Phát hiện luật kết hợp mờ có độ hỗ trợ cực tiểu không giống nhau. pdf

Ta
.
p ch´ı Tin ho
.
c v`a Diˆe
`
u khiˆe
’
n ho
.
c, T.22, S.3 (2006), 244—256
PH
´
AT HI
ˆ
E
.
N LU
ˆ
A
.
T K
ˆ
E
´
T HO
.
.
P M
`
O

.
C
´
O
D
ˆ
O
.
H
ˆ
O
˜
TRO
.
.
CU
.
.
C TI
ˆ
E
’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU
D

ˆ
O
˜
V
˘
AN TH
`
ANH
Bˆo
.
Kˆe
´
hoa
.
ch v`a Dˆa
`
u tu
.
Abstract. Mining Association Rules from transaction databases with unequal minimum supports
is a problem proposed and reseached by the author [3]. The algorithm for mining closed frequent
itemsets with unequal minimum supports of each item in transaction databases was called CHARM-
NEW. This algorithm was indeed improved and developed from the CHARM which is one of the
most efficient algorithms for mining closed frequent itemsets with the same minimum support from
transaction databases.
The goal of this paper is to propose and to find out measures for mining fuzzy association
rules from quantitative databases with unequal minimum supports. The paper will concentrate on
developing an algorithm for mining closed fuzzy frequent itemsets with unequal minimum supports
of each attribute in quantitative databases.
T´om t˘a
´

t. Ph´at hiˆe
.
n luˆa
.
t kˆe
´
t ho
.
.
p t`u
.
c´ac co
.
so
.
’
d˜u
.
liˆe
.
u t´ac vu
.
v´o
.
i
dˆo
.
hˆo
˜
tro

.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng
nhau l`a vˆa
´
n
dˆe
`
du
.
o
.
.
c t´ac gia
’
dˆe
`
xuˆa
´
t v`a nghiˆen c´u
.
u ([3]). Thuˆa
.

t to´an ph´at hiˆe
.
n c´ac tˆa
.
p phˆo
’
biˆe
´
n
d´ong v´o
.
i
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng nhau cu
’
a mˆo
˜

i tˆa
.
p mu
.
c d˜u
.
liˆe
.
u trong c´ac co
.
so
.
’
d˜u
.
liˆe
.
u t´ac
vu
.
du
.
o
.
.
c go
.
i l`a CHARM-NEW. Thˆa
.
t ra thuˆa

.
t to´an n`ay
du
.
o
.
.
c ca
’
i tiˆe
´
n v`a ph´at triˆe
’
n t`u
.
thuˆa
.
t to´an
CHARM,
d´o l`a mˆo
.
t trong nh˜u
.
ng thuˆa
.
t to´an hiˆe
.
u qua
’
nhˆa

´
t
dˆe
’
t`ım tˆa
.
p phˆo
’
biˆe
´
n d´ong v´o
.
i
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u nhu
.
nhau t`u
.
c´ac co

.
so
.
’
d˜u
.
liˆe
.
u t´ac vu
.
.
Mu
.
c
d´ıch cu
’
a b`ai b´ao n`ay l`a dˆe
`
xuˆa
´
t v`a t`ım kiˆe
´
m gia
’
i ph´ap dˆe
’
ph´at hiˆe
.
n c´ac luˆa
.

t kˆe
´
t ho
.
.
p m`o
.
t`u
.
c´ac co
.
so
.
’
d˜u
.
liˆe
.
u
di
.
nh lu
.
o
.
.
ng v´o
.
i
dˆo

.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng nhau. B`ai b´ao s˜e tˆa
.
p trung ph´at
triˆe
’
n thuˆa
.
t to´an ph´at hiˆe
.
n tˆa
.
p phˆo
’
biˆe
´
n m`o
.

d´ong v´o
.
i
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng nhau cu
’
a mˆo
˜
i
tˆa
.
p mu
.
c d˜u
.
liˆe
.

u trong c´ac co
.
so
.
’
d˜u
.
liˆe
.
u
di
.
nh lu
.
o
.
.
ng.
1. GI
´
O
.
I THI
ˆ
E
.
U
Qu´a tr`ınh ph´at hiˆe
.
n luˆa

.
t kˆe
´
t ho
.
.
p
du
.
o
.
.
c chia th`anh hai giai
doa
.
n. Mu
.
c d´ıch cu
’
a giai doa
.
n
dˆa
`
u l`a t`ım c´ac tˆa
.
p phˆo
’
biˆe
´

n c´o dˆo
.
hˆo
˜
tro
.
.
l´o
.
n ho
.
n ho˘a
.
c b˘a
`
ng mˆo
.
t gi´a tri
.
chung n`ao
d´o (go
.
i l`a
dˆo
.
hˆo
˜
tro
.
.

cu
.
.
c tiˆe
’
u, k´y hiˆe
.
u l`a minSupp), c`on cu
’
a giai
doa
.
n 2 l`a t`ım c´ac luˆa
.
t kˆe
´
t ho
.
.
p t`u
.
c´ac
tˆa
.
p t`ım
du
.
o
.
.

c o
.
’
giai
doa
.
n 1 v`a c´o dˆo
.
tin cˆa
.
y l´o
.
n ho
.
n ho˘a
.
c b˘a
`
ng mˆo
.
t gi´a tri
.
chung kh´ac (go
.
i
l`a
dˆo
.
tin cˆa
.

y cu
.
.
c tiˆe
’
u, k´y hiˆe
.
u minConf). Trong qu´a tr`ınh
d´o, giai doa
.
n t`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n
l`a ph´u
.
c ta
.
p v`a tˆo
´
n nhiˆe
`
u chi ph´ı nhˆa
´
t.
Nh˜u
.

ng n˘am qua ngu
.
`o
.
i ta
d˜a tˆa
.
p trung nghiˆen c´u
.
u v`a
dˆe
`
xuˆa
´
t du
.
o
.
.
c nhiˆe
`
u thuˆa
.
t to´an t`ım
tˆa
.
p phˆo
’
biˆe
´

n hiˆe
.
u qua
’
t`u
.
c´ac co
.
so
.
’
d˜u
.
liˆe
.
u (CSDL) t´ac vu
.
(hay nhi
.
phˆan) theo nhiˆe
`
u c´ach
tiˆe
´
p cˆa
.
n kh´ac nhau [1, 9, 15]. Nh˜u
.
ng thuˆa
.

t to´an m´o
.
i v`a hiˆe
.
u qua
’
nhˆa
´
t vˆe
`
vˆa
´
n
dˆe
`
d´o cho dˆe
´
n
nay l`a nh˜u
.
ng thuˆa
.
t to´an chı
’
cˆa
`
n t`ım c´ac tˆa
.
p phˆo
’

biˆe
´
n
d´ong [3, 9, 14, 15] nh`o
.
ch´u
.
ng minh
du
.
o
.
.
c
LU
ˆ
A
.
T K
ˆ
E
´
T HO
.
.
P M
`
O
.
C

´
O
D
ˆ
O
.
H
ˆ
O
˜
TRO
.
.
CU
.
.
C TI
ˆ
E
’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU
245
r˘a
`

ng c´ac luˆa
.
t kˆe
´
t ho
.
.
p
du
.
o
.
.
c sinh ra t`u
.
c´ac tˆa
.
p phˆo
’
biˆe
´
n
d´ong v`a t`u
.
c´ac tˆa
.
p phˆo
’
biˆe
´

n l`a nhu
.
nhau, trong khi khˆong gian c´ac tˆa
.
p phˆo
’
biˆe
´
n
d´ong l`a nho
’
ho
.
n rˆa
´
t nhiˆe
`
u so v´o
.
i khˆong gian c´ac
tˆa
.
p phˆo
’
biˆe
´
n.
Tuy nhiˆen c´ac thuˆa
.
t to´an trˆen

dˆe
`
u du
.
o
.
.
c xˆay du
.
.
ng du
.
.
a trˆen th`u
.
a nhˆa
.
n minSupp cu
’
a c´ac
tˆa
.
p phˆo
’
biˆe
´
n l`a nhu
.
nhau. Mˆo
.

t sˆo
´
ha
.
n chˆe
´
cu
’
a luˆa
.
t kˆe
´
t ho
.
.
p
du
.
o
.
.
c t`ım t`u
.
c´ac tˆa
.
p phˆo
’
biˆe
´
n c´o

dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u nhu
.
nhau
d˜a du
.
o
.
.
c chı
’
ra trong [2—8, 11—13]. Hiˆe
.
n c´o bˆo
´
n c´ach tiˆe
´
p cˆa
.

n
dˆe
’
kh˘a
´
c phu
.
c nh˜u
.
ng ha
.
n chˆe
´
cu
’
a viˆe
.
c t`ım tˆa
.
p phˆo
’
biˆe
´
n c´o
dˆo
.
hˆo
˜
tro
.

.
cu
.
.
c tiˆe
’
u chung giˆo
´
ng nhau
[2—8, 11—13].
Th´u
.
nhˆa
´
t l`a: t`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n trong mˆo
´
i quan hˆe
.
c´o su
.
.
r`ang buˆo
.
c vˆe

`
dˆo
.
hˆo
˜
tro
.
.
([11, 12])
b˘a
`
ng c´ach
dˆe
`
xuˆa
´
t mˆo h`ınh biˆe
’
u diˆe
˜
n r`ang buˆo
.
c dˆo
.
hˆo
˜
tro
.
.
cu

’
a c´ac tˆa
.
p mu
.
c d˜u
.
liˆe
.
u (go
.
i l`a
c´ach tiˆe
´
p cˆa
.
n r`ang buˆo
.
c
dˆo
.
hˆo
˜
tro
.
.
). C´ach tiˆe
´
p cˆa
.

n n`ay c´o nhu
.
o
.
.
c
diˆe
’
m l`a ta
.
o ra nhiˆe
`
u ph´u
.
c
ta
.
p v´o
.
i ngu
.
`o
.
i su
.
’
du
.
ng,
d´o l`a d`oi ho

’
i ho
.
pha
’
i c´o kiˆe
´
n th´u
.
c co
.
so
.
’
nhˆa
´
t
di
.
nh trong l˜ınh vu
.
.
c ´u
.
ng
du
.
ng ([3]).
Th´u
.

hai l`a: g˘a
´
n tro
.
ng sˆo
´
v`ao mˆo
˜
i mu
.
c d˜u
.
liˆe
.
u
dˆe
’
do vai tr`o quan tro
.
ng cu
’
a n´o v`a ´ap du
.
ng
c´o ca
’
i tiˆe
´
n mˆo
.

t trong c´ac thuˆa
.
t to´an t`ım tˆa
.
p phˆo
’
biˆe
´
n
d˜a c´o dˆe
’
t`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n c´o g˘a
´
n
tro
.
ng sˆo
´
[2, 13] (go
.
i l`a c´ach tiˆe
´
p cˆa
.

n tro
.
ng sˆo
´
). Nhu
.
o
.
.
c
diˆe
’
m l´o
.
n nhˆa
´
t cu
’
a c´ach tiˆe
´
p cˆa
.
n n`ay l`a
khˆong
da
’
m ba
’
o du
.

o
.
.
c t´ınh chˆa
´
t tˆa
.
p con cu
’
a tˆa
.
p phˆo
’
biˆe
´
n l`a tˆa
.
p phˆo
’
biˆe
´
n ([1]) m`a trong nhiˆe
`
u
tru
.
`o
.
ng ho
.

.
p ´u
.
ng du
.
ng, t´ınh chˆa
´
t n`ay gˆa
`
n nhu
.
l`a mˆo
.
t
d`oi ho
’
i tˆa
´
t nhiˆen, ch˘a
’
ng ha
.
n trong l˜ınh
vu
.
.
c thu
.
o
.

ng ma
.
i, nˆe
´
u mˆo
.
t nh´om m˘a
.
t h`ang
d˜a du
.
o
.
.
c nhiˆe
`
u ngu
.
`o
.
i mua th`ı mˆo
.
t sˆo
´
m˘a
.
t h`ang
thuˆo
.
c nh´om

d´o c˜ung pha
’
i du
.
o
.
.
c xem l`a nhu
.
vˆa
.
y.
Th´u
.
ba l`a: t`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n theo
dˆo
.
hˆo
˜
tro
.
.
cu
.

.
c tiˆe
’
u kh´ac nhau tu`y thuˆo
.
c v`ao t`u
.
ng m´u
.
c
kh´ai niˆe
.
m cu
’
a c´ac tˆa
.
p mu
.
c d˜u
.
liˆe
.
u ([5, 8]) (go
.
i l`a c´ach tiˆe
´
p cˆa
.
n nhiˆe
`

u m´u
.
c ho˘a
.
c phˆan bˆa
.
c).
C´ach tiˆe
´
p cˆa
.
n n`ay kh´a th´ıch ho
.
.
p v´o
.
i nh˜u
.
ng thuˆa
.
t to´an t`ım tˆa
.
p phˆo
’
biˆe
´
n theo chiˆe
`
u rˆo
.

ng
cu
’
a
dˆo
`
thi
.
biˆe
’
u diˆe
˜
n khˆong gian t`ım kiˆe
´
m cu
’
a c´ac tˆa
.
p mu
.
c d˜u
.
liˆe
.
u theo kiˆe
’
u nhu
.
thuˆa
.

t to´an
Apriori [1, 2],
d´o l`a nh˜u
.
ng thuˆa
.
t to´an t`ım
k
- tˆa
.
p phˆo
’
biˆe
´
n b˘a
`
ng c´ach kˆe
´
t nˆo
´
i 2 tˆa
.
p
(k − 1)
-
tˆa
.
p phˆo
’
biˆe

´
n o
.
’
m´u
.
c trˆen
d´o. C´ach tiˆe
´
p cˆa
.
n n`ay c´o nhu
.
o
.
.
c
diˆe
’
m ch´ınh, kh´o vu
.
o
.
.
t qua, l`a b˘a
`
ng
c´ach n`ao
dˆe
’

x´ac di
.
nh du
.
o
.
.
c mˆo
.
t c´ach ho
.
.
p l´y
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cho t`u
.
ng m´u
.
c.

Th´u
.
tu
.
l`a: c´ach tiˆe
´
p cˆa
.
n
du
.
o
.
.
c
dˆe
`
xuˆa
´
t trong [3] (go
.
i l`a c´ach tiˆe
´
p cˆa
.
n dˆo
.
hˆo
˜
tro

.
.
). O
.
’
d´o vai tr`o
quan tro
.
ng cu
’
a c´ac tˆa
.
p mu
.
c d˜u
.
liˆe
.
u
du
.
o
.
.
c
do b˘a
`
ng dˆo
.
hˆo

˜
tro
.
.
cu
.
.
c tiˆe
’
u, xem c´ac tˆa
.
p mu
.
c d˜u
.
liˆe
.
u kh´ac nhau l`a c´o
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’

u kh´ac nhau. C´ac c´ach tiˆe
´
p cˆa
.
n
dˆo
.
hˆo
˜
tro
.
.
v`a theo tro
.
ng
sˆo
´
du
.
o
.
.
c
dˆe
`
xuˆa
´
t trong [2, 13] c´o ve
’
giˆo

´
ng nhau v`ı tru
.
´o
.
c tiˆen ch´ung c`ung
do tˆa
`
m quan tro
.
ng
cu
’
a mu
.
c d˜u
.
liˆe
.
u b˘a
`
ng
dˆo
.
hˆo
˜
tro
.
.
cu

.
.
c tiˆe
’
u ho˘a
.
c b˘a
`
ng tro
.
ng sˆo
´
nhu
.
ng vˆe
`
ba
’
n chˆa
´
t ch´ung kh´ac
nhau do theo c´ach tiˆe
´
p cˆa
.
n
dˆo
.
hˆo
˜

tro
.
.
th`ı c´ac tˆa
.
p phˆo
’
biˆe
´
n
du
.
o
.
.
c t`ım theo
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u
khˆong giˆo

´
ng nhau
dˆo
´
i v´o
.
i mˆo
˜
i tˆa
.
p mu
.
c d˜u
.
liˆe
.
u v`a quan tro
.
ng ho
.
n l`a t´ınh chˆa
´
t Apriori cu
’
a c´ac
tˆa
.
p phˆo
’
biˆe

´
n nhu
.
tˆa
.
p con cu
’
a tˆa
.
p phˆo
’
biˆe
´
n l`a tˆa
.
p phˆo
’
biˆe
´
n
d˜a du
.
o
.
.
c ba
’
o to`an do
d´o qu´a tr`ınh
t`ım tˆa

.
p phˆo
’
biˆe
´
n s˜e
du
.
o
.
.
c thu
.
.
c hiˆe
.
n hiˆe
.
u qua
’
ho
.
n nhiˆe
`
u. Trong [3]
d˜a dˆe
`
xuˆa
´
t thuˆa

.
t to´an
CHARM-NEW trˆen co
.
so
.
’
ca
’
i tiˆe
´
n thuˆa
.
t to´an CHARM [15]
dˆe
’
t`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n d´ong cu
.
.
c
da
.
i t`u
.

co
.
so
.
’
d˜u
.
liˆe
.
u t´ac vu
.
(hay nhi
.
phˆan) v´o
.
i
diˆe
`
u kiˆe
.
n vˆe
`
dˆo
.
hˆo
˜
tro
.
.
cu

.
.
c tiˆe
’
u nhu
.
vˆa
.
y.
Thu
.
.
c tˆe
´
viˆe
.
c ph´at hiˆe
.
n c´ac luˆa
.
t kˆe
´
t ho
.
.
p thu
.
.
c su
.

.
tro
.
’
nˆen c´o ´y ngh˜ıa ´u
.
ng du
.
ng to l´o
.
n khi
gia
’
i quyˆe
´
t
du
.
o
.
.
c vˆa
´
n
dˆe
`
ph´at hiˆe
.
n luˆa
.

t kˆe
´
t ho
.
.
p t`u
.
c´ac CSDL
di
.
nh lu
.
o
.
.
ng ([10])
Dˆe
’
gia
’
i quyˆe
´
t
vˆa
´
n
dˆe
`
v`u
.

a nˆeu ngu
.
`o
.
i ta
d˜a dˆe
`
xuˆa
´
t ´u
.
ng du
.
ng l´y thuyˆe
´
t tˆa
.
p m`o
.
dˆe
’
chuyˆe
’
n dˆo
’
i CSDL di
.
nh
lu
.

o
.
.
ng th`anh CSDL m´o
.
i (ta
.
m go
.
i l`a CSDL “m`o
.
”), v`a t`u
.
d´o vˆa
´
n dˆe
`
ph´at hiˆe
.
n luˆa
.
t kˆe
´
t ho
.
.
p
246
D
ˆ

O
˜
V
˘
AN TH
`
ANH
m`o
.
du
.
o
.
.
c ra
d`o
.
i ([2, 4). Vˆa
´
n
dˆe
`
n`ay dang du
.
o
.
.
c quan tˆam nghiˆen c´u
.
u, ph´at triˆe

’
n ma
.
nh.
B`ai b´ao tˆa
.
p trung ph´at triˆe
’
n mˆo
.
t sˆo
´
kh´ai niˆe
.
m liˆen quan
dˆe
´
n luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
, thuˆa
.
t to´an
tˆo

’
ng qu´at ph´at hiˆe
.
n luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
,
d˘a
.
c biˆe
.
t l`a thuˆa
.
t to´an t`ım tˆa
.
p phˆo
’
biˆe
´
n m`o
.
d´ong cu
.
.

c
da
.
i v´o
.
i c´ac tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
c´o
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´

ng nhau.
Phˆa
`
n c`on la
.
i cu
’
a b`ai b´ao
du
.
o
.
.
c cˆa
´
u tr´uc nhu
.
sau: Mu
.
c 2 s˜e cung cˆa
´
p mˆo
.
t sˆo
´
kh´ai niˆe
.
m
co
.

ba
’
n tˆo
´
i thiˆe
’
u cˆa
`
n thiˆe
´
t c´o t´ınh chˆa
´
t chuˆa
’
n bi
.
dˆe
’
gia
’
i quyˆe
´
t vˆa
´
n dˆe
`
do b`ai b´ao d˘a
.
t ra. C´ac
kh´ai niˆe

.
m
d´o mˆo
.
t sˆo
´
du
.
o
.
.
c
dˆe
`
xuˆa
´
t m´o
.
i, mˆo
.
t sˆo
´
l`a kˆe
´
th`u
.
a ho˘a
.
c
du

.
o
.
.
c ph´at triˆe
’
n tiˆe
´
p t`u
.
c´ac
kh´ai niˆe
.
m tu
.
o
.
ng tu
.
.
cu
’
a mˆo
.
t sˆo
´
nghiˆen c´u
.
u tru
.

´o
.
c
d´o. Mu
.
c 3 s˜e tr`ınh b`ay nh˜u
.
ng vˆa
´
n
dˆe
`
then
chˆo
´
t nhˆa
´
t cu
’
a thuˆa
.
t to´an ph´at hiˆe
.
n luˆa
.
t kˆe
´
t ho
.
.

p m`o
.
c´o
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng nhau.
Mu
.
c 4 v`a Mu
.
c 5 gi´o
.
i thiˆe
.
u mˆo
.
t sˆo
´

v´ı du
.
minh ho
.
a, mˆo
.
t sˆo
´
kˆe
´
t luˆa
.
n v`a hu
.
´o
.
ng nghiˆen c´u
.
u tiˆe
´
p
theo cu
’
a b`ai b´ao.
2. KI
ˆ
E
´
N TH
´

U
.
C CHU
ˆ
A
’
N BI
.
K´y hiˆe
.
u
I
I
I = {i
1
, i
2
, , i
m
}
l`a tˆa
.
p c´ac mu
.
c d˜u
.
liˆe
.
u
di

.
nh lu
.
o
.
.
ng, l`a mu
.
c d˜u
.
liˆe
.
u sˆo
´
ho˘a
.
c
mu
.
c d˜u
.
liˆe
.
u phˆan loa
.
i; tˆa
.
p
X ⊂ I
I

I
du
.
o
.
.
c go
.
i l`a tˆa
.
p thuˆo
.
c t´ınh;
O
O
O = {t
1
, t
2
, , t
m
}
l`a tˆa
.
p di
.
nh
danh cu
’
a c´ac t´ac vu

.
. Quan hˆe
.
nhi
.
phˆan
D
D
D ⊂ I
I
I × O
O
O
du
.
o
.
.
c go
.
i l`a co
.
so
.
’
d˜u
.
liˆe
.
u

di
.
nh lu
.
o
.
.
ng.
Gia
’
su
.
’
mˆo
˜
i mu
.
c d˜u
.
liˆe
.
u
i
k
(k = 1, , m)
c´o mˆo
.
t sˆo
´
tˆa

.
p m`o
.
tu
.
o
.
ng ´u
.
ng v´o
.
i n´o. K´y hiˆe
.
u
F
i
k
= {χ
1
i
k
, χ
2
i
k
, , χ
h
i
k
}

l`a tˆa
.
p c´ac tˆa
.
p m`o
.
tu
.
o
.
ng ´u
.
ng v´o
.
i mu
.
c d˜u
.
liˆe
.
u
i
k
v`a
χ
j
i
k
l`a tˆa
.

p m`o
.
th´u
.
j
trong
F
i
k
([2, 3, 4, 7]).
Mˆo
.
t luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
c´o da
.
ng
r = X ∈ A → Y ∈ B
(c`on c´o thˆe
’
du
.
o

.
.
c diˆe
˜
n gia
’
i:
X
l`a
A → Y
l`a
B
) v´o
.
i
X = {x
1
, x
2
, , x
p
}, Y = {y
1
, y
2
, , y
q
}
l`a c´ac tˆa
.

p thuˆo
.
c t´ınh,
X ∩ Y = ∅;
A = {χ
x
1
, χ
x
2
, , χ
x
p
}, B = {χ
y
1
, χ
y
2
, , χ
y
q
}
l`a tˆa
.
p c´ac tˆa
.
p m`o
.
liˆen kˆe

´
t v´o
.
i c´ac mu
.
c d˜u
.
liˆe
.
u
trong tˆa
.
p
X
v`a
Y
tu
.
o
.
ng ´u
.
ng, ch˘a
’
ng ha
.
n mu
.
c d˜u
.

liˆe
.
u
x
k
trong
X
s˜e c´o tˆa
.
p m`o
.
χ
x
k
trong
A
([2, 3, 4, 7]). C˘a
.
p
X, A
v´o
.
i
X
l`a tˆa
.
p thuˆo
.
c t´ınh,
A

l`a tˆa
.
p gˆo
`
m mˆo
.
t sˆo
´
tˆa
.
p m`o
.
n`ao
d´o tu
.
o
.
ng
´u
.
ng liˆen kˆe
´
t v´o
.
i c´ac mu
.
c d˜u
.
liˆe
.

u trong
X
du
.
o
.
.
c go
.
i l`a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
.
X, A
du
.
o
.
.
c go
.
i
l`a

k
tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
nˆe
´
u tˆa
.
p
X
ch´u
.
a
k
thuˆo
.
c t´ınh.
Gia
’
su
.
’
{minSupi

1
, minSupi
2
, , minSupi
m
/minSupi
j
∈ [0, 1]}
v´o
.
i mo
.
i
j = 1, , m
l`a tˆa
.
p
c´ac
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’

u cu
’
a c´ac mu
.
c d˜u
.
liˆe
.
u trong
I
I
I = {i
1
, i
2
, , i
m
}
tu
.
o
.
ng ´u
.
ng, n´oi c´ach kh´ac
minSupi
j
du
.
o

.
.
c go
.
i l`a
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a thuˆo
.
c t´ınh
i
j
.
Di
.
nh ngh˜ıa 1. [3] Dˆo
.
hˆo

˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u
X
k´y hiˆe
.
u l`a
minSupX =
max{minSupi
j
}
v´o
.

i mo
.
i mu
.
c d˜u
.
liˆe
.
u
i
j
∈ X
.
Ta dˆe
˜
d`ang thˆa
´
y nˆe
´
u
X ⊇ Y
th`ı
minSupX  minSupY.
Di
.
nh ngh˜ıa 2. [2, 4] Dˆo
.
hˆo
˜
tro

.
.
cu
’
a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
X, A
dˆo
´
i v´o
.
i co
.
so
.
’
d˜u
.
liˆe
.
u
D

D
D
k´y
hiˆe
.
u l`a
SupX, A
du
.
o
.
.
c x´ac
di
.
nh nhu
.
sau:
SupX, A =

t
i
∈O
Π
x
j
∈X
{

χx

j
(t
i
[x
j
])}
O
O
O
trong d´o,

χx
j
(t
i
[x
j
]) =

m
χx
j
(t
i
[x
j
]) nˆe
´
u m
χx

j
 ω
j
0 nˆe
´
u ngu
.
o
.
.
c la
.
i
χ
x
j
∈ A,Π
Π
Π
l`a to´an tu
.
’
nhˆan (tˆo
’
ng qu´at
Π
Π
Π
c´o thˆe
’

l`a ho´an tu
.
’
T
-norm)
t
i
[x
j
]
l`a gi´a tri
.
cu
’
a mu
.
c
LU
ˆ
A
.
T K
ˆ
E
´
T HO
.
.
P M
`

O
.
C
´
O
D
ˆ
O
.
H
ˆ
O
˜
TRO
.
.
CU
.
.
C TI
ˆ
E
’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU

247
d˜u
.
liˆe
.
u
x
j
trong t´ac vu
.
(hay di
.
nh danh) th´u
.
i
l`a
t
i
, cu
’
a
O
O
O
,
m
χx
j
l`a h`am th`anh viˆen cu
’

a tˆa
.
p
m`o
.
χ
x
j
liˆen kˆe
´
t v´o
.
i mu
.
c d˜u
.
liˆe
.
u
x
j
tu
.
o
.
ng ´u
.
ng,
ω
j

∈ [0, 1]
du
.
o
.
.
c go
.
i l`a ngu
.
˜o
.
ng cu
.
.
c tiˆe
’
u cu
’
a
tˆa
.
p m`o
.
χ
x
j
.
Dˆo
.

hˆo
˜
tro
.
.
cu
’
a luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
X ∈ A → Y ∈ B
l`a
SupZ, C
v´o
.
i
Z = {X, Y }, C = {A, B}
v`a dˆo
.
tin cˆa
.
y cu
’
a luˆa

.
t d´o k´y hiˆe
.
u l`a
ConfZ, C
du
.
o
.
.
c x´ac
di
.
nh bo
.
’
i
ConfZ, C = SupZ, C/SupX, A
Di
.
nh ngh˜ıa 3. Tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.

Y, B
du
.
o
.
.
c go
.
i l`a tˆa
.
p con cu
’
a
X, A
nˆe
´
u
Y ⊆ X
v`a
B ⊆ A.
Di
.
nh ngh˜ıa 4. Dˆo
.
hˆo
˜
tro
.
.
cu

.
.
c tiˆe
’
u cu
’
a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
X, A
, k´ı hiˆe
.
u
minSupX, A =
minSupX.
Tˆa
.
p
X, A
du
.
o
.

.
c go
.
i l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
nˆe
´
u
SupX, A  minSupX, A
; tˆa
.
p
X, A
du
.
o
.
.
c go
.
i l`a tˆa
.
p phˆo
’

biˆe
´
n m`o
.
cu
.
.
c
da
.
i nˆe
´
u n´o l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
v`a khˆong tˆo
`
n ta
.
i bˆa
´
t
k`y tˆa
.
p phˆo

’
biˆe
´
n m`o
.
Y, B
n`ao ch´u
.
a n´o nhu
.
l`a mˆo
.
t tˆa
.
p con thu
.
.
c su
.
.
.
T´ınh chˆa
´
t 1. Tˆa
.
p phˆo
’
biˆe
´
n m`o

.
c´o t´ınh chˆa
´
t Apriori, t´u
.
c l`a nˆe
´
u
X, A
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
v`a
Y, B
l`a tˆa
.
p con cu
’
a
X, A
th`ı
Y, B
c˜ung l`a tˆa
.
p phˆo

’
biˆe
´
n m`o
.
.
Ch´u
.
ng minh: Du
.
.
a v`ao nhˆa
.
n x´et r˘a
`
ng do
Y ⊆ X
v`a
B ⊆ A
nˆen

t
i
∈O
Π
y
j
∈Y
{


χx
j
(t
i
[y
j
])} 

t
i
Π
x
j
∈X
{

χx
j
(t
i
[x
j
])},
ta dˆe
˜
d`ang nhˆa
.
n du
.
o

.
.
c:
SupY, B  SupX, A.
M˘a
.
t kh´ac ta la
.
i c´o
SupX, A  minSupX  minSupY
do
X, A
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
v`a
Y ⊆ X.
V`ı vˆa
.
y
SupY, B  minSupY
hay
Y, B
c˜ung l`a tˆa
.

p phˆo
’
biˆe
´
n m`o
.
.

Di
.
nh ngh˜ıa 5. Luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
X ∈ A → Y ∈ B
x´ac di
.
nh t`u
.
CSDL
D
D
D
du
.

o
.
.
c go
.
i l`a luˆa
.
t
tin cˆa
.
y nˆe
´
u
Z, C
v´o
.
i
Z = {X, Y }
v`a
C = {A, B}
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
v`a
dˆo

.
tin cˆa
.
y cu
’
a luˆa
.
t
n`ay khˆong nho
’
ho
.
n
dˆo
.
tin cˆa
.
y cu
.
.
c tiˆe
’
u
minConf
cho tru
.
´o
.
c, t´u
.

c l`a
SupZ, C  minSupZ
v`a
ConfZ, C  minConf.
Di
.
nh ngh˜ıa 6. Ta go
.
i ng˜u
.
ca
’
nh d˜u
.
liˆe
.
u m`o
.
(Data Fuzzy Context) l`a bˆo
.
ba
DFC
DFC
DFC = (O, I, F
I
O, I, F
I
O, I, F
I
)

,
trong
d´o
O
O
O
l`a tˆa
.
p h˜u
.
u ha
.
n c´ac
dˆo
´
i tu
.
o
.
.
ng (object),
I
I
I
l`a tˆa
.
p tˆa
´
t ca
’

c´ac mu
.
c d˜u
.
liˆe
.
u v`a
F
I
F
I
F
I
l`a
tˆa
.
p tˆa
´
t ca
’
c´ac tˆa
.
p m`o
.
liˆen kˆe
´
t v´o
.
i c´ac mu
.

c d˜u
.
liˆe
.
u trong
I
I
I
.
K´y hiˆe
.
u
M
M
M
l`a tˆa
.
p mˆo
.
t sˆo
´
tˆa
.
p m`o
.
n`ao
d´o ´u
.
ng v´o
.

i c´ac mu
.
c d˜u
.
liˆe
.
u trong
I
I
I
sao cho ´u
.
ng v´o
.
i
mˆo
˜
i
i ∈ I
I
I
chı
’
c´o mˆo
.
t tˆa
.
p m`o
.
trong

M
M
M.
Di
.
nh ngh˜ıa 7. Ta go
.
i ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u m`o
.
(Data Fuzzy mining context) l`a bˆo
.
ba
DMC
DMC
DMC = (O, I, M
O, I, M
O, I, M).
Nhˆa
.
n x´et:

- Gia
’
su
.
’
λ
k
l`a sˆo
´
c´ac tˆa
.
p m`o
.
liˆen kˆe
´
t v´o
.
i mu
.
c d˜u
.
liˆe
.
u
i
k
trong tˆa
.
p
I

gˆo
`
m
n
phˆa
`
n tu
.
’
, thˆe
´
th`ı mˆo
˜
i ng˜u
.
ca
’
nh d˜u
.
liˆe
.
u m`o
.
s˜e tu
.
o
.
ng ´u
.
ng v´o

.
i
λ
1
.λ
2
λ
n
ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u m`o
.
.
Viˆe
.
c ph´at hiˆe
.
n c´ac luˆa
.
t kˆe
´
t ho

.
.
p m`o
.
hiˆe
.
n nay ([5, 6, 10]) m´o
.
i chı
’
du
.
o
.
.
c thu
.
.
c hiˆe
.
n
dˆo
´
i v´o
.
i mˆo
˜
i
ng˜u
.

ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u m`o
.
.
- Kh´ai niˆe
.
m ng˜u
.
ca
’
nh d˜u
.
liˆe
.
u v`a ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe

.
u m`o
.
du
.
o
.
.
c ph´at triˆe
’
n v`a c´o
su
.
.
kh´ac biˆe
.
t so v´o
.
i kh´ai niˆe
.
m tu
.
o
.
ng ´u
.
ng trong [9].
248
D
ˆ

O
˜
V
˘
AN TH
`
ANH
C´ac kh´ai niˆe
.
m nhu
.
kˆe
´
t nˆo
´
i Galoa v`a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
d´ong bˆay gi`o
.
c´o thˆe
’
du

.
o
.
.
c ph´at
triˆe
’
n t`u
.
c´ac kh´ai niˆe
.
m c´o liˆen quan nhu
.
sau ([9, 15]):
Di
.
nh ngh˜ıa 8. (Kˆe
´
t nˆo
´
i Galois) Cho
DFC
DFC
DFC = (O, I, M
O, I, M
O, I, M)
l`a mˆo
.
t ng˜u
.

ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u
m`o
.
. Kˆe
´
t nˆo
´
i Galois cu
’
a n´o l`a tˆa
.
p c´ac ´anh xa
.
du
.
o
.
.
c x´ac
di
.
nh nhu

.
sau:
V´o
.
i
C ⊆ O
O
O
v`a
X, A ⊆ I
I
I,M
M
M
f : 2
O
O
O
→ 2
I
I
I
,
f(C) = X, A,
o
.
’
dˆay
X = {i ∈ I
I

I|∀o ∈ C, m
χ
j
(o[i])  ω
χ
i
}  ω
χ
i
)
l`a ngu
.
˜o
.
ng cu
.
.
c tiˆe
’
u
cu
’
a tˆa
.
p m`o
.
χ
i
liˆen kˆe
´

t v´o
.
i c´ac mu
.
c d˜u
.
liˆe
.
u
i
trong
X, χ
i
∈ A ⊆ ω
x
i
.
g : 2
I
I
I
→ 2
O
O
O
g(X, A) = {o ∈ O
O
O|∀i ∈ X, m
χ
i

(o[i])  ω
χ
i
}.
h : 2
O
O
O
→ 2
O
O
O
sao cho h = f.g.
Di
.
nh ngh˜ıa 9. Tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
X, A
du
.
o
.

.
c go
.
i l`a
d´ong nˆe
´
u
h(X, A) = X, A
.
Nhˆa
.
n x´et:
- C´ac ´anh xa
.
h, f, g
du
.
o
.
.
c ph´at triˆe
’
n tiˆe
´
p t`u
.
c´ac ´anh xa
.
h, f, g
tu

.
o
.
ng ´u
.
ng ([9]) cho tru
.
`o
.
ng
ho
.
.
p ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u m`o
.
.
- Trong tru
.
`o
.

ng ho
.
.
p CSDL ban
dˆa
`
u l`a CSDL nhi
.
phˆan (mu
.
c d˜u
.
liˆe
.
u nhˆa
.
n gi´a tri
.
nhi
.
phˆan),
tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o

.
X, A
l`a d´ong khi v`a chı
’
khi
X
l`a tˆa
.
p d´ong, t´u
.
c l`a
h(X) = X
v´o
.
i ´anh
xa
.
h
du
.
o
.
.
c x´ac
di
.
nh nhu
.
trong [9]. Viˆe
.

c ch´u
.
ng minh n´o l`a rˆa
´
t
do
.
n gia
’
n.
- Tru
.
`o
.
ng ho
.
.
p CSDL ban
dˆa
`
u l`a CSDL di
.
nh lu
.
o
.
.
ng th`ı n´oi chung khˆong xa
’
y ra mˆo

´
i quan
hˆe
.
vˆe
`
t´ınh
d´ong gi˜u
.
a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
X, A
v`a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u
X.

Mˆo
´
i quan hˆe
.
n`ay s˜e
du
.
o
.
.
c tr`ınh b`ay trong mˆo
.
t b`ai b´ao kh´ac.
Gia
’
su
.
’
X, A
l`a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
, k´y hiˆe

.
u:
|gX, A| =

o∈O
O
O
Π
x
j
∈X
{

χ
x
j
(o[x
j
])}.
T´ınh chˆa
´
t sau dˆay du
.
o
.
.
c ph´at triˆe
’
n t`u
.

t´ınh chˆa
´
t liˆen quan trong [15], l`a co
.
so
.
’
dˆe
’
xˆay du
.
.
ng
thuˆa
.
t to´an t`ım tˆa
.
p phˆo
’
biˆe
´
n m`o
.
d´ong.
T´ınh chˆa
´
t 2.
a) Gia
’
su

.
’
X, A, Y, B
l`a hai tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
bˆa
´
t k`y, nˆe
´
u
minSupX > |g(Y, B)|/O
O
O
ho˘a
.
c
minSupY > |g(X, A)|/O
O
O
th`ı
X ∪ Y, A ∪ B
khˆong l`a tˆa

.
p phˆo
’
biˆe
´
n m`o
.
.
b) Nˆe
´
u
gX, A ⊂ g(Y, B) X, A
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
, v`a
minSupX  minSupY
ho˘a
.
c
|g(X, A)|/O
O
O  minSupY
th`ı
X ∪ Y, A ∪ B

c˜ung l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
.
c) Nˆe
´
u
g(X, A) = g(Y, B)
v`a
X, A
ho˘a
.
c
Y, B
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
th`ı
X ∪ Y, A∪B
c˜ung l`a tˆa

.
p phˆo
’
biˆe
´
n m`o
.
.
Ch´u
.
ng minh:
a) Theo
di
.
nh ngh˜ıa cu
’
a k´y hiˆe
.
u
| ∗ |
, ta thˆa
´
y
|g(X, A)|/O
O
O = SupX, A.
X´et tru
.
`o
.

ng ho
.
.
p
minSupY > |g(X, A)|/O
O
O
Gia
’
su
.
’
X ∪ Y, A ∪ B
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
thˆe
´
th`ı
SupX ∪ Y, A ∪ B  minSup(X ∪
Y )  minSupY SupX, A,
diˆe
`
u n`ay l`a vˆo l´y do
X, A

l`a tˆa
.
p con cu
’
a
X ∪ Y, A ∪ B
nˆen
SupX, A  SupX ∪ Y, A ∪ B.
LU
ˆ
A
.
T K
ˆ
E
´
T HO
.
.
P M
`
O
.
C
´
O
D
ˆ
O
.

H
ˆ
O
˜
TRO
.
.
CU
.
.
C TI
ˆ
E
’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU
249
Nhˆa
.
n x´et: Theo t´ınh chˆa
´
t a), cho d`u
X, A, Y, B
dˆe
`

u l`a nh˜u
.
ng tˆa
.
p phˆo
’
biˆe
´
n m`o
.
nhu
.
ng
X ∪ Y, A ∪ B
chu
.
a ch˘a
´
c c´o t´ınh chˆa
´
t nhu
.
vˆa
.
y, v`ı thˆe
´
n´o thu
.
`o
.

ng
du
.
o
.
.
c ´ap du
.
ng
dˆe
’
loa
.
i bo
’
ho˘a
.
c t`ım kiˆe
´
m nh˜u
.
ng tˆa
.
p phˆo
’
biˆe
´
n m`o
.
cu

.
.
c
da
.
i trong tru
.
`o
.
ng ho
.
.
p ca
’
hai tˆa
.
p
X, A, Y, B
dˆe
`
u d˜a l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
.
b) T`u

.
g(X, A) ⊂ g(Y, B)
v`a di
.
nh ngh˜ıa cu
’
a
g
, ta nhˆa
.
n du
.
o
.
.
c
gX∪Y, A∪B = g(X, A)
nˆen suy ra
SupX ∪ Y, A ∪ B = SupX, A. (∗)
M˘a
.
t kh´ac do
X, A
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o

.
v`a theo nhˆa
.
n x´et cu
’
a
Di
.
nh ngh˜ıa 1 ta c´o
SupX, A  minSupX, A = minSupX.
- Nˆe
´
u
minSupX  minSupY
th`ı
minSupX = minSup(X ∪ Y ). (∗∗)
T`u
.
(*) v`a (**) suy ra
SupX ∪ Y, A ∪ B  minSup(X ∪ Y )
hay
X ∪ Y, A ∪ B
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.

.
- Nˆe
´
u
|g(X, A)|/O
O
O  minSupY
hay
SupX, A  minSupY
suy ra
SupX, A 
max(minSupX, minSupY ) = minSup(X ∪ Y ), X ∪ Y, A ∪ B
l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
.
c)
Du
.
o
.
.
c suy ra tru
.
.

c tiˆe
´
p t`u
.
ch´u
.
ng minh b).
Theo [3], c´o thˆe
’
n´oi qu´a tr`ınh ph´at hiˆe
.
n c´ac luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
v´o
.
i c´ac tˆa
.
p thuˆo
.
c t´ınh c´o
dˆo
.
hˆo

˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng nhau t`u
.
mˆo
.
t CSDL
di
.
nh lu
.
o
.
.
ng bˆa
´
t k`y c˜ung gˆo
`
m 3 giai
doa
.

n chu
’
yˆe
´
u l`a:
- Giai
doa
.
n 1: Chuyˆe
’
n CSDL di
.
nh lu
.
o
.
.
ng th`anh ng˜u
.
ca
’
nh d˜u
.
liˆe
.
u m`o
.
(ho˘a
.
c CSDL m`o

.
):
trong giai
doa
.
n n`ay c´ac kh´ai niˆe
.
m m`o
.
´u
.
ng v´o
.
i t`u
.
ng thuˆo
.
c t´ınh, c´ac h`am th`anh viˆen cu
’
a c´ac
kh´ai niˆe
.
m m`o
.
, c´ac
dˆo
.
hˆo
˜
tro

.
.
cu
.
.
c tiˆe
’
u cho t`u
.
ng mu
.
c d˜u
.
liˆe
.
u s˜e
du
.
o
.
.
c x´ac
di
.
nh tru
.
´o
.
c tiˆen bo
.

’
i
ngu
.
`o
.
i su
.
’
du
.
ng, v`a t`u
.
d´o ngu
.
`o
.
i su
.
’
du
.
ng quyˆe
´
t
di
.
nh lu
.
.

a cho
.
n mˆo
.
t ng˜u
.
ca
’
nh ph´at hiˆe
.
n luˆa
.
t kˆe
´
t
ho
.
.
p m`o
.
trong ng˜u
.
ca
’
nh d˜u
.
liˆe
.
u m`o
.

d˜a du
.
o
.
.
c x´ac
di
.
nh tru
.
´o
.
c
d´o.
- Giai
doa
.
n 2: T`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n m`o
.
c´o da
.
ng
Z, C
sao cho

SupZ, C  minSupZ =
minSup(Z, C)
l`a dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u
Z, C.
- Giai doa
.
n 3: T`u
.

c´ac tˆa
.
p phˆo
’
biˆe
´
n
d´ong
Z, C
t`ım du
.
o
.
.
c o
.
’
giai
doa
.
n 2, sinh ra c´ac luˆa
.
t
kˆe
´
t ho
.
.
p m`o
.

da
.
ng:
X, A → Z − X, C − A
, o
.
’
dˆay
X ⊂ Z
v`a
A ⊂ C
. Giai doa
.
n n`ay l`a do
.
n
gia
’
n.
Phˆa
`
n tiˆe
´
p theo cu
’
a b`ai b´ao chı
’
tˆa
.
p trung v`ao giai

doa
.
n 2, cu
.
thˆe
’
l`a xˆay du
.
.
ng thuˆa
.
t to´an
t`ım tˆa
.
p phˆo
’
biˆe
´
n m`o
.
d´ong cu
.
.
c
da
.
i v´o
.
i c´ac mu
.

c d˜u
.
liˆe
.
u c´o
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng
nhau, b˘a
`
ng c´ach ph´at triˆe
’
n tiˆe
´
p thuˆa
.
t to´an CHARM-NEW ([3]) cho tru
.

`o
.
ng ho
.
.
p co
.
so
.
’
d˜u
.
liˆe
.
u
di
.
nh lu
.
o
.
.
ng v´o
.
i viˆe
.
c ´u
.
ng du
.

ng l´y thuyˆe
´
t tˆa
.
p m`o
.
.
3. THU
ˆ
A
.
T TO
´
AN PH
´
AT HI
ˆ
E
.
N T
ˆ
A
.
P PH
ˆ
O
’
BI
ˆ
E

´
N M
`
O
.
D
´
ONG
V
´
O
.
I
D
ˆ
O
.
H
ˆ
O
˜
TRO
.
.
CU
.
.
C TI
ˆ
E

’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU
3.1.
´
Y tu
.
o
.
’
ng ch´ınh cu
’
a thuˆa
.
t to´an
Thuˆa
.
t to´an
du
.
o
.
.
c
dˆe

`
xuˆa
´
t theo c´ach nhu
.
sau:
Dˆe
’
t`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n m`o
.
d´ong cu
.
.
c
da
.
i,
tu
.
o
.
ng tu
.
.

nhu
.
c´ac thuˆa
.
t to´an CHARM [15] v`a CHARM-NEW [3], thuˆa
.
t to´an su
.
’
du
.
ng phu
.
o
.
ng
ph´ap duyˆe
.
t theo chiˆe
`
u sˆau trˆen khˆong gian d`an c´ac tˆa
.
p thuˆo
.
c t´ınh cu
’
a
I, M
I,M
I,M

. Tu
.
o
.
ng tu
.
.
250
D
ˆ
O
˜
V
˘
AN TH
`
ANH
CHARM-NEW mˆo
˜
i dı
’
nh cu
’
a dˆo
`
thi
.
biˆe
’
u diˆe

˜
n khˆong gian t`ım kiˆe
´
m c´ac tˆa
.
p phˆo
’
biˆe
´
n d´ong
l`a bˆo
.
ba
{X, A, minSupX, g(X, A)}
. Thuˆa
.
t to´an s˘a
´
p xˆe
´
p c´ac n´ut o
.
’
m´u
.
c 1 cu
’
a cˆay
dˆo
`

thi
.
khˆong gian c´ac tˆa
.
p phˆo
’
biˆe
´
n m`o
.
theo th´u
.
tu
.
.
t˘ang dˆa
`
n cu
’
a
dˆo
.
hˆo
˜
tro
.
.
cu
.
.

c tiˆe
’
u cu
’
a n´o t`u
.
tr´ai qua pha
’
i. V´o
.
i c´ach s˘a
´
p xˆe
´
p
d´o c´ac tˆa
.
p
k
-mu
.
c d˜u
.
liˆe
.
u m`o
.
(
k > 1
) du

.
o
.
.
c sinh ra theo
phu
.
o
.
ng ph´ap duyˆe
.
t theo chiˆe
`
u sˆau t`u
.
ng nh´anh cu
’
a cˆay
dˆo
`
thi
.
vˆa
˜
n du
.
o
.
.
c s˘a

´
p xˆe
´
p theo th´u
.
tu
.
.
t˘ang dˆa
`
n cu
’
a
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a ch´ung theo th´u
.
tu

.
.
t`u
.
tr´ai sang pha
’
i, tˆa
.
p sinh ra
tru
.
´o
.
c c´o
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u nho
’
ho
.

n
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a tˆa
.
p sinh ra sau, c´ac n´ut thuˆo
.
c
nh´anh bˆen tr´ai
dˆe
`
u c´o dˆo
.
hˆo
˜
tro
.
.

cu
.
.
c tiˆe
’
u nho
’
ho
.
n c´ac n´ut o
.
’
nh´anh pha
’
i. Co
.
chˆe
´
hoa
.
t
dˆo
.
ng
cu
’
a thuˆa
.
t to´an t`ım tˆa
.

p phˆo
’
biˆe
´
n m`o
.
c˜ung kh´a tu
.
o
.
ng tu
.
.
nhu
.
CHARM-NEW. Cu
.
thˆe
’
, gia
’
su
.
’
dang xu
.
’
l´y nh´anh c´o n´ut gˆo
´
c l`a

{X, A, minSupX, g(X, A)}
ta muˆo
´
n kˆe
´
t ho
.
.
p n´o v´o
.
i n´ut
{Y, B, minSupB, g(Y, B)}
dˆe
’
sinh ra n´ut con m´o
.
i, trong
d´o
Y, B
du
.
o
.
.
c s˘a
´
p th´u
.
tu
.

.
sau
X, A.
Khi d´o xa
’
y ra c´ac tru
.
`o
.
ng ho
.
.
p sau:
1. Khi
g(X, A) = g(Y, B)
nˆe
´
u
X, A
v`a
Y, B
l`a c´ac tˆa
.
p phˆo
’
biˆe
´
n m`o
.
th`ı

X∪Y, A∪B
c˜ung l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
(T´ınh chˆa
´
t 2c), do
d´o ta c´o thˆe
’
thay thˆe
´
mo
.
i su
.
.
xuˆa
´
t hiˆe
.
n cu
’
a
X, A
bo

.
’
i
X ∪ Y, A ∪ B
v`a khˆong cˆa
`
n xem x´et c´ac nh´anh cu
’
a tˆa
.
p
Y, B
trong c´ac bu
.
´o
.
c t`ım kiˆe
´
m
tiˆe
´
p theo;
2. Khi
g(X, A) ⊃ g(Y, B)
nˆe
´
u
X, A, Y, B
l`a c´ac tˆa
.

p phˆo
’
biˆe
´
n m`o
.
v`a do c´ac n´ut
cu
’
a
dˆo
`
thi
.
du
.
o
.
.
c s˘a
´
p theo th´u
.
tu
.
.
t˘ang dˆa
`
n cu
’

a
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a tˆa
.
p mu
.
c d˜u
.
liˆe
.
u trong
n´ut nˆen
minSupX  minSupY
do d´o
X ∪ Y, A ∪ B
c˜ung l`a tˆa
.

p phˆo
’
biˆe
´
n m`o
.
(T´ınh chˆa
´
t
2b), nˆen ta c´o thˆe
’
loa
.
i bo
’
nh´anh c´o n´ut gˆo
´
c l`a
{Y, B, minSupY, g(Y, B)}
v`a bˆo
’
sung n´ut
{X ∪ Y, A ∪ B, minSupX ∪ Y, g(X ∪ Y, A ∪ B)}
v`ao tˆa
.
p c´ac n´ut.
3. Khi
g(X, A) ⊂ g(Y, B)
v`a
X, A, Y, B

l`a c´ac tˆa
.
p phˆo
’
biˆe
´
n m`o
.
ta chu
.
a thˆe
’
kˆe
´
t
luˆa
.
n
du
.
o
.
.
c
X ∪ Y, A ∪ B
c´o pha
’
i l`a tˆa
.
p phˆo

’
biˆe
´
n m`o
.
hay khˆong, n´oi c´ach kh´ac t`u
.
c´ac n´ut
gˆo
´
c
{X, A, minSupX, g(X, A)}
v`a
{Y, B, minSupY, g(Y, B)}
vˆa
˜
n c´o tiˆe
`
m n˘ang sinh ra
c´ac tˆa
.
p phˆo
’
biˆe
´
n m`o
.
kh´ac nˆen ta khˆong thˆe
’
loa

.
i bo
’
hay thay thˆe
´
ch´ung b˘a
`
ng n´ut kh´ac
du
.
o
.
.
c,
tuy nhiˆen nˆe
´
u thˆem
diˆe
`
u kiˆe
.
n
|g(X, A)|/O  minSupY
ho˘a
.
c
minSupX  minSupY
th`ı
X ∪ Y, A ∪ B
l`a tˆa

.
p phˆo
’
biˆe
´
n m`o
.
nˆen c´o thˆe
’
bˆo
’
sung n´ut
{X ∪ Y, A ∪ B, minSupX ∪
Y,
g(X ∪ Y, A ∪ B)}
v`ao tˆa
.
p c´ac n´ut.
4. Khi
g(X, A) = g(Y, B)
s˜e xa
’
y ra t`ınh huˆo
´
ng tu
.
o
.
ng tu
.

.
nhu
.
tru
.
`o
.
ng ho
.
.
p 3, t´u
.
c l`a
chu
.
a thˆe
’
kˆe
´
t luˆa
.
n
du
.
o
.
.
c
X ∪Y, A∪B
c´o pha

’
i l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
hay khˆong, v`a t`u
.
c´ac nh´anh
c´o n´ut gˆo
´
c
{X, A, minSupX, g(X, A)}, {Y, B, minSupY, g(Y, B)}
dˆe
`
u c´o thˆe
’
ph´at sinh
ra nh˜u
.
ng tˆa
.
p phˆo
’
biˆe
´
n m`o

.
m´o
.
i.
Du
.
´o
.
i
dˆay chı
’
gi´o
.
i thiˆe
.
u phˆa
`
n cˆo
´
t l˜oi nhˆa
´
t cu
’
a thuˆa
.
t to´an t`ım tˆa
.
p phˆo
’
biˆe

´
n m`o
.
d´ong cu
.
.
c
da
.
i du
.
o
.
.
c ca
’
i tiˆe
´
n t`u
.
CHARM [15] v`a
du
.
o
.
.
c ph´at triˆe
’
n t`u
.

CHARM-NEW [3] go
.
i l`a FUZZY-
CHARM-NEW. C´ac thu
’
tu
.
c v`a h`am FUZZY-CHARM-EXTENDED-NEW, FUZZY-CHARM-
PROPERTY-NEW c´o ´y ngh˜ıa v`a vai tr`o nhu
.
CHARM-EXTENDED, CHARM-PROPERTY
nhu
.
trong thuˆa
.
t to´an CHARM [15].
K´y hiˆe
.
u
Ω
Ω
Ω
l`a tˆa
.
p tˆa
´
t ca
’
c´ac tˆa
.

p phˆo
’
biˆe
´
n m`o
.
d´ong,
h(i)
l`a c´ach d´anh sˆo
´
tu
.
.
nhiˆen cu
’
a c´ac
thuˆo
.
c t´ınh
i ∈ I
I
I
, v`a quy u
.
´o
.
c v´o
.
i mu
.

c d˜u
.
liˆe
.
u
i
n
th`ı
h(i
n
) = n
. Ta n´oi
i < j
nˆe
´
u
h(i) < h(j)
v`a
j = i + 1
nˆe
´
u
h(j) = h(i) + 1.
Gia
’
su
.
’
I
I

I
l`a tˆa
.
p gˆo
`
m
m
thuˆo
.
c t´ınh.
LU
ˆ
A
.
T K
ˆ
E
´
T HO
.
.
P M
`
O
.
C
´
O
D
ˆ

O
.
H
ˆ
O
˜
TRO
.
.
CU
.
.
C TI
ˆ
E
’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU
251
3.2. Thuˆa
.
t to´an FUZZY-CHARM-NEW
FUZZY-CHARM-NEW
({i
1

, χ
i
k
, minSupi
1
}, {i
2
, χ
i
2
, minSupi
2
}, , {i
m
, χ
i
m
,
minSupi
m
})
,
Nodes=
({i, χ
i
, minSupi, g(i, χ
i
}/i ∈ I, Supi, χ
i
  minSupi)

. C´ac dı
’
nh n`ay du
.
o
.
.
c
s˘a
´
p xˆe
´
p t`u
.
tr´ai sang pha
’
i theo th´u
.
tu
.
.
t˘ang dˆa
`
n cu
’
a th`anh phˆa
`
n th´u
.
hai

minSupi;
FUZZY-CHARM-EXTENDED-NEW (Nodes,
Ω
Ω
Ω
);
FUZZY-CHARM-EXTENDED-NEW (Nodes,
Ω
Ω
Ω
)
for each
{X
i
, A
i
, minSupX
i
, g(X
i
, A
i
)}
in Nodes
{
NewN := ∅; X := X
i
; h(j) := h(i) + 1; A := A
i
While (h(j)  m and {X

j
, A
j
, minSupX
j
, g(X
j
, A
j
} in Nodes) {
X := X ∪ X
j
; A := A ∪ A
j
v`a Y := g(X
i
, A
i
) ∩ g(X
j
, A
j
); B = A
i
∩ A
j
;
FUZZY-CHARM-PROPERTY-NEW (Nodes, NewN)
j ++ }
If NewN = ∅ then FUZZY-CHARM-EXTEND (NewN, Ω

Ω
Ω)
Ω
Ω
Ω := Ω
Ω
Ω ∪ X, A}
FUZZY-CHARM-PROPERTY-NEW
(Nodes, NewN)
if (|Y |/O  minSupX ) then
if (
g(X
i
, A
i
) = g(X
j
, A
j
)) then
Loai {X
j
, A
j
, minSupX
j
, g(X
j
, A
j

)} ra khoi Nodes
Thay the tat ca X
i
, A
i
 boi X, A
else if (
g(X
i
, A
i
) ⊃ (X
j
, A
j
)) then
Bˆo
’
sung {X, A, minSupX,
g(X, A)} v`ao Notes
Loai {X
j
, A
j
, minSupX
j
, g(X
j
, A
j

)} ra khoi Nodes
else if (
g(X
i
, A
i
) ⊂ g(X
j
, A
j
)) and
(minSupX
j
 |g(X
i
, A
i
)|/O)) then
Thay the tat ca X
i
, A
i
 boi X, A
else if ((
g(X
i
, A
i
 = g(X
j

, A
j
)) and
(minSupX
j
 |g(X
i
, A
i
)|/O)
and (minSupX
i
 |g(X
j
, A
j
)|/O) then
Bˆo
’
sung {X, A, minSupX,
g(X, A)} v`ao NewN;
3.3. Nhˆa
.
n x´et v`a d´anh gi´a thuˆa
.
t to´an
- Thuˆa
.
t to´an FUZZY CHARM-NEW cho ph´ep t`ım c´ac tˆa
.

p mu
.
c d˜u
.
liˆe
.
u m`o
.
d´ong cu
.
.
c
da
.
i
c´o
dˆo
.
hˆo
˜
tro
.
.
l´o
.
n ho
.
n
dˆo
.

hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng nhau ´u
.
ng v´o
.
i t`u
.
ng tˆa
.
p mu
.
c d˜u
.
liˆe
.
u t`u
.
CSDL
di

.
nh lu
.
o
.
.
ng bˆa
´
t k`y
. Thuˆa
.
t to´an n`ay du
.
o
.
.
c ph´at triˆe
’
n tiˆe
´
p t`u
.
thuˆa
.
t to´an CHARM-NEW
[3] t`ım tˆa
.
p phˆo
’
biˆe

´
n
d´ong cu
.
.
c
da
.
i c´o dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u khˆong giˆo
´
ng nhau
t`u
.
c´ac CSDL nhi
.
phˆan
(hay t´ac vu
.

).
- Trong [3]
d˜a chı
’
ra r˘a
`
ng khi dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u l`a chung nhu
.
nhau cho tˆa
´
t ca
’
c´ac tˆa
.
p
phˆo
’
biˆe

´
n th`ı CHARM-NEW s˜e tro
.
’
th`anh CHARM, l`a thuˆa
.
t to´an t`ım c´ac tˆa
.
p phˆo
’
biˆe
´
n
d´ong
cu
.
.
c
da
.
i v´o
.
i
dˆo
.
hˆo
˜
tro
.
.

cu
.
.
c tiˆe
’
u chung t`u
.
CSDL nhi
.
phˆan hiˆe
.
u qua
’
nhˆa
´
t cho
dˆe
´
n nay [15].
-
Dˆo
´
i v´o
.
i FUZZY CHARM-NEW, h`ınh th´u
.
c kh´a giˆo
´
ng CHARM-NEW [3]; FUZZY
CHARM-NEW c˜ung s˜e tro

.
’
th`anh thuˆa
.
t to´an CHARM-NEW khi CSDL
di
.
nh lu
.
o
.
.
ng suy
252
D
ˆ
O
˜
V
˘
AN TH
`
ANH
biˆe
´
n th`anh co
.
so
.
’

d˜u
.
liˆe
.
u nhi
.
phˆan.
Thˆa
.
t vˆa
.
y, c´ac mu
.
c d˜u
.
liˆe
.
u cu
’
a CSDL nhi
.
phˆan do chı
’
nhˆa
.
n mˆo
.
t trong 2 gi´a tri
.
l`a: 1 ho˘a

.
c
0 hay “c´o” ho˘a
.
c “khˆong” khi
d´o liˆen kˆe
´
t mˆo
.
t c´ach tu
.
.
nhiˆen ho
.
.
p l´y v´o
.
i mˆo
˜
i mu
.
c d˜u
.
liˆe
.
u
nhi
.
phˆan x ∈ X c˜ung chı
’

c´o thˆe
’
c´o c´ac kh´ai niˆe
.
m m`o
.
c´o
v`a
khˆong
v´o
.
i c´ac h`am th`anh viˆen
chı
’
nhˆa
.
n 2 gi´a tri
.
1 v`a 0.
V´o
.
i h`am th`anh viˆen x´ac
di
.
nh nhu
.
vˆa
.
y dˆe
˜

d`ang suy ra:
g(X, A = g(X) v`a SupX, A =
SupX, T´ınh chˆa
´
t 2 o
.
’
trˆen tro
.
’
th`anh t´ınh chˆa
´
t
dˆe
’
xˆay du
.
.
ng thuˆa
.
t to´an CHARM-NEW v`a
FUZZY CHARM-NEW tro
.
’
th`anh CHARM-NEW [3].
- Trong [14, 15]
d˜a chı
’
ra dˆo
.

ph´u
.
c ta
.
p cu
’
a c´ac thuˆa
.
t to´an ph´at hiˆe
.
n luˆa
.
t kˆe
´
t ho
.
.
p, n´oi chung
l`a NP kh´o, trong
d´o thuˆa
.
t to´an CHARM l`a ´ıt ph´u
.
c ta
.
p ho
.
n nhiˆe
`
u so v´o

.
i c´ac thuˆa
.
t to´an ph´at
hiˆe
.
n luˆa
.
t kˆe
´
t ho
.
.
p kh´ac. Trong [3] c˜ung
d˜a ra chı
’
ra r˘a
`
ng dˆo
.
ph´u
.
c ta
.
p cu
’
a CHARM-NEW l`a
´ıt ho
.
n CHARM trong tru

.
`o
.
ng ho
.
.
p
dˆo
.
hˆo
˜
tro
.
.
cu
’
a c´ac tˆa
.
p phˆo
’
biˆe
´
n l`a thu
.
.
c su
.
.
kh´ac nhau. So
v´o

.
i CHARM-NEW, thuˆa
.
t to´an FUZZY CHARM-NEW l`a ph´u
.
c ta
.
p ho
.
n v`a chu
’
yˆe
´
u o
.
’
viˆe
.
c
t´ınh c´ac |
g(X
j
, A
j
)| trong c´ac qu´a tr`ınh t`ım kiˆe
´
m v`a tı
’
a b´o
.

t c´ac tˆa
.
p khˆong pha
’
i l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
. U
.
´o
.
c lu
.
o
.
.
ng ch´ınh x´ac
dˆo
.
ph´u
.
c ta
.
p cu
’

a thuˆa
.
t to´an n`ay
dang du
.
o
.
.
c nghiˆen c´u
.
u l`am
r˜o.
- Tu
.
tu
.
o
.
’
ng t`ım kiˆe
´
m v`a tı
’
a b´o
.
t c´ac tˆa
.
p khˆong l`a phˆo
’
biˆe

´
n cu
’
a FUZZY CHARM-NEW
l`a giˆo
´
ng CHARM v`a CHARM-NEW, ch´ung chı
’
kh´ac nhau o
.
’
c´ac biˆe
’
u th´u
.
c
diˆe
`
u kiˆe
.
n trong
thuˆa
.
t to´an v`a
d˜a du
.
o
.
.
c ch´u

.
ng minh trong T´ınh chˆa
´
t 2. N´oi c´ach kh´ac t´ınh
d´ung d˘a
´
n cu
’
a
FUZZY CHARM-NEW
du
.
o
.
.
c kh˘a
’
ng
di
.
nh thˆong qua T´ınh chˆa
´
t 2 o
.
’
trˆen v`a t´ınh
d´ung d˘a
´
n
cu

’
a thuˆa
.
t to´an CHARM.
4. V
´
I DU
.
MINH HO
.
A
CSDL trong Ba
’
ng 1 du
.
´o
.
i
dˆay th`u
.
a nhˆa
.
n r˘a
`
ng
dˆo
.
hˆo
˜
tro

.
.
cu
.
.
c tiˆe
’
u
dˆo
´
i v´o
.
i c´ac mu
.
c d˜u
.
liˆe
.
u Tuˆo
’
i, Sˆo
´
xe m´ay, Thu nhˆa
.
p, C´o gia
d`ınh tu
.
o
.
ng ´u

.
ng l`a: 0,15; 0,1; 0,05; 0,2;
Ba
’
ng 1.
Co
.
so
.
’
d˜u
.
liˆe
.
u
di
.
nh lu
.
o
.
.
ng mˆa
˜
u ban
dˆa
`
u
Di
.

nh danh Tuˆo
’
i Sˆo
´
xe m´ay Thu nhˆa
.
p C´o Gia d`ınh
(triˆe
.
u dˆo
`
ng)
t
1
60 0 0,6 khˆong
t
2
40 3 6,0 c´o
t
3
30 0 1,5 c´o
t
4
25 1 3,0 khˆong
t
5
70 2 0 c´o
t
6
57 4 4,0 c´o

Dˆo
´
i v´o
.
i mu
.
c d˜u
.
liˆe
.
u
Tuˆo
’
i
ta c´o kh´ai niˆe
.
m m`o
.
: a) tre
’
, b) trung niˆen, c) gi`a;
dˆo
´
i v´o
.
i
Sˆo
´
xe m´ay
ta c´o c´ac kh´ai niˆe

.
m m`o
.
: d) nhiˆe
`
u, e) ´ıt;
Thu nhˆa
.
p
c´o c´ac kh´ai niˆe
.
m m`o
.
f) cao, g)
trung b`ınh, h) thˆa
´
p;
C´o gia d`ınh
c´o c´ac kh´ai niˆe
.
m m`o
.
: i) c´o, j) khˆong. Qui u
.
´o
.
c su
.
’
du

.
ng
c´ac ch˜u
.
c´ai a, b, c, d, e, f, g, h, i, j
dˆe
’
biˆe
’
u thi
.
go
.
n tu
.
o
.
ng ´u
.
ng cho c´ac kh´ai niˆe
.
m m`o
.
: tre
’
,
trung niˆen, gi`a, nhiˆe
`
u, ´ıt, cao, trung b`ınh, thˆa
´

p, c´o, khˆong.
Gia
’
su
.
’
c´ac h`am th`anh viˆen tu
.
o
.
ng ´u
.
ng cu
’
a c´ac kh´ai niˆe
.
m m`o
.
trˆen
du
.
o
.
.
c cho
.
n th´ıch ho
.
.
p,

ch˘a
’
ng ha
.
n:
LU
ˆ
A
.
T K
ˆ
E
´
T HO
.
.
P M
`
O
.
C
´
O
D
ˆ
O
.
H
ˆ
O

˜
TRO
.
.
CU
.
.
C TI
ˆ
E
’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU
253
m
b
(t) =

0 nˆe
´
u t  60 ho˘a
.
c t  20
(t − 20)(60 − t)/400 nˆe
´

u 20 < t < 60.
m
d
(t) =

1 nˆe
´
u t  5
(5 − t)/5 nˆe
´
u t < 5.
m
g
(t) =













t/(3 triˆe
.
u) nˆe

´
u t  3. triˆe
.
u
1 nˆe
´
u 3. triˆe
.
u < t  4. triˆe
.
u
5. triˆe
.
u − t
1 triˆe
.
u
nˆe
´
u 4. triˆe
.
u < t  5. triˆe
.
u
0 nˆe
´
u t  5. triˆe
.
u
m

i
(t) =

1 nˆe
´
u t = “co”
0 nˆe
´
u t = “khong”.
Khi
d´o CSDL di
.
nh lu
.
o
.
.
ng
d˜a cho du
.
o
.
.
c chuyˆe
’
n th`anh ng˜u
.
ca
’
nh d˜u

.
liˆe
.
u m`o
.
du
.
o
.
.
c mˆo ta
’
trong Ba
’
ng 2.
Ba
’
ng 2.
Ng˜u
.
ca
’
nh d˜u
.
liˆe
.
u m`o
.
cu
’

a CSDL
di
.
nh lu
.
o
.
.
ng trong Ba
’
ng 1
Di
.
nh Tuˆo
’
i a b c Sˆo
´
d e Thu f g h C´o i j
danh XM nhˆa
.
p GD
t
1
60 0,0 0,0 1,0 0 0,0 1,0 0,6 0,12 0,2 1,0 k 0,0 1,0
t
2
40 0,5 1,0 0,5 3 0,6 0,4 6,0 1,0 0,0 0,0 c 1,0 0,0
t
3
30 0,75 0,75 0,25 0 0,0 1,0 1,5 0,3 0,5 1,0 c 1,0 0,0

t
4
25 0,87 0,44 0,12 1 0,2 0,8 3,0 0,5 1 0,66 k 0,0 1,0
t
5
70 0,0 0,0 1,0 2 0,4 0,6 0,0 0,0 0,0 1,0 c 1,0 0,0
t
6
57 0,08 0,28 0,92 4 0,8 0,2 4,0 0,8 1 0,33 c 1,0 0,0
Gia
’
su
.
’
ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u m`o
.
: v´o
.
i mu
.

c d˜u
.
liˆe
.
u Tuˆo
’
i liˆen kˆe
´
t v´o
.
i kh´ai niˆe
.
m m`o
.
:
b) trung niˆen. Sˆo
´
xe m´ay liˆen kˆe
´
t v´o
.
i d) nhiˆe
`
u. Thu nhˆa
.
p liˆen kˆe
´
t v´o
.
i g) trung b`ınh, v`a C´o

gia
d`ınh liˆen kˆe
´
t v´o
.
i i) c´o. Gia
’
su
.
’
ngu
.
˜o
.
ng cu
.
.
c tiˆe
’
u tu
.
o
.
ng ´u
.
ng
dˆo
´
i v´o
.

i 4 kh´ai niˆe
.
m m`o
.
trˆen
l`a: 0,3; 0,1; 0,15; 0,5.
Khi
d´o ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u m`o
.
tu
.
o
.
ng ´u
.
ng
du
.
o
.

.
c x´ac
di
.
nh trong Ba
’
ng 3, o
.
’
dˆay
O l`a k´y hiˆe
.
u tˆa
.
p
di
.
nh danh:
Ba
’
ng 3.
Mˆo
.
t ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u

.
liˆe
.
u m`o
.
O Tuˆo
’
i b Sˆo
´
XM d Thu nhˆa
.
p g C´o GD i
0,15 0,3 0,1 0,15 0,05 0,1 0,4 0,6
t
1
60 0,0 0 0,0 0,6 0,2 k 0,0
t
2
40 1,0 3 0,6 6,0 0,0 c 1,0
t
3
30 0,75 0 0,0 1,5 0,5 c 1,0
t
4
25 0,44 1 0,2 3,0 1 k 0,0
t
5
70 0,0 2 0,4 0,0 0,0 c 1,0
t
6

57 0,28 4 0,8 4,0 1 c 1,0
254
D
ˆ
O
˜
V
˘
AN TH
`
ANH
K´y hiˆe
.
u B, D, G, I tu
.
o
.
ng ´u
.
ng l`a c´ac mu
.
c d˜u
.
liˆe
.
u Tuˆo
’
i, Sˆo
´
xe m´ay, Thu nhˆa

.
p, C´o gia
d`ınh; sˆo
´
k dˆe
’
biˆe
’
u diˆe
˜
n cho giao di
.
ch t
k
trong tˆa
.
p di
.
nh danh. Cˆay dˆo
`
thi
.
biˆe
’
u diˆe
˜
n khˆong
gian t`ım kiˆe
´
m tˆa

.
p phˆo
’
biˆe
´
n m`o
.
d´ong cu
.
.
c
da
.
i theo thuˆa
.
t to´an FUZZY CHARM-NEW du
.
o
.
.
c
mˆo ta
’
trong H`ınh 1.
M´u
.
c 1 trong cˆay
dˆo
`
thi

.
n`ay l`a tˆa
.
p c´ac dı
’
nh c´o da
.
ng {A, a, minSupA, gA, a}, o
.
’
dˆay A
l`a mˆo
.
t trong c´ac mu
.
c d˜u
.
liˆe
.
u {G, B, D, I}, a l`a kh´ai niˆe
.
m m`o
.
´u
.
ng v´o
.
i mu
.
c d˜u

.
liˆe
.
u A trong
ng˜u
.
ca
’
nh ph´at hiˆe
.
n d˜u
.
liˆe
.
u m`o
.
n´oi trˆen;
g(A, a) du
.
o
.
.
c x´ac
di
.
nh theo Di
.
nh ngh˜ıa 8, ch˘a
’
ng

ha
.
n
g(B, b) = 234 do ngu
.
˜o
.
ng cu
.
.
c tiˆe
’
u cu
’
a kh´ai niˆe
.
m m`o
.
b l`a 0,3 cho nˆen c´ac giao di
.
ch
th´u
.
1, 5, 6 khˆong thuˆo
.
c tˆa
.
p
di
.

nh danh g(B, b).
Do Sup(G, g) = (m
g
(t
1
[G])+m
g
(t
3
[G])+m
g
(t
4
[G])+m
g
(t
6
[G]))/6 = (0, 2+0, 5+1, 0+
1, 0)/6 = 0, 45 > 0, 05 = minSupG; tu
.
o
.
ng tu
.
.
Sup(D, d) = 0, 33 > 0, 1 = minSupD; Sup(B, b) =
0, 37 > 0, 15 = minSupB v`a Sup(I,i) = 0, 66 > 0, 4 = minSupI cho nˆen tˆa
´
t ca
’

4
dı
’
nh thuˆo
.
c
m´u
.
c 1
dˆe
`
u l`a nh˜u
.
ng tˆa
.
p phˆo
’
biˆe
´
n m`o
.
.
<<G,g>, 0.05, 1346> <<D,d>, 0.1, 2456> <<B,b>, 0.15, 234> <<I.i>, 0.4, 2356>
{}
<<GD,gd>, 0.1, 46>
<<G,g>, 0.05, 1346> <<D,d>, 0.1, 2456> <<B,b>, 0.15, 234> <<I.i>, 0.4, 2356>
{}
<<GD,gd>, 0.1, 46>
H`ınh 1.
Khˆong gian t`ım kiˆe

´
m tˆa
.
p phˆo
’
biˆe
´
n m`o
.
cu
.
.
c
da
.
i theo FUZZY CHARM - NEW
C´ac n´ut thuˆo
.
c m´u
.
c 1
du
.
o
.
.
c s˘a
´
p theo th´u
.

tu
.
.
t˘ang dˆa
`
n cu
’
a
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a c´ac
mu
.
c d˜u
.
liˆe
.
u trong CSDL. Viˆe

.
c t`ım tˆa
.
p phˆo
’
biˆe
´
n m`o
.
d´ong cu
.
.
c
da
.
i du
.
o
.
.
c thu
.
.
c hiˆe
.
n theo chiˆe
´
n
lu
.

o
.
.
c t`ım kiˆe
´
m theo chiˆe
`
u sˆau trong khˆong gian t`ım kiˆe
´
m theo th´u
.
tu
.
.
t`u
.
tr´ai sang pha
’
i.
B˘a
´
t
dˆa
`
u t`u
.
n´ut {G, g,0,05, 1346} khi ta kˆe
´
t ho
.

.
p v´o
.
i n´ut {D, d,0,1, 2456}. Ta c´o
g(G, g) ∩ g(D, d) = 46 nˆen |g(G, g) ∩ g(D, d)|/O
O
O = |g(G, g ∪ D, d)|/O
O
O =
(m
g
(t
4
[G]).m
d
(t
4
[D])+m
g
(t
6
[G]).m
d
(t
6
[D])/6 = (1.0, 2+1.0, 8)/6 = 0, 16 = Sup(GD, gd) >
minSupGD = 0, 1. M˘a
.
t kh´ac do
g(G, g) = 1346 = g(D, d) = 2456 v`a minSupD <

|
g(G, b)|/O
O
O, minSupG < |g(D, d)|/O
O
O nˆen c´o thˆe
’
bˆo
’
sung {GD, gd, 0,1, 46} v`ao n´ut
cu
’
a
dˆo
`
thi
.
.
Kˆe
´
t ho
.
.
p {G, g, 0,05, 1346} v´o
.
i {B, b, 0,15, 234}, do Sup(GB, gb) = 0, 09 < 0, 15 =
minSupGB nˆen kˆe
´
t ho
.

.
p n`ay khˆong
du
.
o
.
.
c thu
.
.
c hiˆe
.
n. Kˆe
´
t ho
.
.
p {G, g, 0,05, 1346} v´o
.
i
{I, i, 0,4, 2356}, do Sup(GI, gi) = 0, 25 < 0, 4 = minSupGI nˆen kˆe
´
t ho
.
.
p n`ay c˜ung
khˆong thu
.
.
c hiˆe

.
n
du
.
o
.
.
c. Nhu
.
vˆa
.
y nh´anh v´o
.
i n´ut gˆo
´
c {G, g, 0,05, 1346} khˆong ph´at triˆe
’
n
du
.
o
.
.
c n˜u
.
a v`a GD, gd l`a tˆa
.
p phˆo
’
biˆe

´
n m`o
.
d´ong cu
.
.
c
da
.
i.
Tiˆe
´
p tu
.
c v´o
.
i nh´anh c´o n´ut gˆo
´
c l`a {D, d, 0,1, 2456}, nhˆa
.
n x´et thˆa
´
y Sup(DB, db) =
(m
d
(t
2
[D]).m
b
(t

2
[B]) + m
d
(t
4
[D]).m
b
(t
4
[B])/6 = (0,6 ×1,0 + 0,2 ×0.44)/6 = 0,11 < 0,15 =
minSupDB nˆen kˆe
´
t ho
.
.
p n´ut {D, d, 0,1, 2456} v´o
.
i n´ut {B, b, 0,15, 234} khˆong
du
.
o
.
.
c thu
.
.
c
hiˆe
.
n. Tu

.
o
.
ng tu
.
.
do Sup(DI, di) = (0,6 + 0,4 + 0,8)/6 = 0,3 < 0,4 = minSupDI nˆen khˆong
LU
ˆ
A
.
T K
ˆ
E
´
T HO
.
.
P M
`
O
.
C
´
O
D
ˆ
O
.
H

ˆ
O
˜
TRO
.
.
CU
.
.
C TI
ˆ
E
’
U KH
ˆ
ONG GI
ˆ
O
´
NG NHAU
255
kˆe
´
t ho
.
.
p
du
.
o

.
.
c n´ut {D, d, 0,1, 2456} v´o
.
i n´ut {I, i, 0,4, 2356}. N´oi c´ach c´ac tˆa
.
p phˆo
’
biˆe
´
n
m`o
.
khˆong
du
.
o
.
.
c ph´at triˆe
’
n t`u
.
nh´anh c´o n´ut gˆo
´
c {D, d, 0,1, 2456}.
Thu
.
.
c hiˆe

.
n tu
.
o
.
ng tu
.
.
thuˆa
.
t to´an FUZZY CHARM-NEW cho c´ac nh´anh c`on la
.
i. Kˆe
´
t qua
’
cuˆo
´
i c`ung nhˆa
.
n
du
.
o
.
.
c:
- GD, gd l`a tˆa
.
p phˆo

’
biˆe
´
n m`o
.
d´ong cu
.
.
c
da
.
i v´o
.
i
dˆo
.
hˆo
˜
tro
.
.
l`a Sup(GD, gd) = 0,16 (
dˆo
.
hˆo
˜
tro
.
.
cu

.
.
c tiˆe
’
u cu
’
a n´o l`a 0,1);
- B, b l`a tˆa
.
p phˆo
’
biˆe
´
n m`o
.
d´ong cu
.
.
c
da
.
i v´o
.
i
dˆo
.
hˆo
˜
tro
.

.
l`a Sup(B, b) = 0,37 (
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u cu
’
a n´o l`a 0,15);
- I, i l`a tˆa
.
p phˆo
’
biˆe
´
n cu
.
.
c
da
.
i v´o

.
i
dˆo
.
hˆo
˜
tro
.
.
l`a Sup(I, i) = 0,66 (
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u
cu
’
a n´o l`a 0,4);
5. K
ˆ
E
´

T LU
ˆ
A
.
N
B`ai b´ao d˜a dˆe
`
xuˆa
´
t b`ai to´an t`ım c´ac luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
c´o
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe

’
u cu
’
a c´ac tˆa
.
p
mu
.
c d˜u
.
liˆe
.
u khˆong giˆo
´
ng nhau t`u
.
c´ac CSDL
di
.
nh lu
.
o
.
.
ng.
Dˆe
’
gia
’
i quyˆe

´
t b`ai to´an d˘a
.
t ra, mˆo
.
t
sˆo
´
kh´ai niˆe
.
m m´o
.
i
d˜a du
.
o
.
.
c
dˆe
`
xuˆa
´
t, ph´at triˆe
’
n trˆen co
.
so
.
’

tˆon tro
.
ng v`a kˆe
´
th`u
.
a mˆo
.
t sˆo
´
kh´ai
niˆe
.
m cu
’
a nh˜u
.
ng nghiˆen c´u
.
u tru
.
´o
.
c
d´o. Phu
.
o
.
ng ph´ap gia
’

i quyˆe
´
t vˆa
´
n
dˆe
`
o
.
’
dˆay l`a tiˆe
´
p tu
.
c
ph´at triˆe
’
n thuˆa
.
t to´an CHARM-NEW do t´ac gia
’
dˆe
`
xuˆa
´
t. B`ai b´ao c˜ung chı
’
ra c´ac t´ınh chˆa
´
t

d˘a
.
c tru
.
ng co
.
ba
’
n
dˆe
’
xˆay du
.
.
ng thuˆa
.
t to´an FUZZY CHARM-NEW (T´ınh chˆa
´
t 2).
Nh˜u
.
ng vˆa
´
n
dˆe
`
cˆa
`
n tiˆe
´

p tu
.
c nghiˆen c´u
.
u sau b`ai b´ao n`ay:
-
D´anh gi´a ´y ngh˜ıa c´ac luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
v´o
.
i
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’

u khˆong giˆo
´
ng nhau v´o
.
i
mˆo
.
t sˆo
´
c´ach tiˆe
´
p cˆa
.
n kh´ac;
- So s´anh,
d´anh gi´a dˆo
.
ph´u
.
c ta
.
p cu
’
a c´ac thuˆa
.
t to´an ph´at hiˆe
.
n luˆa
.
t kˆe

´
t ho
.
.
p m`o
.
n´oi chung
v`a thuˆa
.
t to´an ph´at hiˆe
.
n luˆa
.
t kˆe
´
t ho
.
.
p m`o
.
c´o
dˆo
.
hˆo
˜
tro
.
.
cu
.

.
c tiˆe
’
u khˆong giˆo
´
ng nhau.
- Nghiˆen c´u
.
u xem c´ac tˆa
.
p mu
.
c d˜u
.
liˆe
.
u m`o
.
c´o ta
.
o th`anh cˆa
´
u tr´uc d`an khˆong? nˆe
´
u c´o th`ı
t`ım hiˆe
’
u t´ınh chˆa
´
t cu

’
a d`an n`ay.
- Xˆay du
.
.
ng chu
.
o
.
ng tr`ınh thu
.
’
nghiˆe
.
m,
dˆe
`
xuˆa
´
t c´ac ngu
.
˜o
.
ng cu
.
.
c tiˆe
’
u ho
.

.
p l´y cu
’
a
dˆo
.
hˆo
˜
tro
.
.
cu
.
.
c tiˆe
’
u v`a cu
’
a kh´ai niˆe
.
m m`o
.
trong ´u
.
ng du
.
ng thu
.
.
c tˆe

´
.
L`o
.
i ca
’
m o
.
n. T´ac gia
’
xin chˆan th`anh ca
’
m o
.
n nh˜u
.
ng ´y kiˆe
´
n v`a b`ınh luˆa
.
n x´ac
d´ang g´op phˆa
`
n ho`an
thiˆe
.
n ho
.
n cho b`ai b´ao.
T

`
AI LI
ˆ
E
.
U THAM KHA
’
O
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.
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Nhˆa
.
n la
.

i sau su
.
’
a ng`ay 17 - 5- 2006