Use of fuzzy logics to identify associations

2. Content
• Introduction
– Data Mining
– Association Rules
– Fuzzy logic
– Applications
• Procedure
– Support and confidence
– Steps
• Example:Risk analysis
– Funda: Conditional probability
– Example analysis

3. Data Mining
• KDD
• Extraction of
Knowledge from Huge
amounts of data
• This knowledge is
– implicit,
– previously unknown
– and potentially useful

4. Association rules
• Item sets (Z:C)
• Antecedent (X:A)
• Consequent (Y:B)
• Ex: If X is A, then Y is
B

5. Application
• Strategic Decision
Making
• Marketing Strategy
formulation
• Predictive analytics:
– CRM
– Machine Maintenance
– Employee Relations
• Artificial Intelligence :
Video games, Robots
• Machines: Air conditioner,
Washing machines, ABS

7. Procedure
• Two factors: Support and Confidence
Trans_ID Bread Butter Biscuit Milk
1 1 1 0 1
2 0 1 1 0
3 1 0 1 0
4 1 1 0 1
5 1 1 1 0
6 1 1 1 1

8. Procedure
• Hypothesis : Customers who buy bread
and butter, also buy milk.
Trans_ID Bread Butter Biscuit Milk
1 1 1 0 1
2 0 1 1 0
3 1 0 1 0
4 1 1 0 1
5 1 1 1 0
6 1 1 1 1
• Support = Desired Outcome/ Total Opportunities
• Support = 3/6 = 0.5

9. Procedure
• Customers who buy bread and butter, also
buy milk.
Trans_ID Bread Butter Biscuit Milk
1 1 1 0 1
2 0 1 1 0
3 1 0 1 0
4 1 1 0 1
5 1 1 1 0
6 1 1 1 1
• Confident = Desired Outcome/ Desired Opportunities
• Confident = 3/4 = 0.75

10. Inference
• Hypothesis becomes Rule :
Customers who buy bread and butter,
also buy milk.
• With 75% confidence and 50% support
from past transactions records

11. Procedure
Fuzzification
• Continuous to Discrete data
Analysis
• Threshold
Defuzzification
• State rule with confidence and
support

13. Bank customer Data set
Case Age Income Risk Credit Result
1 20 52,623 –38,954 red 0
2 26 23,047 –23,636 green 1
3 46 56,810 45,669 green 1
4 31 38,388 –7,968 amber 1
5 28 80,019 –35,125 green 1
6 21 74,561 –47,592 green 1
7 46 65,341 58,119 green 1
8 25 46,504 –30,022 green 1
9 38 65,735 30,571 green 1
10 27 26,047 –6 red 1
RISK = ASSETS – DEBT – WANTS

14. Bank’s weight for each attribute
and condition for analysis
Attribute Weight
Function Percentage
Credit 0.800
Minimum
Risk 0.700 25
Support
Income 0.550 Minimum
90
Age 0.450 Confidence
Result 0.691
Objective : Provide Confident/Risk
factor for the bank to issue loans for
the customers

15. Membership Function

16. Fuzzification
Attribute Level Representation Weight Membership Support
value (Rjk)
Age Young R11 0.450 0.580 0.261
Age Middle R12 0.450 0.300 0.135
Age Old R13 0.450 0.131 0.059
Income High R21 0.550 0.000 0.000
Income Middle R22 0.550 0.890 0.490
Income Low R23 0.550 0.109 0.060
Risk High R31 0.700 0.457 0.320
Risk Middle R32 0.700 0.208 0.146
Risk Low R33 0.700 0.332 0.233
Credit Good R41 0.800 0.720 0.576
Credit Bad R42 0.800 0.280 0.224
Result On Time R51 0.691 0.930 0.643
Result Default R52 0.691 0.069 0.048

17. Item set
• C = complete sets, individual items
• L = Set of items above minimum support,
grouped items
• minsupp = 0.25
• Conditional probability = support

18. Apriori Algorithm
START
Compute
Eliminate
conditional
items < minsupp
probability of each
to form SET L
element in SET C
Is
L=0 YES : STOP
NO : nCr to form
new SET C

19. C1 -> L1 - >C2
C1 Support L1
R11 0.261 R11 C2
R12 0.135 (R11 , R22)
R13 0.059 (R11 , R31)
R21 0.000 (R11 , R41)
R22 0.490 R22 (R11 , R51)
R23 0.060 (R22 , R31)
R31 0.320 R31 (R22 , R41)
R32 0.146 (R22 , R51)
R33 0.233 (R31 , R41)
R41 0.576 R41 (R31 , R51)
R42 0.224 (R41 , R51)
R51 0.643 R51
R52 0.048

20. C2 -> L2 -> C3
C2 Support L2
(R11 , R22) 0.235
(R11 , R31) 0.207 C3
(R11 , R41) 0.212 (R22, R41, R51)
(R11 , R51) 0.230 (R22, R31, R41)
(R22 , R31) 0.237 (R22, R51, R31)
(R22 , R41) 0.419 (R22 , (R31, R41, R51)
(R22 , R51) 0.449 R41)
(R31 , R41) 0.266 (R22 ,
(R31 , R51) 0.264 R51)
(R41 , R51) 0.560 (R31 ,
R41)
(R31 ,

21. C3 -> L3 -> C4
C3 Support L3 C4
(R22, R41, R51) 0.417 (R22, R41, R51) (R22, R31, R41, R51)
(R22, R31, R41) 0.198
(R22, R51, R31) 0.196
(R31, R41, R51) 0.264 (R31, R41, R51)

22. C4 -> L4
C4 Support L4
STOP
(R22, R31, R41,
0.1957
R51)

23. Possible Associations
Items from L2 Associations Items from L3 Associations
R22->R41
(R22, R41) R22, R41->R51
R41->R22
R22->R51 (R22, R41,
(R22, R51) R22, R51->R41
R51->R22 R51)
R3`->R41 R51, R41->R22
(R31,R41)
R41->R31
R31->R51 R31, R41->R51
(R31, R51) (R31, R41,
R31->R51
R31, R51->R41
R41->R51 R51)
(R41, R51) R51, R41->R33
R51->R41

24. Confidence of each association
Items from Confide Items from Association
Associations Confidence
L2 nc L3 s
(R22, R22->R41 0.855 R22, R41-
0.995
>R51
R41) R41->R22 0.727
(R22, R41, R22, R51-
R22->R51 0.916 0.928
(R22, R51) >R41
R51) R51->R22 0.697 R51, R41-
0.744
R3`->R41 0.831 >R22
(R31,R41) R31, R41-
R41->R31 0.462 0.993
>R51
(R31, R31->R51 0.825
(R31, R41, R31, R51-
1.000
R51) R31->R51 0.410
R51) >R41
(R41, R41->R51 0.972 R51, R41-
0.472
>R31
R51) R51->R41 0.870

25. Associations meeting minconf
Items from Confide Items from Association
Associations Confidence
L2 nc L3 s
(R22, R22->R41 0.855 R22, R41-
0.995
>R51
R41) R41->R22 0.727
(R22, R41, R22, R51-
R22->R51 0.916 0.928
(R22, R51) >R41
R51) R51->R22 0.697 R51, R41-
0.744
R3`->R41 0.831 >R22
(R31,R41) R31, R41-
R41->R31 0.462 0.993
>R51
(R31, R31->R51 0.825
(R31, R41, R31, R51-
1.000
R51) R31->R51 0.410
R51) >R41
(R41, R41->R51 0.972 R51, R41-
0.472
>R31
R51) R51->R41 0.870

26. Confident Associations that meet
the objective of the analysis
Items from Confide Items from Association
Associations Confidence
L2 nc L3 s
(R22, R22->R41 0.855 R22, R41-
0.995
>R51
R41) R41->R22 0.727
(R22, R41, R22, R51-
R22->R51 0.916 0.928
(R22, R51) >R41
R51) R51->R22 0.697 R51, R41-
0.744
R3`->R41 0.831 >R22
(R31,R41) R31, R41-
R41->R31 0.462 0.993
>R51
(R31, R31->R51 0.825
(R31, R41, R31, R51-
1.000
R51) R31->R51 0.410
R51) >R41
(R41, R41->R51 0.972 R51, R41-
0.472
>R31
R51) R51->R41 0.870

27. Defuzzification
• If Income is middle, then payment will be
received on time
R22->R51;(91.6%)
• If Credit is good, then payment will be
received on time
R41->R51;(97.2%)
• If Income is middle and Credit is good, then
payment will be received ontime
R41, R22-> R51; (99.5%)
• If Risk is high and Credit is good, then
payment will be received on time
R31, R41->R51; (99.25%)

28. Conclusion

29. References