1 Introduction
2 Background work
2.1 Transformation-based FRI
2.2 Information gain
2.3 Iterative rule base generation
3 Antecedent weighted T-FRI
3.1 Illustrative case
3.2 Turning rules into training data via reverse engineering
-
Identifying all possible antecedent variables appearing in the rules and all value domains for these variables, and
-
Expanding iteratively each existing rule into one which involves all domain variables such that if a certain antecedent variable is not originally involved in a rule, then that rule is replaced by q rules, with q being the cardinality of the value domain of that variable, so that the variable within each of the expanded rule takes one possible and different value from its domain.
Rules | Variables | ||||
---|---|---|---|---|---|
Temperature | Outlook | Humidity | Wind | Decision | |
\(r^1\)
|
Hot
|
Sunny
| – | – |
Swimming
|
\(r^2\)
|
Hot
|
Cloudy
| – | – |
Swimming
|
\(r^3\)
| – |
Rain
| – | – |
Weight lifting
|
\(r^4\)
|
Mild
| – | – |
Windy
|
Weight lifting
|
\(r^5\)
|
Mild
| – | – |
Not windy
|
Volleyball
|
3.3 Weighting of individual variables
Rules | Variables | ||||
---|---|---|---|---|---|
\(a_1\)
|
\(a_2\)
|
\(\cdots \)
|
\(a_m\)
|
z
| |
\(r^1\)
|
\(A_1^1\)
|
\(A_2^1\)
|
\(\cdots \)
|
\(A_m^1\)
|
\(z^1\)
|
\(r^2\)
|
\(A_1^2\)
|
\(A_2^2\)
|
\(\cdots \)
|
\(A_m^2\)
|
\(z^2\)
|
\(\vdots \)
|
\(\vdots \)
|
\(\vdots \)
|
\(\ddots \)
|
\(\vdots \)
|
\(\vdots \)
|
\(r^N\)
|
\(A_1^N\)
|
\(A_2^N\)
|
\(\cdots \)
|
\(A_m^N\)
|
\(z^N\)
|
Weight |
\(IG_1\)
|
\(IG_2\)
|
\(\cdots \)
|
\(IG_m\)
|
Antecedent |
Temperature
|
Outlook
|
Humidity
|
Wind
|
---|---|---|---|---|
Normalised IG | 0.5000 | 0.4515 | 0.0000 | 0.0485 |
Antecedent attribute | Temperature | Outlook | Humidity | Wind | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Observed value | 0.91 | 0.42 | 0.5 | 0.51 | ||||||
Membership value |
Hot
|
Mild
|
Cool
|
Sunny
|
Cloudy
|
Rain
|
Humid
|
Normal
|
Windy
|
Not windy
|
0.0 | 0.0 | 0.775 | 0.0 | 0.733 | 0.0 | 0.5 | 0.5 | 0.49 | 0.51 |
3.4 Weighted T-FRI
3.4.1 Weight-guided selection of n closest rules
3.4.2 Weighted parameters for intermediate-rule construction
3.4.3 Weighted transformation
4 Experimental evaluation
4.1 Experimental set-up
4.1.1 Datasets
Dataset | Attributes # | Classes # | Instances # |
---|---|---|---|
Iris | 4 | 3 | 150 |
Diabetes | 8 | 2 | 768 |
Phoneme | 5 | 2 | 5404 |
Appendicitis | 7 | 2 | 106 |
Magic | 10 | 2 | 1902 |
NewThyroid | 5 | 3 | 215 |
Banana | 2 | 2 | 5300 |
Haberman | 3 | 2 | 306 |
Monk-2 | 6 | 2 | 432 |
4.1.2 Experimental methodology
Dataset |
CRI
|
T-FRI
|
IG-T-FRI
|
---|---|---|---|
Iris | 66.66 ± 0.25 | 76.99 ± 0.16* | 82.53 ± 0.13* |
Diabetes | 32.10 ± 0.08 | 62.50 ± 0.06* | 68.49 ± 0.05* |
Phoneme | 38.40 ± 0.09 | 60.53 ± 0.05* | 66.18 ± 0.07* |
Appendicitis | 32.27 ± 0.10 | 57.72 ± 0.12* | 69.69 ± 0.13* |
Magic | 49.15 ± 0.05 | 58.40 ± 0.09* | 64.67 ± 0.05* |
NewThyroid | 43.33 ± 0.28 | 47.43 ± 0.24* | 53.28 ± 0.22* |
Banana | 44.83 ± 0.08 | 60.49 ± 0.05* | 63.27 ± 0.04* |
Haberman | 54.00 ± 0.09 | 71.73 ± 0.08* | 77.47 ± 0.07* |
Monk-2 | 32.63 ± 0.05 | 60.01 ± 0.11* | 63.31 ± 0.06* |
Average | 43.70 ± 0.12 | 61.75 ± 0.11 | 67.65 ± 0.09 |
4.2 Results and discussion
4.2.1 Comparison on overall classification accuracy
Classified | ||
---|---|---|
Positive | Negative | |
Actual | ||
Positive | 9.5 | 17.6 |
Negative | 11.2 | 38.5 |
Classified | ||
---|---|---|
Positive | Negative | |
Actual | ||
Positive | 17.2 | 9.9 |
Negative | 14.3 | 35.4 |