Some errors in this paper, especially the flowchart and the fitness function. I'm sorry to say that the experiments are misleading!

1. Learning the membership
function contexts for mining
fuzzy association rules by using
genetic algorithms
Jesús Alcalá-Fdez, Rafael Alcalá
María José Gacto, Francisco Herrera
Fuzzy Sets and Systems (2008), article in press
Presenter: Chia-Ming Wang

2. Before we go
Thanks to Prof. Hong who provide me the second paper today.

3. Before we go
• T. Hong, C. Chen,Y. Wu,Y. Lee, Using divide-
and-conquer GA strategy in fuzzy data
mining, in: IEEE Symp. on Fuzzy Systems,
Budapest, Hungary, 2004, pp. 116–121.
• T. Hong, C. Kuo, S. Chi,Trade-off between
time complexity and number of rules for
fuzzy mining from quantitative data, Journal
of Uncertain Fuzziness Knowledge-Based
Systems 9 (5) (2001) 587–604.
Thanks to Prof. Hong who provide me the second paper today.

4. Problem Description
2-tuples Quantitative
GA model Association
Rule

5. A Transaction Database
TID items
1 Bread, Milk
2 Bread, Diaper, Beer, Eggs
3 Milk, Diaper, Beer, Coke
4 Bread, Milk, Diaper, Beer
5 Bread, Milk, Diaper, Coke

6. Association Rule Mining
Examples:
TID items
{Diaper}→{Beer}
1 Bread, Milk {Milk, Bread}→{Eggs, coke}
2 Bread, Diaper, Beer, Eggs {Beer, Bread}→{Milk}
3 Milk, Diaper, Beer, Coke
X→Y, X∩Y=∅
4 Bread, Milk, Diaper, Beer
5 Bread, Milk, Diaper, Coke

7. Association Rule Mining
Examples:
TID items
{Diaper}→{Beer}
1 Bread, Milk {Milk, Bread}→{Eggs, coke}
2 Bread, Diaper, Beer, Eggs {Beer, Bread}→{Milk}
3 Milk, Diaper, Beer, Coke
X→Y, X∩Y=∅
4 Bread, Milk, Diaper, Beer
Implication means co-occurrence,
5 Bread, Milk, Diaper, Coke
not causality!

8. Terminology
Examples:
{Milk, Diaper}→{Beer}
TID items
1 Bread, Milk
2 Bread, Diaper, Beer, Eggs
3 Milk, Diaper, Beer, Coke
4 Bread, Milk, Diaper, Beer
5 Bread, Milk, Diaper, Coke

9. Terminology
Examples:
{Milk, Diaper}→{Beer}
TID items
support
1 Bread, Milk
σ{Milk, Diaper, Beer} 2
s= = = 0.4
2 Bread, Diaper, Beer, Eggs |T| 5
3 Milk, Diaper, Beer, Coke
4 Bread, Milk, Diaper, Beer
5 Bread, Milk, Diaper, Coke

10. Terminology
Examples:
{Milk, Diaper}→{Beer}
TID items
support
1 Bread, Milk
σ{Milk, Diaper, Beer} 2
s= = = 0.4
2 Bread, Diaper, Beer, Eggs |T| 5
3 Milk, Diaper, Beer, Coke confident
4 Bread, Milk, Diaper, Beer c=
σ{Milk, Diaper, Beer} 2
= = 0.67
σ{Milk, Diaper} 3
5 Bread, Milk, Diaper, Coke

11. Terminology
Examples:
{Milk, Diaper}→{Beer}
TID items
support
1 Bread, Milk
σ{Milk, Diaper, Beer} 2
s= = = 0.4
2 Bread, Diaper, Beer, Eggs |T| 5
3 Milk, Diaper, Beer, Coke confident
4 Bread, Milk, Diaper, Beer c=
σ{Milk, Diaper, Beer} 2
= = 0.67
σ{Milk, Diaper} 3
5 Bread, Milk, Diaper, Coke
Itemset, minsup, minconf

12. Real-world
Transaction Database
TID (item, quantity)
1 (Bread, 3), (Milk, 1)
2 (Bread, 1), (Diaper, 2), (Beer, 3), (Eggs, 12)
3 (Milk,2), (Diaper, 4), (Beer, 5), (Coke, 2)
4 (Bread, 3), (Milk, 1), (Diaper, 2), (Beer, 12)
5 (Bread, 2), (Milk, 4), (Diaper, 5), (Coke, 3)

13. Real-world
Transaction Database
TID (item, quantity)
1 (Bread, 3), (Milk, 1)
2 Quantitative 3), (Eggs, 12)
(Bread, 1), (Diaper, 2), (Beer,
Association Rule
3 (Milk,2), (Diaper, 4), (Beer, 5), (Coke, 2)
Mining
4 (Bread, 3), (Milk, 1), (Diaper, 2), (Beer, 12)
5 (Bread, 2), (Milk, 4), (Diaper, 5), (Coke, 3)

14. Quantitative
Association
Rule

15. 2-tuples Quantitative
model Association
Rule

16. Linguistic terms
Low Middle High Low Middle High
age weight
if age is Middle then weight is High

17. The 2-tuples linguistic
representation
if age is Middle then weight is High
F. Herrera, L. Martínez, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans.
Fuzzy Systems 8 (6) (2000) 746–752.

18. The 2-tuples linguistic
representation
if age is Middle then weight is High
if age is (Middle, 0.3) then weight is (High, -0.1)
(si , αi ), si ∈ S, αi ∈ [−0.5, 0.5)
F. Herrera, L. Martínez, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans.
Fuzzy Systems 8 (6) (2000) 746–752.

19. -1 -0.5 0.5 1
s0 s1 s2 s3 s4
domain
0 1 2 3 4
(s2, -0.3)

20. -1 -0.5 0.5 1
s0 s1 s2 s3 s4
-0.3
domain 1.7
0 1 2 3 4
(s2, -0.3)

21. -1 -0.5 0.5 1
s0 s1 s2 s3 s4
-0.3
domain 1.7
0 1 2 3 4
(s2, -0.3)
-0.5 0.5 -0.5 0.5 -0.5 0.5
-0.5 0.5 -0.5 0.5
s0 s1 s2 s3 s4
0 1 2 3 4

22. -1 -0.5 0.5 1
s0 s1 s2 s3 s4
-0.3
domain 1.7
0 1 2 3 4
(s2, -0.3)
-0.5 0.5 -0.5 0.5 -0.5 0.5
-0.5 0.5 -0.5 0.5
α=-0.3
s0 s1 s2 s3 s4
(s2, -0.3)
0 1 2 3 4

23. Interpretation
if age is (Middle, 0.3) then weight is (High, -0.1)

24. Interpretation
if age is (Middle, 0.3) then weight is (High, -0.1)
if age is (higher than Middle)
then weight is (a bit smaller than High)

25. 2-tuples
model

26. 2-tuples
GA model

27. Traditional GA

28. Traditional GA
Population
(chromosomes)

29. Traditional GA
Population
(chromosomes)
parents
Evaluation
(fitness)

30. Traditional GA
Population
(chromosomes)
parents
Evaluation
(fitness)
Reproduction
Mating pool
(selection)

31. Traditional GA
Population
(chromosomes)
parents
‣ crossover Genetic Evaluation
‣ mutation operators (fitness)
Mates Reproduction
Mating pool
(recombination) (selection)

32. Traditional GA
Population
(chromosomes)
offsprings parents
‣ crossover Genetic Evaluation
‣ mutation operators (fitness)
Mates Reproduction
Mating pool
(recombination) (selection)

33. GA Used in this paper
• CHC genetic model
• MFs codification and initial gene pool
• Chromosome evaluation
• Crossover operator

34. GA Used in this paper
• CHC genetic model
• MFs codification and initial gene pool
• Chromosome evaluation
• Crossover operator

35. Scheme of CHC model
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

36. Scheme of CHC model
Initialize population
and THRESHOLD
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

37. Scheme of CHC model
Initialize population Crossover of N
and THRESHOLD parents
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

38. Scheme of CHC model
Initialize population Crossover of N
and THRESHOLD parents
Incest prevention
1/2 * hamming distance > L
L = (#Genes *BITSGENE)/4
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

39. Scheme of CHC model
Initialize population Crossover of N Evaluation of the
and THRESHOLD parents New Individuals
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

40. Scheme of CHC model
Initialize population Crossover of N Evaluation of the
and THRESHOLD parents New Individuals
Selection of the best N
individuals between
parents and offsprings
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

41. Scheme of CHC model
Initialize population Crossover of N Evaluation of the
and THRESHOLD parents New Individuals
Selection of the best N
individuals between
parents and offsprings
if NO new individual,
decrement THRESHOLD
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

42. Scheme of CHC model
Initialize population Crossover of N Evaluation of the
and THRESHOLD parents New Individuals
Selection of the best N
individuals between
parents and offsprings
THRESHOLD if NO new individual,
<0 decrement THRESHOLD
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

43. Scheme of CHC model
Initialize population Crossover of N Evaluation of the
and THRESHOLD parents New Individuals
Selection of the best N
individuals between
parents and offsprings
no
THRESHOLD if NO new individual,
<0 decrement THRESHOLD
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

44. Scheme of CHC model
Initialize population Crossover of N Evaluation of the
and THRESHOLD parents New Individuals
Selection of the best N
individuals between
parents and offsprings
no
Restart the population THRESHOLD if NO new individual,
and THRESHOLD <0 decrement THRESHOLD
yes
L. Eshelman, The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic
recombination, Foundations of Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.

45. GA Used in this paper
• CHC genetic model
• MFs codification and initial gene pool
• Chromosome evaluation
• Crossover operator

46. age L1 M1 H1 L2 M2 H2 weight
L1 M1 H1 L2 M2 H2
0 0 0 0 0 0
MFs
Codification

47. age L1 M1 H1 L2 M2 H2 weight
L1 M1 H1 L2 M2 H2
0 0 0 0 0 0
MFs
Codification
L1 M1 H1 L2 M2 H2
0.2 0.4 0 -0.2 -0.3 -0.5
age L1 M1 H1 L2 M2 H2 weight

48. Initial Gene Pool
chromosome: (c11,...,c1m,c21,...,c2m,...,cn1,...,cnm)
1 item with m MFs
• initial MFs obtained from expert knowledge
• individuals generated at random in [-0.5, 0.5)

49. Implementation:
Gray Code
Decimal Binary Gray Code
0 000 000
1 001 001
2 010 011
3 011 010
4 100 110
5 101 111
6 110 101
7 111 100

50. Implementation:
Gray Code
Decimal Binary Gray Code
0 000 000
1 001 001
2 010 011
3 011 010
4 100 110
5 101 111
6 110 101
7 111 100

51. GA Used in this paper
• CHC genetic model
• MFs codification and initial gene pool
• Chromosome evaluation
• Crossover operator

52. Equation Mania
x∈L1 f uzzy support
f itness(Cq ) =
suitability(Cq )
n
suitability(Cq ) = [overlap f actor(Cqk ) + coverage f actor(Cqk )]
k=1
m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
1
coverage f actor(Cqk )= range(R
1 ,...,Rm )
max(Ik )
n
suitability(Cq ) = [overlap f actor(Cqk ) + 1]
k=1

53. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )

54. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
qth chromosome kth item

55. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
qth chromosome kth item
Ri Rj

56. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
qth chromosome kth item
Ri Rj
overlap

57. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
qth chromosome kth item
Ri Rj
overlap
SpanR

58. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
qth chromosome kth item
Ri Rj
overlap
SpanR
SpanL

59. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
qth chromosome kth item
Ri Rj Ri Rj
overlap overlap
SpanR SpanR
SpanL SpanL

60. m m
overlap(Ri , Rj )
overlap f actor(Cqk ) = [max( , 1) − 1]
i=1 j=i+1
min(spanRRi , spanLRi )
qth chromosome kth item
Ri Rj Ri Rj
penalty
overlap overlap
SpanR SpanR
SpanL SpanL

61. 1
coverage f actor(Cqk )= range(R
1 ,...,Rm )
max(Ik )

62. 1
coverage f actor(Cqk )= range(R
1 ,...,Rm )
max(Ik )
qth chromosome kth item

63. 1
coverage f actor(Cqk )= range(R
1 ,...,Rm )
max(Ik )
qth chromosome kth item
R1 R2 R3
Milk
0 5 10

64. 1
coverage f actor(Cqk )= range(R
1 ,...,Rm )
max(Ik )
qth chromosome kth item
R1 R2 R3 R1 R2 R3
Milk Milk
0 5 10 0 5 10

65. 1
coverage f actor(Cqk )= range(R
1 ,...,Rm )
max(Ik )
qth chromosome kth item
R1 R2 R3 R1 R2 R3
Milk Milk
0 5 10 0 5 10
range

66. 1
coverage f actor(Cqk )= range(R
1 ,...,Rm )
max(Ik )
qth chromosome kth item
R1 R2 R3 R1 R2 R3
Milk Milk
0 5 10 0 5 10
coverage f actor(Cqk ) = 1
range

67. Fuzzy Support (count)

68. Fuzzy Support (count)
DB n item
T

69. Fuzzy Support (count)
DB n item
(i)
vj
T ith

70. Fuzzy Support (count)
DB n item
(i)
vj
T ith
(i) (i)
(i) fj1 fjm
bread fj = + ···
Rj1 Rjm

71. Fuzzy Support (count)
DB n item
(i)
vj
T ith
(i) (i)
(i) fj1 fjm
bread fj = + ···
Rj1 Rjm
item
m mf

72. Fuzzy Support (count)
DB n item
(i)
vj degree
T ith
(i) (i)
(i) fj1 fjm
bread fj = + ···
Rj1 Rjm
item
m mf

73. Fuzzy Support (count)
DB n item
(i)
vj degree
T ith
(i) (i)
(i) fj1 fjm
bread fj = + ···
Rj1 Rjm
T
(i)
countjk = fjk item
i=1 m mf
bread.low.count

74. Fuzzy Support (count)
DB n item
(i)
vj degree
T ith
(i) (i)
(i) fj1 fjm
bread fj = + ···
Rj1 Rjm
T
(i)
countjk = fjk item
i=1 m mf
bread.low.count
L1 = {Rjk |countjk ≥ α, 1 ≤ j ≤ n and 1 ≤ k ≤ m
n item

75. Fuzzy Support
x∈L1 f uzzy support
f itness(Cq ) =
suitability(Cq )

76. Fuzzy Support
x∈L1 f uzzy support
f itness(Cq ) =
suitability(Cq )
n
suitability(Cq ) = [overlap f actor(Cqk ) + 1]
k=1

77. Fuzzy Support
x∈L1 f uzzy support
f itness(Cq ) =
suitability(Cq )
n
suitability(Cq ) = [overlap f actor(Cqk ) + 1]
k=1
n item

78. Fuzzy Support
L1
x∈L1 f uzzy support
f itness(Cq ) =
suitability(Cq )
n
suitability(Cq ) = [overlap f actor(Cqk ) + 1]
k=1
n item

79. Fuzzy Support
L1 count / T # transaction
x∈L1 f uzzy support
f itness(Cq ) =
suitability(Cq )
n
suitability(Cq ) = [overlap f actor(Cqk ) + 1]
k=1
n item

80. GA Used in this paper
• CHC genetic model
• MFs codification and initial gene pool
• Chromosome evaluation
• Crossover operator

81. PCBLX Crossover
X = (x1 · · · xn ) Y = (y1 · · · yn ) (xi , yi ∈ [ai , bi ] ⊂ R, i = 1 · · · n)
O1 = (o11 · · · o1n ) [li , u1 ] li = max{ai , xi − Ii · α} u2 = min{bi , xi + Ii · α}
1
i
1
i
O2 = (o21 · · · o2n ) [li , u2 ] li = max{ai , yi − Ii · α} u2 = min{bi , yi + Ii · α}
2
i
2
i
Ii = |xi − yi |
F. Herrera, M. Lozano, A.M. Sánchez, A taxonomy for the crossover operator for real-coded genetic
algorithms: An experimental study. Int. J. Intell. Syst. 18 (2003) 309-338.

82. PCBLX Crossover
X = (x1 · · · xn ) Y = (y1 · · · yn ) (xi , yi ∈ [ai , bi ] ⊂ R, i = 1 · · · n)
O1 = (o11 · · · o1n ) [li , u1 ] li = max{ai , xi − Ii · α} u2 = min{bi , xi + Ii · α}
1
i
1
i
O2 = (o21 · · · o2n ) [li , u2 ] li = max{ai , yi − Ii · α} u2 = min{bi , yi + Ii · α}
2
i
2
i
Ii = |xi − yi |
ai xi yi bi
PCBLX BLX
F. Herrera, M. Lozano, A.M. Sánchez, A taxonomy for the crossover operator for real-coded genetic
algorithms: An experimental study. Int. J. Intell. Syst. 18 (2003) 309-338.

83. Conceptual Flowchart

84. Conceptual Flowchart
Learning
Membership Function

85. Conceptual Flowchart
Learning
Membership Function
Learning
Process
Predefined MFs
Transaction
Database

86. Conceptual Flowchart
Learning
Membership Function
Learning
Process
Predefined MFs
Evaluation
Module
(Fitness)
Transaction
Database
MFs

87. Conceptual Flowchart
Learning Mining Fuzzy
Membership Function Association Rules
Learning
Process
Predefined MFs
Evaluation
Module
(Fitness)
Transaction
Database
MFs

88. Conceptual Flowchart
Learning Mining Fuzzy
Membership Function Association Rules
Learning Fuzzy
Process mining
Predefined MFs Definitive MFs
Evaluation
Module
(Fitness)
Transaction Transaction
Database Database
MFs

89. Conceptual Flowchart
Learning Mining Fuzzy
Membership Function Association Rules
Learning Fuzzy
Process mining
Predefined MFs Definitive MFs
Evaluation
Module
(Fitness)
Transaction Transaction
Database Database Fuzzy
Association Rules
MFs

90. Procedures
Stage 1
1. initialization
2. evaluate the initial chromosomes
1. for all items in transaction, transfer the
quantitative values to fuzzy sets
2. calculate count, fuzzy support
3. calculate fitness
3. set threshold L
4. generate the next population
5. CHC procedure
6. if # run not reach, goto step4
Stage 2
Mining Fuzzy association rules by (Hong 2001)

91. Experiments

92. Parameters
Proposed Hong’s
• # 50 individuals • 0.01 mutation rate
• 10,000 evaluations • 0.35 d factor
• 30 bits per gene
• 0.6 crossover rate
• 0.8 fuzzy rule
confident

93. Data Set
Bureau of the Census
FAM95
#63,756 instance
#23 attr.
#10 attr.
This data set was obtained from the Statistics Data Sets Archive website http://www.stat.ucla.edu/data/fpp.

94. Results obtained in the
genetic process
Proposed approach Hong el al.’s approach Uniform fuzzy partition
Sup Fit Fsup Suit #1I Sup Fit Fsup Suit #1I Sup Fit Fsup Suit #1I
With three linguistic terms
0.2 0.99 11.68 11.85 20 0.2 0.68 10.83 15.83 19 0.2 0.92 9.24 10.00 16
0.5 0.94 11.68 12.39 17 0.5 0.53 10.28 19.45 15 0.5 0.76 7.55 10.00 10
0.7 0.66 6.98 10.63 9 0.7 0.37 6.55 17.94 8 0.7 0.57 5.71 10.00 7
0.9 0.28 2.80 10.00 3 0.9 0.00 0.00 14.75 0 0.9 0.00 0.00 10.00 0
With five linguistic terms
0.2 0.95 10.46 10.99 22 0.2 0.53 10.22 19.27 22 0.2 0.94 9.43 10.00 21
0.5 0.77 9.92 12.92 15 0.5 0.38 7.95 20.63 12 0.5 0.46 4.57 10.00 7
0.7 0.61 7.69 12.57 10 0.7 0.20 3.96 19.54 5 0.7 0.24 2.36 10.00 3
0.9 0.10 0.92 10.00 1 0.9 0.06 0.90 15.01 1 0.9 0.00 0.00 10.00 0

95. Results obtained in the
genetic process
Proposed approach Hong el al.’s approach Uniform fuzzy partition
Sup Fit Fsup Suit #1I Sup Fit Fsup Suit #1I Sup Fit Fsup Suit #1I
With three linguistic terms
0.2 0.99 11.68 11.85 20 0.2 0.68 10.83 15.83 19 0.2 0.92 9.24 10.00 16
0.5 0.94 11.68 12.39 17 0.5 0.53 10.28 19.45 15 0.5 0.76 7.55 10.00 10
0.7 0.66 6.98 10.63 9 0.7 0.37 6.55 17.94 8 0.7 0.57 5.71 10.00 7
0.9 0.28 2.80 10.00 3 0.9 0.00 0.00 14.75 0 0.9 0.00 0.00 10.00 0
With five linguistic terms
0.2 0.95 10.46 10.99 22 0.2 0.53 10.22 19.27 22 0.2 0.94 9.43 10.00 21
0.5 0.77 9.92 12.92 15 0.5 0.38 7.95 20.63 12 0.5 0.46 4.57 10.00 7
0.7 0.61 7.69 12.57 10 0.7 0.20 3.96 19.54 5 0.7 0.24 2.36 10.00 3
0.9 0.10 0.92 10.00 1 0.9 0.06 0.90 15.01 1 0.9 0.00 0.00 10.00 0

96. Results obtained in the
genetic process
Proposed approach Hong el al.’s approach Uniform fuzzy partition
Sup Fit Fsup Suit #1I Sup Fit Fsup Suit #1I Sup Fit Fsup Suit #1I
With three linguistic terms
0.2 0.99 11.68 11.85 20 0.2 0.68 10.83 15.83 19 0.2 0.92 9.24 10.00 16
0.5 0.94 11.68 12.39 17 0.5 0.53 10.28 19.45 15 0.5 0.76 7.55 10.00 10
0.7 0.66 6.98 10.63 9 0.7 0.37 6.55 17.94 8 0.7 0.57 5.71 10.00 7
0.9 0.28 2.80 10.00 3 0.9 0.00 0.00 14.75 0 0.9 0.00 0.00 10.00 0
With five linguistic terms
0.2 0.95 10.46 10.99 22 0.2 0.53 10.22 19.27 22 0.2 0.94 9.43 10.00 21
0.5 0.77 9.92 12.92 15 0.5 0.38 7.95 20.63 12 0.5 0.46 4.57 10.00 7
0.7 0.61 7.69 12.57 10 0.7 0.20 3.96 19.54 5 0.7 0.24 2.36 10.00 3
0.9 0.10 0.92 10.00 1 0.9 0.06 0.90 15.01 1 0.9 0.00 0.00 10.00 0

97. Results obtained in the
genetic process
Hong el al.’s approach with the 2-tuples
Support Fitness Fsup Suit #1Itemset
With three linguistic terms
0.2 0.97 10.90 11.18 20
0.5 0.89 11.36 12.64 18
0.7 0.59 6.20 10.33 7
0.9 0.26 2.79 10.52 3
With five linguistic terms
0.2 0.93 10.18 10.93 22
0.5 0.64 7.39 11.80 11
0.7 0.41 0.476 11.60 6
0.9 0.08 0.91 10.92 1

98. Fitness vs Function Evaluation
1
Average Fitness Values.
0.8
0.6
0.4
0.2
0
0 2000 4000 6000 8000 10000
Evaluations
The Proposed Approach Hong et al.'s Approach

99. Frequent 1-itemsets vs minsup
Number of Large 1-itemsets
20
15
10
5
0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
Minimum Support
The Proposed Approach Hong et al.'s Approach Uniform Fuzzy Partition

100. MFs w/o lateral displacement
l1' = (l1,0.4) l2' = (l2,0.4) l3' = (l3,0.5) l1' = (l1,0.0) l2' = (l2,-0.2) l3' = (l3,0.0) l1' = (l1,-0.1) l2' = (l2,-0.2) l3' = (l3,0.2)
X1 X2 X3
l1 l2 l3 l1 l2 l3 l1 l2 l3
l1' = (l1,0.0) l2' = (l2,0.0) l3' = (l3,0.4) l1' = (l1,0.1) l2' = (l2,-0.2) l3' = (l3,0.1) l1' = (l1,0.1) l2' = (l2,-0.5) l3' = (l3,0.1)
X4 X5 X6
l1 l2 l3 l1 l2 l3 l1 l2 l3
l1' = (l1,-0.1) l2' = (l2,-0.1) l3' = (l3,0.4) l1' = (l1,0.0) l2' = (l2,-0.2) l3' = (l3,-0.2) l1' = (l1,0.0) l2' = (l2,-0.3) l3' = (l3,0.1)
X7 X8 X9
l1 l2 l3 l1 l2 l3 l1 l2 l3
l1' = (l1,0.0) l2' = (l2,-0.2) l3' = (l3,0.2)
X10
l1 l2 l3

101. Hong’s MFs
l1' l2' l3' l1' l2' l3' l1' l2' l3'
X1 X2 X3
l1 l2 l3 l1 l2 l3 l1 l2 l3
l1' l2' l3' l1' l2' l3' l1' l2' l3'
X4 X5 X6
l1 l2 l3 l1 l2 l3 l1 l2 l3
l1' l2' l3' l1' l2' l3' l1' l2' l3'
X7 X8 X9
l1 l2 l3 l1 l2 l3 l1 l2 l3
l1' l2' l3'
X10
l1 l2 l3

102. #rules vs minsup
minconf = 0.8
160000
140000
120000
Number of Rules
100000
80000
60000
40000
20000
0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
Minimum Support
Proposed Approach Hong et al.'s Approach Uniform Fuzzy Partition

103. #rules vs minconf
minsup = 0.2
90000
80000
70000
Number of Rules
60000
50000
40000
30000
20000
10000
0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
Minimum Confidence
Proposed Approach Hong et al.'s Approach Uniform Fuzzy Partition

104. #rules vs minsup vs
minsup
200000
Number of Rules
150000
100000
50000
0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
Minimum Support
Conf = 0.5 Conf = 0.6 Conf = 0.7 Conf = 0.8 Conf = 0.9

105. #rules vs minsup vs
minsup
200000
Number of Rules
150000
100000
50000
0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
Minimum Confidence
Minsup = 0.1 Minsup = 0.2 Minsup = 0.3
Minsup = 0.4 Minsup = 0.5 Minsup = 0.6

106. Time vs #Transaction
30.00
25.00
Runtime (minutes)
20.00
15.00
10.00
5.00
0.00
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Number of Transactions
Proposed Approach Hong et al.'s Approach

107. Time vs #Attribute
30.00
25.00
Runtime (minutes)
20.00
15.00
10.00
5.00
0.00
2 3 4 5 6 7 8 9 10
Number of Attributes
Proposed Approach Hong et al.'s Approach

108. Time vs #Linguistic terms
70.00
Runtime (minutes)
60.00
50.00
40.00
30.00
20.00
3 4 5 6 7
Number of Linguistic Terms
Proposed Approach Hong et al.'s Approach

109. Example of Rules
If number if children is Low and
Classic Fuzzy hours head worked last week is Low
Association Rule then head’s personal income is Low
(Factor of confidence 0.87)
If number if children is (Low, -0.16) and
Rule with 2-Tuples hours head worked last week is (Low, -0.06)
Representation then head’s personal income is (Low, 0.1)
(Factor of confidence 0.99)

110. Author’s conclusion

111. Author’s conclusion
2-tuples linguistic
representation works!!

112. Discussions

113. T. Hong, C. Chen,Y. Wu,Y. Lee, Using divide-and-conquer GA strategy in fuzzy data mining, IEEE Symp. on Fuzzy Systems,
Budapest, Hungary, 2004, pp. 116–121.

117. Pitfalls
• domain knowledge & Symmetric assumption
• flowchart
• Hong’s method
• inadequate fitness function
• gray code and crossover
• fuzzy association?
• dataset
• replication?
• scalability

118. Pitfalls
• domain knowledge & Symmetric assumption
• flowchart
• Hong’s method
n
suitability(Cq ) = [overlap f actor(Cqk ) + coverage f actor(Cqk )]
k=1
• inadequate fitness function
• gray code and crossover
• fuzzy association?
• dataset
• replication?
• scalability

119. Pitfalls
• domain knowledge & Symmetric assumption
• flowchart
• Hong’s method
• inadequate fitness function
• gray code and crossover
• fuzzy association?
• dataset
• replication?
• scalability

120. Reference
• L. Eshelman, The CHC adaptive search algorithm: How to have safe search when
engaging in nontraditional genetic recombination, in: G. Rawlin (Ed.), Foundations of
Genetic Algorithms, Vol. 1, Morgan Kaufmann, Los Altos, CA, 1991, pp. 265–283.
• F. Herrera, L. Martínez, A 2-tuple fuzzy linguistic representation model for computing
with words, IEEE Trans. Fuzzy Systems 8 (6) (2000) 746–752.
• F. Herrera, M. Lozano, A.M. Sánchez, A taxonomy for the crossover operator for real-
coded genetic algorithms: An experimental study. Int. J. Intell. Syst. 18 (2003) 309-338.
• T. Hong, C. Chen, Y. Wu,Y. Lee, Using divide-and-conquer GA strategy in fuzzy data
mining, in: IEEE Symp. on Fuzzy Systems, Budapest, Hungary, 2004, pp. 116–121.
• T. Hong, C. Chen, Y. Wu,Y. Lee, quot;Genetic-Fuzzy Data Mining with Divide-and-Conquer
Strategyquot;, IEEE Transactions on Evolutionary Computation 12 (2) 252-265.
• T. Hong, C. Kuo, S. Chi, Trade-off between time complexity and number of rules for
fuzzy mining from quantitative data, Journal of Uncertain Fuzziness Knowledge-Based
Systems 9 (5) (2001) 587–604.
• H. Ishibuchi, T. Nakashima, T.Yamamoto, Fuzzy association rules for handling continuous
attributes, in: IEEE Internat. Symp. on Industrial Electronics Proceedings, Pusan, Korea,
2001, pp. 118–121.
• P.-N. Tan, M. Steinbach, and V. Kumar. Introduction to Data Mining, Addison Wesley, May
2005.

121. Thank you!

122. Questions?