ DU˜
.
LIEˆ. U QUAN HEˆ. 173
= fm(c+) = 0, 6, fm(nho’) = fm(c−) = 0, 4, µ(kha´) = 0, 15, µ(´ıt) = 0, 25, µ(ho.n) = 0, 25
va` µ(raˆ´t) = 0, 35. Nhu. vaˆ.y, α = 0, 6 va` β = 0, 4.
Ta phaˆn hoa.ch doa.n [0, 20] tha`nh 5 khoa’ng tu
.o.ng tu.. mu´
.c 1 la`:
fm(kc+)× 60 = 0, 35× 0, 6× 20 = 4, 20. Vaˆ.y, S(1)× 60 = (15, 80, 20, 00].
(fm(h′c+) + fm(hc+))× 20 = (0, 25× 0, 6 + 0, 15× 0, 6)× 20 = 4, 80 va`
S(c+)× 60 = (11, 00, 15, 80].
(fm(k′c−) + fm(k′c+))× 20 = (0, 25× 0, 6+ 0, 25× 0, 4)× 20 = 5, 00 va`
S(W )× 60 = (06, 00, 11, 00].
(fm(h′c−) + fm(hc−))× 20 = (0, 25× 0, 4 + 0, 15× 0, 4)× 20 = 3, 20 va`
S(c−)× 60 = (02, 80, 06, 00].
Cuoˆ´i cu`ng, S(0)× 60 = [00, 00, 02, 80].
- Doˆ´i vo´.i thuoˆ.c t´ınh NLTC: Ta gia’ thieˆ´t ra`˘ng vieˆ.c da´nh gia´ theo thu’ tu. c la` ca´c chuyeˆn gia
cho dieˆ’m, t´ınh trung b`ınh coˆ.ng va` sau do´ phaˆn theo thang baˆ. c suaˆ´t sa˘´c, gio’i, kha´, trung b`ınh,
ke´m. Thoˆng thu.`o.ng, ta su.’ du. ng ca´c thang ngoˆn ngu˜
. na`y tu.o.ng u´.ng vo´.i ca´c khoa’ng phaˆn
hoa.ch [9, 5, 10, 0], [8, 5, 9, 5), [7, 0, 8, 5), [5, 0, 7, 0) va` [0, 0, 5, 0). Tuy nhieˆn, khi ta xa´c di.nh ca´c
phu.o.ng tr`ınh t´ınh ca´c khoa’ng tu.o.ng tu.. nhu
. treˆn deˆ’ xa´c di.nh ca´c tham soˆ´ doˆ. do t´ınh mo`
.
th`ı heˆ. voˆ nghieˆ.m. Ly´ do la` khoa’ng [0, 0, 5, 0] co´ doˆ. da`i kha´ baˆ´t thu
.`o.ng. Deˆ’ gia’ i quyeˆ´t vaˆ´n
de`ˆ na`y, ta giu˜. nguyeˆn ca´c khoa’ng phaˆn hoa.ch treˆn, tru`
. khoa’ng baˆ´t thu.`o.ng co´ doˆ. da`i ba`˘ng
toˆ’ng doˆ. da`i ca´c khoa’ng co`n la. i, du
.o.. c thay ba`˘ng khoa’ng [l, 5, 0), vo´
.i l la` tham soˆ´, deˆ’ t´ınh
ca´c tham soˆ´ doˆ. do t´ınh mo`
.. Sau do´ treˆn thu.. c teˆ´ ta vaˆ˜n su
.’ du.ng khoa’ng [0, 0, 5, 0). Vo´
.i quy
u.´o.c do´ ta t´ınh du.o.. c ca´c tham soˆ´ sau: µ(´ıt) = 0, 25, fm(lo´
.n) = fm(c+) = 0, 333, fm(nho’) =
fm(c−) = 0, 667, µ(kha´) + µ(ho.n) = 0, 5 va` µ(raˆ´t) = 0, 25. Khi do´ ca´c khoa’ng phaˆn hoa.ch
treˆn du.o.. c xem la` ca´c khoa’ng tu
.o.ng tu.. mu´
.c 1.
Quan heˆ. r trong v´ı du. na`y du
.o.. c cho trong Ba’ng 1.
Ba’ng 1. Quan heˆ. vo´
.i thuoˆ.c t´ınh ngoˆn ngu˜
.
TEˆN TCNC CTTN CTNN NLTC
#1 55 16 9,9
#2 12 2 4,4
#3 46 17 9,8
#4 46 17 9,5
#5 53 14 9,1
#6 56 13 8,8
#7 17 4 6,2
#8 23 8 7,9
Trong quan heˆ. na`y, TEˆN TCNC la` kho´a (theo ngh˜ıa kinh dieˆ’n) nhu
.ng taˆ.p hai thuoˆ. c t´ınh
CTTN va` CTNN khoˆng xa´c di.nh ha`m thuoˆ.c t´ınh NLTC do ca´c du˜
. lieˆ.u trong hai ha`ng 3 va` 4.
Die`ˆu na`y treˆn thu.. c teˆ´ co´ theˆ’ xa’y ra do keˆ´t qua’ bo’ phieˆ´u da´nh gia´. Ca˘n cu´
. thu.. c tie˜ˆn co´ theˆ’
do taˆ.p theˆ’ nghieˆn cu´
.u #3 do moˆ. t ca´n boˆ. khoa ho.c tre’ co´ na˘ng lu
.
. c phu. tra´ch va` du
.o.. c ca´c u’y
vieˆn hoˆ. i doˆ`ng thu
.o.’ ng dieˆ’m trong da´nh gia´ theo quan dieˆ’m cu’a ho. . Cu˜ng tu
.o.ng tu.. , co´ theˆ’
gia´o vieˆn da´nh gia´ ho. c vieˆn na`y suaˆ´t sa˘´c ho
.n ho.c vieˆn kia du` dieˆ’m ba`˘ng nhau hoa˘. c ke´m ho
.n.
Tuy nhieˆn, ta co´ theˆ’ kieˆ’m chu´.ng ra`˘ng {CTTN, CTNN} κ→ NLTC, trong do´ k(U) de`ˆu la`
mu´.c 1 treˆn ca´c thuoˆ. c t´ınh ngoˆn ngu˜
..
174 NGUYE˜ˆN VA˘N LONG
Ta ca`ˆn nhaˆ´n ma.nh ra`˘ng, phu. thuoˆ.c tu
.o.ng tu.. {CTTN, CTNN} κ→ NLTC la` moˆ.t ra`ng
buoˆ.c me`ˆm de’o, theˆ’ hieˆ.n moˆ. t quy di.nh da´nh gia´ buoˆ.c pha’ i tuaˆn thu’ . Cha˘’ ng ha.n, o
.’ ha`ng 3 va`
4, neˆ´u tieˆu ch´ı soˆ´ dieˆ’m CTNN du.o.. c “phaˆn loa. i” suaˆ´t sa˘´c (v`ı no´ thuoˆ.c phaˆn hoa.ch lo´
.n nhaˆ´t)
co`n doˆ´i vo´.i tieˆu ch´ı CTTN du.o.. c “phaˆn loa. i” gio’ i (thuoˆ. c phaˆn hoa.ch thu´
. hai) th`ı du.o.. c da´nh
gia´ thuoˆ.c nho´m suaˆ´t sa˘´c. Tuy nhieˆn, neˆ´u thuoˆ.c t´ınh NLTC chı’ nhaˆ.n ca´c gia´ tri. ngoˆn ngu˜
. th`ı
no´ se˜ tro.’ tha`nh phu. thuoˆ.c ha`m. Nhu
.ng vieˆ.c cho phe´p thuoˆ.c t´ınh na`y nhaˆ.n gia´ tri. thu
.
. c co´
u.u dieˆ’m la` ta co´ theˆ’ thay doˆ’i ca´ch phaˆn hoa.ch ca´c khoa’ng dieˆ’m da´nh gia´, ngh˜ıa la` cho phe´p
ngu˜. ngh˜ıa cu’a ca´c gia´ tri. ngoˆn ngu˜
. khoˆng tie`ˆn di.nh.
Nhu. vaˆ.y, phu. thuoˆ.c tu
.o.ng tu.. , beˆn ca.nh ngu˜
. ngh˜ıa mo`. vaˆ˜n de`ˆ caˆ.p, no´ co`n co´ y´ ngh˜ıa thu
.
. c
tie˜ˆn quan tro.ng.
Go.i Fκ la` ho. taˆ´t ca’ ca´c phu. thuoˆ. c ha`m mu´
.c κ treˆn lu.o.. c doˆ` CSDL DB. Ta ky´ hieˆ.u F
∗
κ la`
taˆ.p taˆ´t ca’ ca´c phu. thuoˆ.c tu
.o.ng tu.. f mu´
.c κ ma` la` heˆ. qua’ ngu˜
. ngh˜ıa cu’a Fκ, tu´.c la`, vo´.i mo. i
quan heˆ. r treˆn U , neˆ´u r tho’a ca´c thu. thuoˆ.c du˜
. lieˆ.u trong Fκ th`ı r cu˜ng tho’a f . Ta co´ theˆ’ de˜ˆ
da`ng kieˆ’m chu´.ng ho. ca´c phu. thuoˆ.c tu
.o.ng tu.. F
∗
κ co´ ca´c t´ınh chaˆ´t sau.
Di.nh ly´ 3.1. Trong CSDL ngoˆn ngu˜
. vo´.i taˆ. p vu˜ tru. ca´c thuoˆ. c t´ınh U, ho. F
∗
κ tho’a ma˜n ca´c
t´ınh chaˆ´t sau:
(i) Pha’n xa. : Xκ → X ∈ F
∗
κ.
(ii) Gia ta˘ng: Xκ → Y ∈ F
∗
κ ⇒ XZκ → Y Z ∈ F
∗
κ.
(iii) Ba˘´c ca`ˆu: Xκ → Y, Yκ → Z ∈ F ∗κ ⇒ Xκ → Z ∈ F
∗
κ.
Cho taˆ.p Fκ va` ky´ hieˆ.u F
+
κ la` taˆ.p nho’ nhaˆ´t chu´
.a Fκ va` do´ng doˆ´i vo´.i ca´c t´ınh chaˆ´t, du.o.. c
go. i la` ca´c tieˆn de`ˆ neˆu trong Di.nh ly´ 3.1. Khi do´, Di.nh ly´ 3.1 ba’o da’m ra`˘ng neˆ´u quan heˆ. r
tho’a Fκ th`ı no´ cu˜ng tho’a F+κ , hay F
+
κ ⊆ F
∗
κ.
Di.nh ly´ 3.2. Heˆ. tieˆn de`ˆ (i)− (iii) trong Di.nh ly´ 3.1 la` da`ˆy du’, ngh˜ıa la` F
+
κ = F
∗
κ hay ta no´i
heˆ. tieˆn de`ˆ (i) - (iii) la` du’ deˆ’ sinh ra toa`n boˆ. taˆ. p F
∗
κ.
Chu´.ng minh. Ta de˜ˆ da`ng thaˆ´y ra`˘ng trong moˆ. t quan heˆ. 2-boˆ. r vo´
.i ca´c boˆ. t va` s chı’ chu´
.a ca´c
gia´ tri. lo´
.n nhaˆ´t va` nho’ nhaˆ´t trong mie`ˆn gia´ tri. thuoˆ.c t´ınh, die`ˆu kieˆ.n t[X ] =κ s[X ] la` tu
.o.ng
du.o.ng vo´.i die`ˆu kieˆ.n t[X ] = s[X ], v`ı khi do´ ca´c khoa’ng phaˆn hoa.ch (do no´ chu´
.a ı´t nhaˆ´t hai
lo´.p tu.o.ng du.o.ng) cu’a ca´c thuoˆ. c t´ınh ngoˆn ngu˜
. chı’ chu´.a moˆ. t trong hai gia´ tri. na`y. Do do´, neˆ´u
quan heˆ. 2-boˆ. r nhu
. vaˆ.y tho’a moˆ.t phu. thuoˆ.c tu
.o.ng tu.. na`o do´ (mu´
.c κ), th`ı no´ cu˜ng tho’a phu.
thuoˆ.c do´ khi du
.o.. c xem nhu
. la` moˆ. t phu. thuoˆ.c ha`m. Vı` vaˆ.y, cu˜ng nhu
. doˆ´i vo´.i ho. phu. thuoˆ.c
ha`m kinh dieˆ’n, neˆ´u f = Xκ→ X 6∈ F+κ th`ı toˆ`n ta. i moˆ.t quan heˆ. 2-boˆ. r sao cho r tho’a Fκ
nhu.ng khoˆng tho’a phu. thuoˆ.c tu
.o.ng tu.. f. Ngh˜ıa la`, heˆ. tieˆn de`ˆ trong Di.nh ly´ 3.1 la` da`ˆy du’ .
Nhu. vaˆ.y, ta thaˆ´y o
.’ mu´.c ky´ pha´p, phu. thuoˆ.c tu
.o.ng tu.. tru`ng vo´
.i phu. thuoˆ.c ha`m kinh dieˆ’n
nhu.ng ngu˜. ngh˜ıa kha´c nhau, da˘.c bieˆ.t moˆ.t quan heˆ. r co´ theˆ’ tho’a moˆ. t quan heˆ. ha`m tu
.o.ng tu..
f nhu.ng no´ khoˆng nhaˆ´t thieˆ´t tho’a f vo´.i tu. ca´ch la` moˆ.t phu. thuoˆ.c ha`m kinh dieˆ’n. Vı` vaˆ.y,
trong moˆ.t CSDL ngoˆn ngu˜
. co´ theˆ’ toˆ`n ta. i hai loa. i ra`ng buoˆ.c du˜
. lieˆ.u: (i) Phu. thuoˆ. c ha`m kinh
dieˆ’n, no´ co´ gia´ tri. cho thieˆ´t keˆ´ CSDL theo ca´c da.ng chuaˆ’n. (ii) Phu. thuoˆ.c ha`m tu
.o.ng tu..
nhu.ng quan heˆ. r khoˆng nhaˆ´t thieˆ´t tho’a no´ nhu
. la` moˆ.t phu. thuoˆ.c ha`m. Tuy nhieˆn, no´ vaˆ˜n la`
moˆ. t ra`ng buoˆ.c yeˆ´u doˆ´i vo´
.i CSDL nhu. ta thaˆ´y trong Vı´ du. 3.1. Do do´, moˆ. t CSDL ngoˆn ngu˜
.
co´ theˆ’ bieˆ’u thi. ba`˘ng moˆ. t boˆ. sau
DB = {U ;J−, Fκ},
trong do´ J− la` taˆ.p phu. thuoˆ.c ha`m, co`n Fκ la` taˆ.p phu. thuoˆ.c tu
.o.ng tu.. va` J− ∩Fκ = ∅.
PHU. THUOˆ. C DU˜
.
LIEˆ. U TRONG CO
.
SO
.’ DU˜
.
LIEˆ. U QUAN HEˆ. 175
Nhu. thu.`o.ng leˆ., Y phu. thuoˆ.c ha`m va`o X se˜ du
.o.. c ky´ hieˆ.u ba`˘ng X → Y va` lu
.u y´ ra`˘ng doˆ´i
vo´.i phu. thuoˆ.c ha`m nhu
. vaˆ.y X hay Y vaˆ˜n chu´
.a ca´c thuoˆ.c t´ınh ngoˆn ngu˜
., tuy nhieˆn no´ xem
ca´c gia´ tri. ngoˆn ngu˜
. nhu. la` ca´c ky´ hieˆ.u (mu´
.c cu´ pha´p).
Phu. thuoˆ.c ha`m la` moˆ. t ra`ng buoˆ.c cu’a co
. so.’ du˜. lieˆ.u o
.’ mu´.c cu´ pha´p, tu´.c la` mu´.c ky´ hieˆ.u,
phu. c vu. cho vieˆ.c thao ta´c du˜
. lieˆ.u o
.’ mu´.c ky´ hieˆ.u. Vı´ du. , neˆ´u f = X → A vo´
.i A la` thuoˆ.c t´ınh
ngoˆn ngu˜. LU´
.
A TUOˆ’I, th`ı gia´ tri. “tre’” xuaˆ´t hieˆ.n trong coˆ.t thuoˆ.c t´ınh A cu˜ng bi. ra`ng buoˆ.c
bo.’ i phu. thuoˆ.c ha`m f , trong khi co´ theˆ’ co´ phu. thuoˆ.c tu
.o.ng tu.. Yκ→ A. Phu. thuoˆ.c tu
.o.ng tu..
trong Fκ cu˜ng la` moˆ.t ra`ng buoˆ.c CSDL nhu
.ng khoˆng cha˘.t v`ı no´ cho phe´p quan heˆ. giu˜
.a ca´c
gia´ tri. thuoˆ. c t´ınh khoˆng nhaˆ´t thieˆ´t tuaˆn theo phu. thuoˆ.c ha`m. No´ xa´c di.nh moˆ´i quan heˆ. giu˜
.a
ca´c gia´ tri. cu’a moˆ.t thuoˆ.c t´ınh trong moˆ. t phaˆn hoa.ch doˆ. tu
.o.ng tu.. mu´
.c k na`o do´.
Do hai loa. i phu. thuoˆ.c ha`m na`y co´ quan heˆ. ga`ˆn gu˜i vo´
.i nhau, ca’ o.’ mu´.c h`ınh thu´.c ho´a,
neˆn chu´ng co´ theˆ’ sinh theˆm ca´c phu. thuoˆ.c ha`m mo´
.i khoˆng na`˘m trong J−+ ∪F+κ .
Go.i J−DB la` taˆ.p ca´c phu. thuoˆ.c ha`m du
.o.. c sinh ngu˜
. ngh˜ıa tu`. J− va` Fκ theo ngh˜ıa J−DB
la` taˆ.p nho’ nhaˆ´t sao cho no´ chu´
.a mo. i phu. thuoˆ.c X → Y tho’a trong mo.i quan heˆ. r treˆn U ma`
no´ bi. ra`ng buoˆ.c bo
.’ i ca´c phu. thuoˆ.c du˜
. lieˆ.u trong J− ∪Fκ. Tu
.o.ng tu.. nhu
. vaˆ.y, ta di.nh ngh˜ıa
taˆ.p FDB la` taˆ.p taˆ´t ca’ ca´c phu. thuoˆ.c tu
.o.ng tu.. du
.o.. c sinh ngu˜
. ngh˜ıa tu`. hai taˆ.p J− va` Fκ.
Trong ca´ch tieˆ´p caˆ.n da. i soˆ´, ta co´ theˆ’ thieˆ´t laˆ. p moˆ´i lieˆn heˆ. kha´ chı’nh giu˜
.a hai loa. i phu.
thuoˆ.c du˜
. lieˆ.u na`y, cu. theˆ’ no´ du
.o.. c pha´t bieˆ’u trong meˆ.nh de`ˆ sau.
Di.nh ly´ 3.3. Trong CSDL ngoˆn ngu˜
. DB = {U ;J−,Fκ} ta co´:
(i) X → Y ∈ J−DB va` Yκ→ Z ∈ FDB ⇒ Xκ→ Z ∈ FDB, neˆ´u X khoˆng chu´.a thuoˆ. c t´ınh
ngoˆn ngu˜..
(ii) Xκ→ Y ∈ FDB ⇒ X → Y ∈ J−DB, neˆ´u Y khoˆng chu´.a thuoˆ. c t´ınh ngoˆn ngu˜
..
(iii) Xκ→ Y ∈ FDB va` Y → Z ∈ J−DB ⇒ X → Z ∈ J−DB, neˆ´u Y khoˆng chu´.a thuoˆ. c t´ınh
ngoˆn ngu˜..
(iv) Xκ→ Y ∈ FDB va` Z →W ∈ J−DB ⇒ XZκ→ YW ∈ FDB, neˆ´u Z khoˆng chu´.a thuoˆ. c
t´ınh ngoˆn ngu˜..
Chu´.ng minh. Vieˆ.c chu´
.ng minh di.nh ly´ khoˆng kho´, nhu
.ng ca`ˆn die˜ˆn da. t cu. theˆ’ deˆ’ phaˆn bieˆ.t
vai tro` cu’a hai loa. i phu. thuoˆ.c ha`m da˜ de`ˆ caˆ.p. Trong ca´c laˆ.p luaˆ.n du
.´o.i daˆy, ta gia’ thieˆ´t quan
heˆ. r tho’a ca´c phu. thuoˆ.c du˜
. lieˆ.u trong J− va` Fκ, t va` s la` hai boˆ. trong r.
Deˆ’ chu´.ng minh (i), ta gia’ su.’ t[X ] =κ s[X ]. Vı` X khoˆng chu´
.a thuoˆ.c t´ınh ngoˆn ngu˜
. neˆn ta
suy ra t[X ] = s[X ]. Do do´, t[Y ] = s[Y ] o.’ mu´.c ky´ hieˆ.u va` vieˆ.c na`y ke´o theo t[Y ] =κ s[Y ]. Tu`
.
do´ ta co´ t[Z] =κ s[Z], ngh˜ıa la` Xκ→ Z tho’a trong r (hay Xκ→ Z ∈ FDB).
Kha˘’ ng di.nh (ii) ru´t ra tu`
. su.. kieˆ.n la` t[X ] = s[X ] ke´o theo t[X ] =κ s[X ], va` do do´
t[Y ] =κ s[Y ]. Vı` Y chı’ chu´
.a ca´c thuoˆ.c t´ınh kinh dieˆ’n neˆn bieˆ’u thu´
.c cuoˆ´i cu`ng co´ ngh˜ıa
t[Y ] = s[Y ], tu´.c la` X → Y tho’a trong r.
Deˆ’ chu´.ng minh (iii), gia’ su.’ t[X ] =κ s[X ], khi do´ ta co´ t[Y ] =κ s[Y ]. Tu
.o.ng tu.. nhu
. treˆn,
v`ı Y khoˆng chu´.a thuoˆ.c t´ınh ngoˆn ngu˜
., neˆn ta suy ra t[Y ] = s[Y ] va` do do´, theo gia’ thieˆ´t
Y → Z ∈ J−, ta thu du.o.. c t[Z] = s[Z] o
.’ mu´.c ky´ hieˆ.u. Vaˆ.y, X → Z tho’a trong r.
Baˆy gio`. ta chu´.ng minh (iv). Theo t´ınh chaˆ´t (i), ta co´ Zκ→ W du´ng trong quan heˆ. dang
xe´t r. Vı`, theo Di.nh ly´ 3.1, ca´c phu. thuoˆ. c ha`m tu
.o.ng tu.. trong quan heˆ. r do´ng doˆ´i vo´
.i ca´c
tieˆn de`ˆ (i) - (iii), neˆn theo Tieˆn de`ˆ (ii) va` tu`. gia’ thieˆ´t cu’a (iv) ta co´ XZκ→ Y Z va` Y Zκ→ Y Z.
Vaˆ.y, theo tieˆn de`ˆ ba˘´c ca`ˆu (iii) ta thu du
.o.. c bieˆ’u thu´
.c ca`ˆn chu´.ng minh.
176 NGUYE˜ˆN VA˘N LONG
Lu.u y´: Ma˘.c du` kha´i nieˆ.m phu. thuoˆ.c ha`m tu
.o.ng tu.. la` su
.
. mo
.’ roˆ.ng kha´ tru
.
. c tieˆ´p tu`
. kha´i nieˆ.m
phu. thuoˆ.c ha`m (khi ma` taˆ´t ca’ ca´c thuoˆ. c t´ınh de`ˆu la` kinh dieˆ’n), nhu
.ng trong CSDL ngoˆn ngu˜.
(va` ca’ trong CSDL mo`.), chu´ng ta ca`ˆn pha’ i phaˆn bieˆ.t ro˜ ra`ng hai lo´
.p phu. thuoˆ.c du˜
. lieˆ.u na`y
v`ı vai tro` cu’a chu´ng raˆ´t kha´c nhau. Vı` vaˆ.y, ca´c gia’ thieˆ´t chu´
.a cu.m tu`
. “khoˆng chu´.a thuoˆ.c
t´ınh ngoˆn ngu˜.” trong Di.nh ly´ 3.3 la` thieˆ´t yeˆ´u.
4. KEˆ´T LUAˆ. N
Cho deˆ´n nay vieˆ.c nghieˆn cu´
.u CSDL vo´.i thoˆng tin mo`., khoˆng cha˘´c cha˘´n chu’ yeˆ´u du.. a treˆn
ca´ch tieˆ´p caˆ.n cu’a ly´ thuyeˆ´t taˆ.p mo`
. va` ly´ thuyeˆ´t kha’ na˘ng. DSGT cho ta moˆ. t ca´ch tieˆ´p caˆ.n
mo´.i deˆ´n vieˆ.c bieˆ’u die˜ˆn ngu˜
. ngh˜ıa cu’a ca´c kha´i nieˆ.m mo`
., no´ gia’ i quyeˆ´t ca´c moˆ´i quan heˆ. ngu˜
.
ngh˜ıa va` nhu. vaˆ.y no´ chu´
.a du.. ng ca´c thoˆng tin ngu˜
. ngh˜ıa o.’ mu´.c toˆ’ng theˆ’, mu´.c heˆ. thoˆ´ng ho
.n.
Vı` vaˆ.y, ma˘. c du` ca´c khoa’ng mo`
. bieˆ’u thi. laˆn caˆ.n ve`ˆ doˆ. tu
.o.ng tu.. co´ ve’ gioˆ´ng nhu
. ca´ch tieˆ´p
caˆ.n du
.
. a treˆn gia´ tri. khoa’ng, nhu
.ng ca´c laˆn caˆ.n trong ca´ch tieˆ´p caˆ.n DSGT khoˆng du
.o.. c phe´p
tu`y tieˆ.n ma` chu´ng pha’ i du
.o.. c xa´c di.nh du
.
. a treˆn ca´c tham soˆ´ doˆ. do t´ınh mo
.’ cu’a ngoˆn ngu˜..
Nho`. ca´c khoa’ng laˆn caˆ.n nhu
. vaˆ.y va` nho`
. 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 da˜ cho phe´p ta chuyeˆ’n ca´c thao ta´c du˜. lieˆ.u trong CSDL ngoˆn ngu˜
.
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 va` ga`ˆn gu˜i
ho.n so vo´.i ca´c ca´ch tieˆ´p caˆ.n kha´c.
Vo´.i u.u dieˆ’m nhu. vaˆ.y, vieˆ.c nghieˆn cu´
.u phu. thuoˆ. c ha`m mo`
. trong CSDL ngoˆn ngu˜., du.o.. c
go. i la` phu. thuoˆ.c ha`m tu
.o.ng tu.. , trong ngu˜
. ca’nh ca´c phu. thuoˆ.c kinh dieˆ’n da˜ gia’ i quyeˆ´t. Hieˆ.n
nay, vaˆ´n de`ˆ na`y vaˆ˜n co`n mo´.i me’ va` chu.a du.o.. c la`m ro˜. Do do´, trong ba`i ba´o na`y, ta´c gia’ da˜
la`m ro˜ ho.n moˆ´i quan heˆ. giu˜
.a phu. thuoˆ.c du˜
. lieˆ.u kinh dieˆ’n va` phu. thuoˆ.c mo`
., va` theo do´, moˆ. t
soˆ´ vaˆ´n de`ˆ na’y sinh vaˆ˜n co`n deˆ’ ngo’ :
• Trong pha.m vi nghieˆn cu´
.u cu’a ba`i ba´o na`y, gia’ thieˆ´t ra`˘ng hai taˆ.p J− va` Fκ la` ro`
.i nhau
va` co´ vai tro` hoa`n toa`n kha´c nhau, trong do´ moˆ. t phu. thuoˆ.c trong Fκ (chu´
. khoˆng pha’ i trong
FDB) khoˆng pha’ i la` phu. thuoˆ.c ha`m. Ve`ˆ tru
.
. c quan ta mong muoˆ´n J−
+ la` taˆ.p taˆ´t ca’ ca´c ra`ng
buoˆ.c phu. thuoˆ. c ha`m cu’a CSDL DB, va` nhu
. vaˆ.y vaˆ´n de`ˆ da˘.t ra la` lieˆ.u J−
+ = J−DB?
• Taˆ.p FDB thu
.
. c su
.
. lo´
.n ho.n taˆ.p F
+
κ va` neˆ´u caˆu tra’ lo`
.i cho caˆu ho’ i treˆn la` khoˆng du´ng
th`ı vaˆ´n de`ˆ t`ım moˆ.t heˆ. tieˆn de`ˆ da`ˆy du’ cho hai taˆ.p FDB va` J−DB vaˆ˜n co`n la` deˆ’ mo
.’ .
TA`I LIEˆ. U THAM KHA
’O
[1] T.K. Bhattacharjee and A.K. Mazumdar, Axiomatisation of fuzzy multivalued depen-
dencies in fuzzy relational data model, Fuzzy Sets and Systems 96 (1998) 343–352.
[2] D.A. Chiang, L.R. Chow, and N.C. Hsien, Fuzzy information in extended fuzzy relational
databases, Fuzzy Sets and Systems 92 (1997) 1–20.
[3] N.C. Ho, A model of relational databases with linguistic data of hedge algebras - based
semantics, Hoˆ. i tha’o quoˆ´c gia la`ˆn thu´
. ba ve`ˆ “Nghieˆn cu´.u pha´t trieˆ’n va` u´.ng du. ng CNTT
va` Truye`ˆn thoˆng” ICT.rda’2006, 20-21/05/2006.
PHU. THUOˆ. C DU˜
.
LIEˆ. U TRONG CO
.
SO
.’ DU˜
.
LIEˆ. U QUAN HEˆ. 177
[4] N.C. Ho, Fuzziness in structure of linguistic truth values: a foundation for development of
fuzzy reasoning, Proc. of Int. Symp. on Multiple-Valued Logic, Boston University, Boston,
Massachusetts, IEEE Computer Society Press, May 26-28, 1987 (325–335).
[5] N.C. Ho, Quantifying hedge algebras and interpolation methods in approximate reason-
ing, Proc. of the 5th Inter. Conf. on Fuzzy Information Processing, Beijing, March 1-4,
2003 (105–112).
[6] N.C. Ho, N.V. Long, Complete and linear hedge algebras, fuzziness measure of vague
concepts and linguistic hedges and application, (Best paper Award of the Conference),
AIP Conf. Proceed. on Computing Anticipatory Systems, CASYS’05, Liege, Belgium,
8-13 August 2005 (ed. Daniel M. Dubois, 331-339).
[7] N.C. Ho, N.V. Long, Fuzziness measure on complete hedge algebras and quantitative
semantics of terms in linear hedge algebras, Fuzzy Sets and Systems 158 (2007) 452–471.
[8] N.C. Ho, L.H. Chau, Quantitative semantics in hedge algebras and interpolation meth-
ods, Proc. of ICT, Hanoi (2003).
[9] N.C. Ho, H.V. Nam, Ordered structure-based semantics of linguistic terms of linguistic
variables and approximate reasoning, AIP Conf. Proceed. on Computing Anticipatory
Systems, CASYS’99, 3th Inter. Conf., 1999 (98–116).
[10] N.C. Ho, H.V. Nam, A theory of refinement structure of hedge algebras and its appli-
cation to linguistic-valued fuzzy logic. In D. Niwinski & M. Zawadowski (Eds), Logic,
Algebra and Computer ScienceVol. 46 (1999) (Banach Center Publications, Polish Sci-
entific Publishers - PSP).
[11] N.C. Ho, H.V. Nam, Towards an algebraic foundation for a zadeh fuzzy logic, Fuzzy Set
and System 129 (2002) 229–254.
[12] N.C. Ho, H.V. Nam, T.D. Khang, and L.H. Chau, Hedge Algebras, Linguistic- valued
Logic and their Application to Fuzzy Reasoning, Inter. J. of Uncertainty, Fuzziness and
Knowledge-Based System 7 (1999) 347–361.
[13] N.C. Ho and W. Wechler, Hedge algebras: An algebraic approach to structures of sets of
linguistic domains of linguistic truth variable, Fuzzy Sets and Systems 35 (1990) 281–293.
[14] N.C. Ho and W. Wechler, Extended hedge algebras and their application to fuzzy logic,
Fuzzy Sets and Systems 52 (1992) 259–281.
[15] N.C. Ho, Quantifying hedge algebras and interpolation methods in approximate reason-
ing, Proc. of the 5th Inter. Conf. on Fuzzy Information Processing, Beijing, March 1-4,
2003 (105–112).
[16] N.C. Ho, L.H. Chau, T.D. Khang, and H.V. Nam, Hedge algebras, linguistic- valued
logic and their application to fuzzy reasoning, International Journal of Uncertainty, Fuzzi-
ness and Knowledge-Based System 7 (1999) 347–361.
[17] S. Jyothi, M. Syam Babu, Multidependencies in fuzzy relational databases and lossless
join decomposition, Fuzzy Sets and Systems 88 (1997) 315–332.
[18] L. Di Lascio, A. Gisolfi, and V. Loia, A new model for linguistic modifiers, International
Journal of Approximate Reasoning 15 (1996) 25–47.
178 NGUYE˜ˆN VA˘N LONG
[19] L. Di Lascio and A. Gisolfi, Averaging linguistic truth values in fuzzy approximate rea-
soning, International Journal of Intelligent Systems 13 (1998) 301–318.
[20] Weip Yi Liu, A relational data model with fuzzy inheritance dependencies, Fuzzy Sets
ans Systems 89 (1997) 205–213.
[21] M. Umano and O. Freedom, A fuzzy database system, Fuzzy Information and Decision
Processes, North-Holland, Armsterdam, 1982 (339–347).
Nhaˆ. n ba`i nga`y 08 - 5 - 2007
Nhaˆ. n la. i sau su
.’ a nga`y 19 - 7 -2007