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

Ta.p ch´ı Tin ho. c va` Die`ˆu khieˆ’n ho. c, T.23, S.2 (2007), 164–178
PHU. THUOˆ. C DU˜
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LIEˆ. U TRONG CO
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SO
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LIEˆ. U QUAN HEˆ.
VO´
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I THOˆNG TIN NGOˆN NGU˜
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NGUYE˜ˆN VA˘N LONG
Khoa Coˆng ngheˆ. Thoˆng tin, Da. i ho. c Giao thoˆng Vaˆ. n ta’i Ha` Noˆ. i
Abstract. Relational databases with linguistic data based on hedge algebras - based semantics
were introduced and investigated in [3], in which the evaluation of queries containing linguistic data
was transformed into that of traditional queries. On this new viewpoint, in the present paper a
notion of “fuzzy” functional dependencies in these databases will be defined reasonably. These new
dependencies will be examined in the context of traditional functional dependencies, which play as
syntaxtical constraints of the databases under consideration. Relationship between these two kinds
of such dependencies will also be considered.
To´m ta˘´t. CSDL ngoˆn ngu˜. vo´.i ngu˜. ngh˜ıa du.. a treˆn ca´ch tieˆ´p caˆ.n da. i soˆ´ gia tu
.’ da˜ du.o.. c nghieˆn cu´
.u
trong [3], trong do´ vieˆ.c lu
.o.. ng gia´ ca´c truy vaˆ´n lieˆn quan deˆ´n thoˆng tin ngoˆn ngu˜
. du.o.. c du
.a ve`ˆ vieˆ.c
thao ta´c lu.o.. ng gia´ kinh dieˆ’n. Treˆn co
. so.’ do´, phu. thuoˆ.c ha`m mo`
. trong CSDL ngoˆn ngu˜. se˜ du.o.. c di.nh
ngh˜ıa va` nghieˆn cu´.u trong ngu˜. ca’nh vo´.i phu. thuoˆ.c ha`m kinh dieˆ’n va` co´ ra`ng buoˆ.c CSDL o
.’ mu´.c cu´
pha´p. Moˆ´i quan heˆ. giu˜
.a hai loa.i phu. thuoˆ.c na`y cu˜ng du
.o.. c xem xe´t.
1. MO
.’ DA`ˆU
Co. so.’ du˜. lieˆ.u (CSDL) quan heˆ. mo`
. da˜ du.o.. c nghieˆn cu´
.u pha´t trieˆ’n tu`. cuoˆ´i nhu˜.ng na˘m 70
theˆ’ ky’ XX va` tu`. do´ da˜ du.o.. c u´
.ng du. ng ([1, 2, 17, 21, 22]) deˆ’ gia’ i quyeˆ´t ca´c ba`i toa´n thu
.
. c tie˜ˆn
trong moˆi tru.`o.ng thoˆng tin mo`., khoˆng cha˘´c cha˘´n. Nhu˜.ng u´.ng du. ng heˆ. thoˆ´ng CSDL trong
thu.. c tie˜ˆn kinh teˆ´, xa˜ hoˆ. i thu
.`o.ng ga˘.p nhu˜
.ng thoˆng tin khoˆng cha˘´c cha˘´n nhu. vaˆ.y. Vı` vaˆ.y, vieˆ.c
nghieˆn cu´.u ca´c CSDL vo´.i thoˆng tin mo`., khoˆng cha˘´c cha˘´n, khoˆng ch´ınh xa´c se˜ co´ nhu˜.ng u´.ng
du. ng thieˆ´t thu
.
. c.
Su.. hieˆ.n dieˆ.n ca´c thoˆng tin mo`
., khoˆng cha˘´c cha˘´n trong CSDL, taˆ´t nhieˆn se˜ la`m thay doˆ’i
ca˘n ba’n vieˆ.c thao ta´c du˜
. lieˆ.u ca’ trong pha.m vi cu´ pha´p (thao ta´c treˆn ky´ hieˆ.u) va` trong pha.m
vi ngu˜. ngh˜ıa. Tuy nhieˆn, theo su.. hieˆ’u bieˆ´t cu’a ca´c ta´c gia’ ba`i ba´o na`y, khoˆng co´ nhie`ˆu ca´c
coˆng tr`ınh nghieˆn cu´.u de`ˆ caˆ.p deˆ´n nhu˜
.ng su.. kha´c bieˆ.t saˆu sa˘´c trong pha.m vi cu´ pha´p cu’a
CSDL mo`. so vo´.i CSDL kinh dieˆ’n. Pha`ˆn lo´.n ca´c nghieˆn cu´.u ca´c phu. thuoˆ.c du˜
. lieˆ.u (PTDL)
trong CSDL mo`. de`ˆu la` su.. mo
.’ roˆ.ng cu’a ca´c PTDL kinh dieˆ’n, ngh˜ıa la` ca´c PTDL do´ vaˆ˜n du´ng
khi ca´c du˜. lieˆ.u trong CSDL de`ˆu la` thu
.
. c. Trong nhu˜
.ng tru.`o.ng ho.. p nhu
. vaˆ.y, doˆ´i vo´
.i CSDL
mo`., chu´ng ta da˜ khoˆng mo.’ roˆ.ng du
.o.. c cu´ pha´p cu’a lo´
.p ca´c PTDL, va` do do´ khoˆng a’nh hu.o.’ ng
deˆ´n vieˆ.c thieˆ´t keˆ´ CSDL. Khi do´, ta chı’ mo
.’ roˆ.ng du
.o.. c ngu˜
. ngh˜ıa hay ca´c quan heˆ. ngu˜
. ngh˜ıa
cu’a ca´c du˜. lieˆ.u deˆ’ cho phe´p khai tha´c du˜
. lieˆ.u trong CSDL mo`
..
Nho`. nhu˜.ng u.u vieˆ.t cu’a caˆ´u tru´c da. i soˆ´ gia tu
.’ (DSGT) ([4–16, 18, 19]), trong [3] da˜ du.a ra
va` nghieˆn cu´.u CSDL mo`. du.. a treˆn ca´ch tieˆ´p caˆ.n cu’a da. i soˆ´ gia tu
.’ , trong do´ ngu˜. ngh˜ıa ngoˆn
PHU. THUOˆ. C DU˜
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ngu˜. du.o.. c lu
.o.. ng ho´a ba`˘ng ca´c a´nh xa. di.nh lu
.o.. ng cu’a DSGT. Theo ca´ch tieˆ´p caˆ.n na`y, gia´
tri. ngoˆn ngu˜
. la` du˜. lieˆ.u, khoˆng pha’ i la` nha˜n cu’a ca´c taˆ.p mo`
. bieˆ’u die˜ˆn ngu˜. ngh˜ıa cu’a gia´ tri.
ngoˆn ngu˜. va` u.u dieˆ’m co. ba’n cu’a no´ la` cho phe´p t`ım kieˆ´m, da´nh gia´ ngu˜. ngh˜ıa cu’a thoˆng tin
khoˆng cha˘´c cha˘´n chı’ ba`˘ng ca´c thao ta´c du˜. lieˆ.u kinh dieˆ’n thu
.`o.ng du`ng va` do do´ ba’o da’m t´ınh
thua`ˆn nhaˆ´t cu’a kieˆ’u du˜. lieˆ.u trong xu
.’ ly´ ngu˜. ngh˜ıa cu’a chu´ng. Die`ˆu na`y kha´c vo´.i CSDL mo`.
la` vu`.a pha’ i xu.’ ly´ ngu˜. ngh˜ıa kinh dieˆ’n, vu`.a pha’ i xu.’ ly´ ngu˜. ngh˜ıa du.o.. c bieˆ’u die˜ˆn du
.´o.i da.ng
ca´c taˆ.p mo`
. hay ha`m thuoˆ.c cu’a chu´ng. Theo ca´ch tieˆ´p caˆ.n cu’a DSGT, ngu˜
. ngh˜ıa ngoˆn ngu˜.
co´ theˆ’ bieˆ’u thi. ba`˘ng moˆ.t laˆn caˆ.n ca´c khoa’ng du
.o.. c xa´c di.nh bo
.’ i doˆ. do t´ınh mo`
. cu’a ca´c gia´
tri. ngoˆn ngu˜
. cu’a moˆ. t thuoˆ.c t´ınh vo´
.i vai tro` la` bieˆ´n ngoˆn ngu˜.. Vı´ du. , ngu˜
. ngh˜ıa cu’a gia´ tri.
ngoˆn ngu˜. (GTNNg) raˆ´t lo´.n cu’a thuoˆ.c t´ınh “Soˆ´ ba`i treˆn ta.p ch´ı nu
.´o.c ngoa`i” se˜ du.o.. c bieˆ’u thi.
ba`˘ng nhu˜.ng khoa’ng laˆn caˆ.n cu’a gia´ tri. da. i dieˆ.n cu’a GTNNg raˆ´t lo´
.n thoˆng qua a´nh xa. di.nh
lu.o.. ng cu’a DSGT cu’a thuoˆ. c t´ınh “Soˆ´ ba`i treˆn ta.p ch´ı nu
.´o.c ngoa`i”. Theo ngh˜ıa do´, trong [3]
da˜ su.’ du.ng thuaˆ. t ngu˜
. CSDL ngoˆn ngu˜. thay cho thuaˆ.t ngu˜
. CSDL mo`..
Ba`i ba´o na`y se˜ nghieˆn cu´.u ca´c PTDL mo`. trong CSDL ngoˆn ngu˜. treˆn ca’ hai kh´ıa ca.nh cu´
pha´p (syntax) va` ngu˜. ngh˜ıa (semantics). Ta se˜ thaˆ´y trong CSDL ngoˆn ngu˜. vu`.a toˆ`n ta. i ca´c
PTDL mo.’ roˆ.ng kinh dieˆ’n, vu`
.a toˆ`n ta. i nhu˜
.ng PTDL mo`., tu´.c la` khoˆng co´ su.. PTDL kinh dieˆ’n
du.o.. c bieˆ’u thi. ba`˘ng ca´c PTDL mo`
. na`y.
Tieˆ´p theo, nhu˜.ng kha´i nieˆ.m co
. ba’n ve`ˆ DSGT va` CSDL ngoˆn ngu˜. se˜ du.o.. c tr`ınh ba`y nga˘´n
go.n trong Mu. c 2, da˘.c bieˆ.t kha´i nieˆ.m ve`ˆ doˆ. tu
.o.ng tu.. giu˜
.a ca´c du˜. lieˆ.u cu’a thuoˆ.c t´ınh ngoˆn
ngu˜. se˜ du.o.. c de`ˆ caˆ.p la. i. Trong Mu. c 3, kha´i nieˆ.m phu. thuoˆ. c ha`m tu
.o.ng tu.. se˜ du
.o.. c di.nh ngh˜ıa
va` nghieˆn cu´.u. No´ se˜ la` moˆ. t su
.
. mo
.’ roˆ.ng raˆ´t ga`ˆn gu˜i vo´
.i phu. thuoˆ.c ha`m kinh dieˆ’n va` do vaˆ.y
chu´ng co´ theˆ’ du.o.. c nghieˆn cu´
.u trong moˆ´i lieˆn heˆ. cha˘.t che˜ vo´
.i nhau. Heˆ. tieˆn de`ˆ Armstrong va`
t´ınh da`ˆy du’ cu’a no´ vaˆ˜n co`n du´ng doˆ´i vo´.i lo´.p phu. thuoˆ.c mo´
.i va` do do´ vai tro` kha´c bieˆ.t cu’a
hai loa. i phu. thuoˆ.c du˜
. lieˆ.u na`y trong cu`ng moˆ. t CSDL ngoˆn ngu˜
. cu˜ng du.o.. c xem xe´t. Moˆ.t soˆ´
keˆ´t luaˆ.n va` ca´c vaˆ´n de`ˆ ngo’ du
.o.. c tr`ınh ba`y trong pha`ˆn keˆ´t luaˆ.n, Mu. c 4.
2. NHU˜
.
NG KHA´I NIEˆ.M CO
.
BA’N VE`ˆ DSGT VA` CSDL
VO´
.
I THOˆNG TIN NGOˆN NGU˜
.
2.1. Ve`ˆ da. i soˆ´ gia tu
.’ (DSGT)
Deˆ’ de˜ˆ theo do˜i phu.o.ng pha´p xu.’ ly´ ngu˜. ngh˜ıa ngoˆn ngu˜. theo ca´ch tieˆ´p caˆ.n DSGT, ta to´m
ta˘´t la. i moˆ.t soˆ´ kha´i nieˆ.m ve`ˆ a´nh xa. di.nh lu
.o.. ng va` ca´ch thu´
.c xa´c di.nh ca´c heˆ. laˆn caˆ.n ngu˜
.
ngh˜ıa di.nh lu
.o.. ng. Trong CSDL ngoˆn ngu˜
., ca´c thuoˆ.c t´ınh ngoˆn ngu˜
., ngoa`i ca´c gia´ tri. kinh
dieˆ’n chu´ng co´ theˆ’ co´ ca´c ky´ hieˆ.u gia´ tri. ngoˆn ngu˜
.. Vı` vaˆ.y, moˆ˜i thuoˆ.c t´ınh ngoˆn ngu˜
. se˜ du.o.. c
ga˘´n keˆ´t vo´.i moˆ. t DSGT.
Cho moˆ.t DSGT tuyeˆ´n t´ınh da`ˆy du’ AX = (X,G,H,σ,Φ,6), trong do´ Dom(X ) = X
la` mie`ˆn ca´c gia´ tri. ngoˆn ngu˜
. cu’a thuoˆ.c t´ınh ngoˆn ngu˜
. X du.o.. c sinh tu
.
. do tu`
. taˆ.p ca´c pha`ˆn
thu.’ sinh G = {1, c+,W , c−,0} ba`˘ng vieˆ.c ta´c doˆ.ng tu
.
. do ca´c phe´p toa´n moˆ.t ngoˆi (ca´c gia
tu.’ ) trong taˆ.p H ; σ va` φ la` hai phe´p t´ınh vo´
.i ngu˜. ngh˜ıa la` caˆ.n treˆn du´ng va` caˆ.n du
.´o.i
du´ng cu’a taˆ.p H (x), tu´
.c la` σx = supremumH (x) and φx = infimumH(x), trong do´ H (x)
la` taˆ.p ca´c pha`ˆn tu`
. sinh ra tu`. x, co`n quan heˆ. 6 la` quan heˆ. sa˘´p thu´
. tu.. tuyeˆ´n t´ınh treˆn
X ca’m sinh tu.’ ngu˜. ngh˜ıa cu’a ngoˆn ngu˜.. Vı´ du. , neˆ´u ta co´ thuoˆ.c t´ınh NumIP (Num-
ber of International Papers) la` “Soˆ´ ba`i ba´o da˘ng treˆn ta.p ch´ı quoˆ´c teˆ´”, th`ı Dom(NumIP) =
166 NGUYE˜ˆN VA˘N LONG
{large, small, verylarge,morelarge, possiblylarge, verysmall, possiblysmall, lesssmall, ...},
G = {1, large,W, small,0}, H = {very,more, possibly, little} va` 6 moˆ. t quan heˆ. thu´
. tu..
ca’m sinh tu`. ngu˜. ngh˜ıa cu’a ca´c tu`. trong Dom(NumIP), cha˘’ ng ha.n ta co´ verylarge >
large,morelarge > large, possiblylarge < large, littlelarge < large, ...
Du.. a treˆn caˆ´u tru´c cu’a DSGT, trong do´ quan heˆ. giu˜
.a ca´c pha`ˆn tu.’ la` quan heˆ. thu´
. tu.. ngu˜
.
ngh˜ıa, moˆ h`ınh toa´n ho.c cu’a t´ınh mo`
. va` doˆ. do t´ınh mo`
. cu’a ca´c kha´i nieˆ.m mo`
. da˜ du.o.. c di.nh
ngh˜ıa trong [6, 7].
Gia’ su.’ ca´c gia tu.’ trong taˆ.p H =H
− ∪H+, du.o.. c lieˆ. t keˆ nhu
. sau:
H+ = {h1, ..., hp} va` H
− = {h−1, ..., h−q}, vo´.i h1 < ... < hp va` h−1 < ... < h−q ,
trong do´ p, q > 1.
Cho fm : X → [0, 1] la` doˆ. do t´ınh mo`
. cu’a DSGT AX , ta co´ meˆ.nh de`ˆ sau.
Meˆ.nh de`ˆ 2.1. ([6, 7]) Doˆ. do t´ınh mo`
. fm va` doˆ. do t´ınh mo`
. cu’a gia tu.’ µ(h), ∀h ∈H, co´ ca´c
t´ınh chaˆ´t sau:
1) fm(hx) = µ(h)fm(x), ∀x ∈X
2) fm(c−) + fm(c+) = 1
3)
∑
−q i p, i6=0
fm(hic) = fm(c), trong do´ c ∈ {c−, c+}
4)
∑
−q i p, i6=0
fm(hix) = fm(x), x ∈X
5)
∑
{µ(hi) : −q 6 i 6 −1} = α va`,
∑
{µ(hi) : 1 6 i 6 p} = β, trong do´ α + β > 0 va`
α + β = 1.
O
.’ daˆy ma˘. c du` 3) la` tru
.`o.ng ho..p rieˆng cu’a 4), nhu
.ng vaˆ˜n du.o.. c vieˆ´t ra deˆ’ de˜ˆ h`ınh dung
vieˆ.c h`ınh tha`nh ca´c khoa’ng t´ınh mo`
. cu’a ca´c kha´i nieˆ.m mo`
..
Khoa’ng mo`. cu’a kha´i nieˆ.m mo`
.. Gia’ su.’ thuoˆ.c t´ınh (hay bieˆ´n ngoˆn ngu˜
.) X co´ mie`ˆn tham
chieˆ´u thu.. c la` khoa’ng [a, b]. Deˆ’ chuaˆ’n ho´a, nho`
. moˆ.t phe´p bieˆ´n doˆ’i tuyeˆ´n t´ınh, ta gia’ thieˆ´t
mo. i mie`ˆn nhu
. vaˆ.y de`ˆu la` khoa’ng [0, 1]. Vı` doˆ. do t´ınh mo`
. fm la` moˆ.t a´nh xa. X → [0, 1], neˆn
no´ go.. i y´ deˆ´n vieˆ.c bieˆ’u die˜ˆn ca´c gia´ tri. fm(x), x ∈ X , ba˘`ng ca´c khoa’ng con cu’a doa.n [0, 1]
va` du.o.. c go. i la` khoa’ng mo`
. cu’a kha´i nieˆ.m x. Nhu
. vaˆ.y, ca´c khoa’ng mo`
. la` moˆ. t bieˆ’u die˜ˆn di.nh
lu.o.. ng ca´c kha´i nieˆ.m mo`
. cu’a moˆ. t bieˆ´n ngoˆn ngu˜
.. Cho tru.´o.c fm, ca´c khoa’ng mo`. cu’a ca´c kha´i
nieˆ.m mo`
. trong X du.o.. c xaˆy du
.
. ng quy na.p theo doˆ. da`i cu’a x ∈X nhu
. sau:
- Khoa’ng mo`. cu’a hai kha´i nieˆ.m nguyeˆn thu’y c
− va` c+: Ro˜ ra`ng la` tu`. t´ınh chaˆ´t 2) ta co´
theˆ’ xaˆy du.. ng hai khoa’ng mo`
. =(c−) va` =(c+) cu’a hai kha´i nieˆ.m nguyeˆn thu’y c
− va` c+, vo´.i
|=(c−)| = fm(c−) va` |=(c+)| = fm(c+), trong do´ |=(x)| chı’ doˆ. da`i cu’a khoa’ng =(x), sao
cho va` chu´ng ta.o tha`nh moˆ. t phaˆn hoa.ch cu’a [0, 1] va` =(c
−), =(c+) doˆ`ng bieˆ´n vo´.i c−, c+, tu´.c
la` c− 6 c+ ke´o theo =(c−) 6 =(c+), o.’ daˆy =(c−) 6 =(c+) du.o.. c hieˆ’u la` vo´
.i ∀x ∈ =(c−) va`
∀y ∈ =(c+), ta co´ x 6 y.
- Khoa’ng mo`. cu’a x doˆ. da`i k > 1: Moˆ.t ca´ch quy na.p, ta gia’ su
.’ ra`˘ng vo´.i ∀x ∈ Xk−1 =
{x ∈ X : x co´ doˆ. da`i |x| = k−1}, ta da˜ xaˆy du
.
. ng du
.o.. c khoa’ng mo`
.=(x), vo´.i |((x)| = fm(x),
sao cho {=(x) : x ∈ X k−1} doˆ`ng bieˆ´n vo´.i thu´. tu.. treˆn taˆ.p Xk−1 va` ta.o tha`nh moˆ. t phaˆn
hoa.ch cu’a doa.n [0, 1]. Khi do´, treˆn moˆ˜i khoa’ng mo`
. =(x) cu’a x ∈ Xk−1, do t´ınh chaˆ´t 4), ta
co´ theˆ’ xaˆy du.. ng du
.o.. c ho. ca´c khoa’ng {=(hix) : q 6 i 6 p, i 6= 0, |=(hix)| = fm(hix)}
sao cho chu´ng la` moˆ.t phaˆn hoa.ch cu’a khoa’ng mo`
. =(x) va` doˆ`ng bieˆ´n vo´.i thu´. tu.. ca´c pha`ˆn tu
.’
{hix : q 6 i 6 p, i 6= 0}.
Co´ theˆ’ thaˆ´y ho. {=(hix) : q 6 i 6 p, i 6= 0, |=(hix)| = fm(hix) va` x ∈ Xk−1} = {=(y) :
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y ∈Xk va` |=(y)| = fm(y)} la` moˆ.t phaˆn hoa.ch cu’a [0, 1]. Ca´c khoa’ng na`y go. i la` ca´c khoa’ng
mo`. mu´.c k.
Nhu. vaˆ.y, co´ moˆ. t su
.
. lieˆn heˆ. cha˘.t che˜ giu˜
.a ngu˜. ngh˜ıa ngoˆn ngu˜. cu’a ca´c kha´i nieˆ.m mo`
. va`
ca´c khoa’ng mo`. trong doa.n [0, 1] nhu
. sau: (i) Moˆ˜i pha`ˆn tu.’ x ∈ X de`ˆu du.o.. c ga˘´n vo´
.i moˆ. t
khoa’ng mo`. =(x) co´ doˆ. da`i ch´ınh ba`˘ng doˆ. do t´ınh mo`
. cu’a x; (ii) Neˆ´u x′ la` haˆ.u toˆ´ cu’a x, tu´
.c
la` no´ la` xaˆu con beˆn tra´i cu`ng cu’a xaˆu x hay, no´i kha´c di, x′ sinh ra xaˆu x, th`ı =(x) ⊂ =(x′);
(iii) Neˆ´u x va` x′ co´ cu`ng doˆ. da`i va` x 6 x
′ th`ı =(x) 6 =(x′).
Daˆy la` nhu˜.ng t´ınh chaˆ´t raˆ´t quan tro.ng cu’a ca´c khoa’ng mo`
. du.o.. c di.nh ngh˜ıa du
.
. a treˆn caˆ´u
tru´c DSGT va` la` co. so.’ deˆ’ di.nh ngh˜ıa heˆ. laˆn caˆ.n ngu˜
. ngh˜ıa cu’a x da˜ du.o.. c di.nh ngh˜ıa trong
[3] va` se˜ du.o.. c tr`ınh ba`y to´m ta˘´t du
.´o.i daˆy.
Di.nh ngh˜ıa 2.1. A´nh xa. f : X → [0, 1] du
.o.. c go. i la` a´nh xa. di.nh lu
.o.. ng cu’a DSGT AX neˆ´u
no´ tho’a ma˜n ca´c die`ˆu kieˆ.n sau:
Q1) f la` a´nh xa. do
.n a´nh.
Q2) f ba’o toa`n quan heˆ. thu´
. tu.. ngu˜
. ngh˜ıa treˆn X , ngh˜ıa la` x < y ⇒ f(x) < f(y), va`
f(0) = 0, f(1) = 1.
Q3) f lieˆn tu. c theo ngh˜ıa vo´
.i ∀x ∈X, f(φx) = inf f(H(x)) va` f(σx) = sup f(H (x)).
Trong da. i soˆ´ gia tu
.’ , moˆ˜i pha`ˆn tu.’ x ∈X de`ˆu mang daˆ´u aˆm hay du.o.ng, du.o.. c go. i la` PN-daˆ´u
va` du.o.. c di.nh ngh˜ıa deˆ. quy nhu
. sau.
Di.nh ngh˜ıa 2.2. (Ha`m PN-daˆ´u Sgn) Sgn : X → {−1, 0, 1} la` ha`m daˆ´u du
.o.. c xa´c di.nh nhu
.
sau, o.’ daˆy h, h′ ∈H, va` c ∈ {c−, c+}
a) Sgn(c−) = −1, Sgn(c+) = +1.
b) Sgn(h′hx) = 0, neˆ´u h′hx = hx, ngu.o.. c la. i ta co´:
Sgn(h′hx) = −Sgn(hx), neˆ´u h′hx 6= hx va` h′ la` aˆm t´ınh doˆ´i vo´.i h
(hoa˘. c c, neˆ´u h = I va` x = c),
Sgn(h′hx) = +Sgn(hx), neˆ´u h′hx 6= hx va` h′ du.o.ng t´ınh doˆ´i vo´.i h
(hoa˘. c c, neˆ´u h = I va` x = c).
Y´ ngh˜ıa cu’a PN-daˆ´u theˆ’ hieˆ.n trong meˆ.nh de`ˆ du
.´o.i daˆy.
Meˆ.nh de`ˆ 2.2. Vo´
.i mo. i x ∈X, ∀h ∈ H, neˆ´u Sgn(hx) = +1 th`ı hx > x, neˆ´u Sgn(hx) = −1
th`ı hx < x va` neˆ´u Sgn(hx) = 0 th`ı hx = x.
Vo´.i ca´c t´ınh chaˆ´t cu’a t´ınh mo`. va` ha`m PN-daˆ´u, a´nh xa. ngu˜
. ngh˜ıa di.nh lu
.o.. ng cu’a DSGT
du.o.. c di.nh ngh˜ıa nhu
. sau.
Di.nh ngh˜ıa 2.3. Gia’ su
.’ AX = (X,G,H,σ,Φ,6) la` moˆ. t DSGT da`ˆy du’ , tuyeˆ´n t´ınh va` tu
.
.
do, fm(x) va` µ(h) tu.o.ng u´.ng la` ca´c doˆ. do t´ınh mo`
. cu’a ngoˆn ngu˜. va` cu’a gia tu.’ h tho’a ma˜n
ca´c t´ınh chaˆ´t trong Meˆ.nh de`ˆ 2.1. Khi do´, ta no´i ν la` a´nh xa. ca’m sinh bo
.’ i doˆ. do t´ınh mo`
. fm
cu’a ngoˆn ngu˜. neˆ´u no´ du.o.. c xa´c di.nh nhu
. sau:
1) ν(W ) = κ = fm(c−), ν(c−) = κ− αfm(c−) = βfm(c−), ν(c+) = κ+ αfm(c+).
2) ν(hjx) = ν(x) + Sgn(hjx){
j∑
i=Sgn(j)
µ(hi)fm(x)− ω(hjx)µ(hj)fm(x)} trong do´,
ω(hjx) =
1
2 [1+Sgn(hjx)Sgn(hphjx)(β−α)] ∈ {α, β}, vo´
.i mo. i j,−q 6 j 6 p va` j 6= 0.
3) ν(φc−) = 0, ν(σ(c−) = κ = ν(φc+), ν(σc+) = 1, va` vo´.i mo. i j,−q 6 j 6 p va` j 6= 0,
chu´ng ta co´:
168 NGUYE˜ˆN VA˘N LONG
ν(φhjx) = ν(x) + Sgn(hjx){
j−1∑
i=Sign(j)
µ(hi)fm(x)} va`
ν(σhjx) = ν(x) + Sgn(hjx){
j∑
i=Sign(j)
µ(hi)fm(x)}.
Thu´.c chaˆ´t cu’a a´nh xa. ν la`, vo´
.i mo. i x = hju, ν(x) ch´ınh la` dieˆ’m chia trong khoa’ng mo`
.
=(x) theo ty’ leˆ. α : β neˆ´u Sgn(hphju) = ... 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
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Nhaˆ. n ba`i nga`y 08 - 5 - 2007
Nhaˆ. n la. i sau su
.’ a nga`y 19 - 7 -2007