=Paper=
{{Paper
|id=Vol-1494/paper7
|storemode=property
|title=New Approach to Mining Fuzzy Association Rule with
Linguistic Threshold Based on Hedge Algebras
|pdfUrl=https://ceur-ws.org/Vol-1494/paper7.pdf
|volume=Vol-1494
|dblpUrl=https://dblp.org/rec/conf/iwost/PhuongKT15
}}
==New Approach to Mining Fuzzy Association Rule with
Linguistic Threshold Based on Hedge Algebras==
https://ceur-ws.org/Vol-1494/paper7.pdf
New Approach to Mining
Fuzzy Association Rule with Linguistic
Threshold Based on Hedge Algebras
Le Anh Phuong1 , Tran Dinh Khang2 , Nguyen Vinh Trung3
1
Department of Computer Science, Hue University of Education, Hue University
2
SoICT, Hanoi University of Science and Technology
3
Information Technology Center, Hue University of Education, Hue University
Abstract. The authors [2-5] have studied and presented the quantita-
tive method of linguistic variables and linguistic threshold by fuzzy set.
Chien-Hua Wang, Chin-Pang Tzong proposed an algorithms for min-
ing fuzzy association rule [2]. In this paper, we extend the algorithms
proposed in [2] for number data and linguistic variables by using hedge
algebras.
Keywords: fuzzy association rules, linguistic threshold, hedge algebra
1 Introduction
Data mining with the approach of association rules is one of important aspects
in the field of data mining.
Many authors have presented various methods, algorithms of data mining
by association rules with numerical support and confidence value. However, in
reality, these values are natural linguistic ones. Besides, importance value of each
item is evaluated not only by quantity, frequency of occurrence in each trans-
action but also by the qualitative evaluation of administrators (for those items)
by natural language. And hedge algebra have met the requirements for directly
processing calculation on linguistic value (without fuzzification, but with di-
rect calculation based on qualitative semantic function and flexible calculation).
Thus, it is necessary to establish a method of data mining by association rules
with hedge algebra, in which the input is qualitative transactional database and
qualitative evaluation table of those database items and the support, confidence
values are also natural language ones.
2 Knowledge Base
2.1 Association rules
Let I = I1 , I2 , . . . , Im be a set of items. Let D, the task-relevant data, be a set of
database transactions where each transaction T is a set of items, such is T ✓ I.
Each transaction is associated with an identi er, called TID.
2 Le Anh Phuong, Tran Dinh Khang & Nguyen Vinh Trung
Definition 1. An association rule has the form of X ! Y , where X ✓ I,
Y ✓ I, and X \ Y = ✓.
Definition 2. The support of association rule X ! Y the probability that X [Y
exists in a transaction in the database D.
|X \ Y |
support(X ! Y ) =
|N |
Definition 3. The confidence of the association rule X ! Y is the probability
that X [ Y exists given that a transaction contains X, i.e.
support(X [ Y ) |X \ Y |
confidence (X ! Y ) = =
support(X) |X|
Where: |X| is the number of transactions, including X; |X \ Y | is the number
of transactions, including X and Y ; N is the total of transaction database.
Mining the association rules of the database is finding all of the rules that
have the degree of support and confidence greater than degree of support minsup
and confidence minconf determined by the available user.
2.2 Hedge algebras (HA)
Let X be a linguistic variable and X be a set of its terms, called a term-domain of
X. E.g. if X is the rotation speed of an electrical motor and linguistic hedges used
to describe its speed are V ery, M ore, P ossibly, Little, denoted correspondingly
for short by V, M, P and L, then X = {f ast, V f ast, M f ast, LP f ast, Lf ast,
P f ast, Lslow, slow, P slow, V slow, ...} U 0, W, 1 is a term-domain of X.
It can be considered as an abstract algebra AX = (X, C, H, ), where H is
a set of linguistic hedges, which can be regarded as one-argument operations,
is called a semantics-based ordering relation on X and W, 0, 1 is a set of
constants in X with fast and slow being primary terms of X and W, 0, 1 being
additional elements in X interpreted as the neutral, the least and the greatest
ones, respectively. Denote by hx the result of applying an h 2 H to x 2 X and
by H(x) the set of all u 2 X generated algebraically from x by using hedges in
H, i.e. H(x) = u: u = hn ...h1 x, h1 , ..., hn 2 H.
It is natural that there is a demand to transform fuzzy sets defined on a
real interval [a, b], which represents the meaning of terms in a term-domain X,
into [a, b] or, for normalization, into [0, 1]. This defines a mapping of the term-
domain X into [0, 1], called in the algebraic approach a semantically quantifying
mapping. Now, we take these mappings in mind to define a notion of fuzziness
measure. Let us consider a mapping f from X into [0, 1], which preserves the
ordering relation on X. Then, the “size” of the set H(x), for x 2 X, can be
measured by the diameter of f (H(x)) ✓ [0, 1]. That is that this diameter will
be considered as a fuzzy measure of the term x. Taking this model of fuzziness
measure in mind, we may adopt the following definition:
Let AX = (X, C, H, ) be a linear HA. An f m: X ! [0, 1] is said to be a
fuzzy measure of terms in X if:
New Approach to Mining Fuzzy Association Rule... 3
Definition 4. For each x 2 X, the length of x is denoted by |x|, and defined
as follows:
1) if x = c+ or x = c then |x| = 1.
2) if x = hx0 then |x| = 1 + |x0 |, for all h 2 H.
Proposition 1. The fuzziness measure (f m) and the fuzziness measure of hedge
h, denoted by µ (h), 8h 2 H, with the following properties:
1) f m(hx) = µ(h) ⇥ f m(x) with 8x 2 X;
2) fPm(c+ ) + f m(c ) = 1;
3) P qip,i6=0 f m(hi c) = f m(c), c 2 {c+ , c };
4) P qip,i6=0 f m(hi x) P = f m(x);
5) qi 1 µ(h i ) = ↵, 1jp µ(hj ) = , ↵ + = 1, (↵, > 0)
3 Algorithm
Table 1. The symbols used in the algorithm
Symbol The meaning Symbol The meaning
D transaction database D⇠ fuzzy transaction database
minsup minimum support minconf minimum confidence
min s threshold language of minsup min c threshold language of minconf
N the total number of transac- M the total number of items
tion data
d the total number of managers V hedge “Very”
X linguistics variable M hedge “More”
P hedge “Possibly” L hedge “Less”
K The number of fuzzy parti-
tions in each items
Input:
- D: The data set includes n quantitative transactions;
- Table qualitative: A set of m items with their importance evaluated by d
managers;
- A pre-defined linguistic minimum support valuemin s and linguistic mini-
mum confidence valuemin c.
Output: A set of fuzzy association rules.
Method: Includes 9 following general steps:
Step 1: Identify minsup, minconf from the pre-definedthreshold lin-
guistic.
Transform min sas X variables in HA. Including:
+ Calculate the fuzzy of variable X: f m(X);
+ Identify fuzzy approximately of X: I(X) = [a, b];
4 Le Anh Phuong, Tran Dinh Khang & Nguyen Vinh Trung
+ The fuzzy average value of the variable X:
a+b
gt(X) = ; (1)
2
+ Similarly, the linguistic confidence min c;
+ Select linguistic thresholds (X, Y ), respectively to the fuzzy value of (X, Y )
as minsup, minconf: minsup(X) = gt(X); minconf (X) = gt(Y).
Step 2: Handling qualitative table: A set of m items with their importance
evaluated by d managers
+ Calculate the fuzzy of linguistic variables;
+ Calculate the average o↵uzzy approximatelyqualitativeterms for all items.
d
X
1
kdt⇠
tb (j) = ⇥ (a(j)i , b(j)i ) ; (has the form: [aj , bj ]) (2)
d i=1
+ Calculate the average of fuzzy value for each item:
a j + bj
gtdt⇠
tb (j) = ; (3)
2
where: aj and bj are the values of kdt⇠ ⇠
tb (j), which kdttb (j) = [aj , bj ]
Step 3: Handling n quantitative transactions.
+ Transform the quantitative valueas Aj (j = (1, m)) as X variables in HA
(X 2 X), determined as follows:
Xsl = (Xsl , Gsl , Hsl , ), with: Gsl = {High, Low}, (High = H, Low = L);
+
c+ = {H}; c = {L}; Hsl = {V ery, M ore}; Hsl = {Less, P ossibly}; (with
V ery > M ore; Less > P ossibly)
- Selection: Dom(sl); fm(H); fm(L); fm(V); fm(M); fm(L); fm(P);
- Identify fuzzy approximately of X is I(X), with X 2 X
- Transform the quantitative value of item into [0, 1] respectively;
With each Aj 2 [0, 1] that into fuzzy approximately I(X), respectively;
+ Statistics of fuzzy partitions in D⇠
+ Find the largest fuzzy partition as representative of each item j th :
max countj = max(countji ), with i = (1, K); (4)
Step 4: Calculate the fuzzy support of each item (j = 1, m), as:
gtdt⇠
tb (j) ⇥ max countj
sup(j) = ; (5)
N
where gtdt⇠tb (j) is the qualitative value (calculated by formula (3), in step 2);
max countj is the quantitative vaule (calculated by formula (4), in step 3); and
N is the total number of transaction data, N = |D|.
Step 5: Filter out all items in D⇠ , such that: satisfied frequent item
of minimum support: sup(item) minsup.
Step 6: Establish Fuzzy FP-tree: establish Header table; establish FP-tree
Step 7: Calculate the fuzzy qualitative of n-itemset (K n 2).
New Approach to Mining Fuzzy Association Rule... 5
+ Find out of all frequent itemsets (denote by n-itemset) from FP-tree;
+ Calculate the qualitative of n-itemset.
Step 8: Calculate the fuzzy support of each n-itemset.
+ Using the formula (5) - in step 4:
gtdt⇠
tb (j) ⇥ max countj
sup(n itemset) = ;
N
+ Filter out all n-itemset, such that: satisfied frequent items of minimum sup-
port: sup(n itemset) minsup. (n 2)
Step 9: Export rules, calculate the confidence and check with minconf.
Using the following substeps:
+ Check the association rules from result of step 8, each n-itemset with items
(A1 , A2 , ..., An ), (n = 2, M ): A1^ ... ^ Ai 1^ Ai+1 ...An ! Ai ; (i = 1, M )
+ Calculate the fuzzy confidence value of each possible fuzzy association rule as:
sup(A [ B)
conf (A ! B) = ; (6)
sup(A)
+ Select the satisfied fuzzy association rule of minimum confidence.
During use of HA for fuzzy transaction database and quantify of linguitics,
we view each element of HA is a fuzzy region. So, the process of creating fuzzy
region based on the structure of HA will simple, intuitive, and more fficient.
4 An example
In this section, an example is given to illustrate the proposed algorithm.
Input: includes three data follows:
1. The data set includes six quantitative transactions, as show in Table 2.
2. The importance of the items is evaluated by three managers as shown in
Table 3.
3. A pre-defined linguistic minimum support value min s and linguistic min-
imum confidence value min c.
Table 2. Data transactions (denoted by D)
TID Items
1 (A, 3) (B, 4) (C, 2) (D, 3) (E, 7) (F, 2)
2 (A, 3) (B, 7) (D, 3) (E, 10) (F, 7)
3 (A, 2) (B, 10) (C, 5) (D, 2) (E, 10) (F, 5)
4 (B, 10) (C, 10) (E, 10) (F, 10)
5 (A, 7) (D, 7) (E, 7) (F, 10)
6 (A, 2) (B, 10) (D, 2) (E,10) (F,10)
6 Le Anh Phuong, Tran Dinh Khang & Nguyen Vinh Trung
Table 3. The item importance evaluated by three managers
Item Manager 1 Manger 2 Manager 3
A Important Ordinary Ordinary
B Very Important Important Important
C Ordinary Important Important
D UnImportant UnImportant Very UnImportant
E Important Important Important
F Important Important Ordinary
Output: A set of fuzzy association rules.
Method: Includes 9 following general steps:
Step 1: Identify minsup, minconf from the pre-defined threshold lin-
guistic
Identify parameters in HA: X = (X, G, H, ), with:
G = {Low, High}; c+ = High (denoted by H); c = Low (denoted by L); H+ =
{V ery, M ore}, H = {Less, P ossibly}; (with: V ery > M ore; Less > P ossibly)
with: f m(L) = 0.3; f m(H) = 0.7; f m(V ) = f m(M ) = f m(L) = f m(P ) = 0.25;
Identify fuzzy degree and fuzzy approximately of X:
With the variable X contains c = “Low”:
+ f m(V L) = 0.25 ⇥ 0.3 = 0.075 ) I(V L) = [0, 0.075] ) I(V L)T B = 3.75%
+ f m(M L) = 0.25 ⇥ 0.3 = 0.075 ) I(M L) = [0.075, 0.15] ) I(M L)T B =
11.25%
+ f m(P L) = 0.25 ⇥ 0.3 = 0.075 ) I(P L) = [0.15, 0.225] ) I(P L)T B =
18.75%
+ f m(LL) = 0.25 ⇥ 0.3 = 0.075 ) I(LL) = [0.225, 0.3] ) I(LL)T B = 26.25%
Similar, with the variable X contains c+ = “High”:
+ f m(LH) = 0.25⇥0.7 = 0.175 ) I(LH) = [0.3, 0.475] ) I(LH)T B = 38.75%
+ f m(P H) = 0.25 ⇥ 0.7 = 0.175 ) I(P H) = [0.475, 0.65] ) I(P H)T B =
56.25%
+ f m(M H) = 0.25 ⇥ 0.7 = 0.175 ) I(M H) = [0.65, 0.825] ) I(M H)T B =
73.75%
+ f m(V H) = 0.25 ⇥ 0.7 = 0.175 ) I(V H) = [0.825, 0.1] ) I(V H)T B =
91.25%
- Select minsupport with linguistic thresholds as “Less Low” (denoted by LL)
minsup = minsup(LL) = 26.25%
- Select minconf with linguistic thresholds as “More High” (denoted by MH)
minconf = minconf (M H) = 73.75%
Step 2: Handling qualitative table: A set of m items with their importance
evaluated by 03 managers.
Identify parameters in HA: Denote:
I: Important; uI: UnImportant; O: Ordinary;
VI: Very Important; VuI: Very UnImportant;
New Approach to Mining Fuzzy Association Rule... 7
Xqt = (Xqt , Gqt , Hqt , ), with: Gqt = {Important, U nImportant}; c+ =
+
Important; c = U nImportant; Hqt = {V ery, M ore}; Hqt = {Less, P ossibly};
(with: V ery > M ore; Less > P ossibly).
Let: Wqt = 0.5; f m(I) = 0.4; f m(uI) = 0.6; f m(V ) = 0.3; f m(M ) = 0.2;
f m(L) = 0.3; f m(P ) = 0.2;
Should have: f m(V I) = 0.3 ⇥ 0.4 = 0.12 ) I(V I) = [0.88, 1]; f m(V uI) =
0.3 ⇥ 0.6 = 0.18 ) I(V uI) = [0, 0.18]; f m(O) = 0.5 ) I(O) = [0.25, 0.75];
Table 3 is converted into Table 4, where kdt⇠ tb is the average of fuzzy approx-
imately qualitative; gtdt⇠
tb is the average of fuzzy value.
Table 4. The item importance evaluated by three managers
Item Manager 1 Manger 2 Manager 3 kdt⇠tb gtdt⇠
tb
A [0.6, 1] [0.25, 0.75] [0.25, 0.75] [0.367, 0.833] 0.6
B [0.88, 1] [0.6, 1] [0.6, 1] [0.693, 1] 0.85
C [0.25, 0.75] [0.6, 1] [0.6, 1] [0.483, 0.92] 0.7
D [0, 0.6] [0, 0.6] [0, 0.18] [0, 0.46] 0.23
E [0.6, 1] [0.6, 1] [0.6, 1] [0.6, 1] 0.8
F [0.6, 1] [0.6, 1] [0.25, 0.75] [0.483, 0.92] 0.7
Step 3: Handling n quantitative transactions.
Transform the quantitative valueas Aj (j = 1, m) as X variables in HA
(X 2 X), determined as follows:
Xsl = (Xsl , Gsl , Hsl , ), with:
Gsl = {c , c+ }, with: c+ = High (denoted by H); c = Low (denoted by L);
+
Hsl = {V ery, M ore}; Hsl = {Less, P ossibly}; (with: V ery > M ore; Less >
P ossibly) (V ery, M ore, Less, P ossibly denoted by: V , M , L, P respectively)
Let: Dom(sl) = [0, 13]; f m(H) = 0.4; f m(L) = 0.6; f m(V ) = 0.15; f m(M ) =
0.25; f m(L) = 0.35; f m(P ) = 0.25;
Should have: f m(V L) = 0.15 ⇥ 0.6 = 0.09; f m(M L) = 0.25 ⇥ 0.6 = 0.15;
f m(P L) = 0.25 ⇥ 0.6 = 0.15; f m(LL) = 0.35 ⇥ 0.6 = 0.21;
Because: V L < M L < Low < P L < LL, should: I(V L) = [0, 0.09]; I(M L) =
[0.09, 0.24]; I(P L) = [0.24, 0.39]; I(LL) = [0.39, 0.6];
Similar: f m(V H) = 0.15 ⇥ 0.4 = 0.06; f m(M H) = 0.25 ⇥ 0.4 = 0.1;
f m(P H) = 0.25 ⇥ 0.4 = 0.1; f m(LH) = 0.35 ⇥ 0.4 = 0.14;
Because: V H > M H > High > P L > LH, should: I(LH) = [0.6, 0.74];
I(P H) = [0.74, 0.84]; I(M H) = [0.84, 0.94]; I(V H) = [0.94, 1.0].
From: Dom(sl) = 2, 3, 4, 5, 7, 8, 9, 10 convert into [0, 1]
Converted into: Dom(sl) = {0.15, 0.23, 0.3, 0.38, 0.53, 0.61, 0.69, 0.76}
Because: 0.15, 0.23 2 [0.09, 0.24] ⌘ M L should: 0.15 and 0.23 2 M L;
Similar: 0.3 and 0.38 2 [0.24, 0.39] ⌘ P L; 0.53 2 [0.39, 0.6] ⌘ LL; 0.61 and
0.69 2 [0.6, 0.74] ⌘ LH; 0.76 2 [0.74, 0.84] ⌘ P H.
We tabulated transaction was fuzzy
Next, statistics of fuzzy partitions in D⇠ (result from table 5)
8 Le Anh Phuong, Tran Dinh Khang & Nguyen Vinh Trung
Table 5. Database transaction was fuzzy (denoted by D⇠ )
TID Fuzzy items
1 (0.23/A.ML) (0.3/B.PL) (0.15/C.ML) (0.23/D.ML) (0.53/E.LL) (0.15/F.ML)
2 (0.23/A.ML) (0.53/B.LL) (0.23/D.ML) (0.76/E.PH) (0.53/F.LL)
3 (0.15/A.ML) (0.76/B.PH) (0.38/C.PL) (0.15/D.ML) (0.76/E.PH) (0.53/F.LL)
4 (0.76/B.PH) (0.76/C.PH) (0.76/E.PH) (0.76/F.PH)
5 (0.53/A.LL) (0.53/D.LL) (0.53/E.LL) (0.76/F.PH)
6 (0.15A.ML) (0.76/B.PH) (0.15/D.ML) (0.76/E.PH)(0.76/F.PH)
Table 6. Statistics of fuzzy partitions
Fuzzy item Count Fuzzy item Count
A.ML 0.76 D.ML 0.76
A.LL 0.53 D.LL 0.53
B.PL 0.30 E.LL 1.06
B.LL 0.53 E.PH 3.04
B.PH 2.28 E.LL 0.53
C.ML 0.15 F.ML 0.15
C.ML 0.38 F.LL 1.06
C.PH 0.76 F.PH 2.28
Using formula (4), find out the largest fuzzy partition (result from table 6)
as representative of each item:
Table 7. Fuzzy item
Fuzzy item Count Fuzzy item Count
E.PH 3.04 A.ML 0.76
F.PH 2.28 D.ML 0.76
B.PH 2.28 C.PH 0.76
Step 4: Calculate the fuzzy support of each item (1-itemset).
Using formula (5): For example with item E.P H:
+ fuzzy approximately of support: ([0.6, 1] ⇥ 3.04)/6 = [0.304, 0.51];
+ fuzzy value of support: (0.304 + 0.51)/2 = 0.41 = 41%.
Step 5: Filter out all items in D⇠ . Such that: satisfied frequent item of
minimum support: sup(item) minsup.
If: sup(item) < minsup (with: minsup = 26.25%, result at Step 1)
Then: remove item in table 8.
Step 6: Establish fuzzy FP-tree: see figure 1
Step 7: Calculate the fuzzy qualitative of n-itemset
Substep 7.1: Find out of all frequent itemsets (denote by n-itemset) from FP-tree
(see Table 11)
New Approach to Mining Fuzzy Association Rule... 9
Table 8. Fuzzy support
Item fuzzy Fuzzy approximately Fuzzy support
E.PH (0.304, 0.51) 41%
F.PH (0.483, 0.92) ⇥ 2.28/6 27%
B.PH (0.693, 1) ⇥ 2.28/6 32%
A.ML (0.367, 0.833) ⇥ 0.76/6 7.6%
Establish Header table Table 10. Filter D⇠
Table 9. Header
TID Transaction
Item fuzzy Support 1 (0.76/E.PH)
E.PH 41% 2 (0.76/B.PH) (0.76/E.PH)
B.PH 32% 3 (0.76/B.PH) (0.76/E.PH) (0.76/F.PH)
F.PH 27% 4 (0.76/F.PH)
5 (0.76/B.PH) (0.76/E.PH) (0.76/F.PH)
Fig. 2. Fuzzy approximately of 2 items
Fig. 1. Tree FP-tree on the qualitative attributes
Substep 7.2: Calculate the fuzzyqualitative of n-itemset.
For example with itemset BF: Fuzzyqualitative of B, F as [0.483, 0.92],
[0.693,1], respectiely in figure 2.
Fuzzyqualitative of itemset BF as [0.693, 0.92]. Similar for other itemset.
Step 8: Calculate the fuzzy support of each n-itemset (n 2)
Using the formula (5), example for itemset FE:
1.52 ⇥ 0.76
sup(F.P H, E.P H) = = 0.19 = 19%
6
Thus, only itemset E.PH, B.PH satisfied frequent items of minsup.
Step 9: Export rules, calculate the confidence and check with minconf.
Result from step 8, we check two rules:
+ E.P H ! B.P H:
sup(E.P H [ B.P H) 0.32
conf (E.P H ! B.P H) = = = 78%
sup(E.P H) 0.41
> minconf (M H) = 73.75%;
+ B.P H ! E.P H:
sup(E.P H [ B.P H) 0.32
conf (B.P H ! E.P H) = = = 99%
sup(B.P H) 0.323
> minconf (V H) = 91.25%.
10 Le Anh Phuong, Tran Dinh Khang & Nguyen Vinh Trung
Table 11. Itemset should check the frequently
2-item 3-item
F.PH, B.PH: 1.52; F.PH, E.PH: 1.52; B.PH, E.PH: 2.28 F.PH, B.PH, E.PH: 1.52
Table 12. Fuzzy approximately of 2
items on the qualitative attributes Table 13. Supportof itemset
itemset kdt⇠
tb gtdt⇠
tb Itemset Support Minsup = 26.25%
F.PH, B.PH (0.693, 0.92) 81% F.PH, E.PH 19% unselected
F.PH, E.PH (0.6, 0.92) 76% F.PH, B.PH 21% unselected
B.PH, E.PH (0.693, 1) 85% E.PH, B.PH 32% selected
F.PH, B.PH, (0.693, 0.92) 81% F.PH, B.PH, 21% unselected
E.PH E.PH
Result, we have 2 rules:
+ If E.PH then B.PH with a LL support and a MH confidence.
If a Possibly High number of item E is bought, then a Possibly High number
of item B is bought with a Less Low support and a MoreHigh confidence.
+ If B.PH then E.PH with a LL support and a VH confidence.
If a Possibly High number of item B is bought, then a Possibly High number
of item E is bought with a Less Low support and a Very High confidence.
5 Conclusion
The paper is an extension of the evaluation of fuzzy association rules was re-
searched by Chien-Hua Wang and Chin-Pang Tzong [2], using algebras instead of
fuzzy sets. The optimization of the parameters of quantitative semantic content
in order to fit various problems will be discussed in our next papers.
References
1. Tran Thai Son and Nguyen Anh Tuan, Improve efficiency of fuzzy association rule
using hedge algebra approach, Journal of Computer Science and Cybernetics, v.30,
n.4, 397–408, 2014
2. Chien-Hua Wang and Chin-Tzong Pang, Finding Fuzzy Association Rules Using
FWFP-Growth with linguistic Supports and Confidences, World Academy of Sci-
ence, Engineering and Technology, 29, 1133-1141, 2009
3. Chien-Hua Wang, Chin-Tzong Pang and Sheng-Hsing Liu, Mining association rules
uses fuzzy weighted FP-growth, Soft Computing and Intelligent Systems (SCIS) and
13th International Symposium on Advanced Intelligent Systems (ISIS), 2012 Joint
6th International Conference on, 13498461, 983 – 988, 2012
4. Tzung-Pei Hong , Chun-Wei Lin and Wen-Hsiang Lu, Lingguitic data mining with
fuzzy FP-trees, Expert Systems with Applications 37, 4560-4567, 2010
5. Tzung-Pei Hong, Minh-Jer Chiang and Shyue-Liang Wang, Data Mining with Lin-
guistic Thresholds, Int.Jcontemp. Math. Sciences, vol 7, n. 35, 1711 - 1725, 2012