1. Creating fuzzy rules from numerical data using a neural network
References:
T. Nishina & M. Hagiwara, “Fuzzy Inference Neural Network,” Neurocomputing 14(1997),

2. Preconditions
Assume some numerical training data, which has been obtained empirically
Assume a known number of inputs and outputs

3. Three phases Self-organised learning (competitive learning)
Rule extraction
Rule refinement (supervised learning)

4. Network architecture

5. Network architecture(2)
Connections from the inputs have both a weight and a width
Connections to the outputs have only a weight
Initialize all widths to “lots”
Input weights = centres

6. Network behaviour
Rule layer:
Output layer:

7. Self-organised learning
Uses competitive learning
Winning rule node (middle layer) is the one whose weight vector produces the “best” results, i.e. Whose outputs are nearest to the actual data
All weight vectors of all rule nodes are updated, taking into account how close their weight vectors are to the that of the winning node

8. Learning Rule
Each weight vector is updated according to:

9. Rule extraction Starting off with many rule nodes
Now merge similar ones together
Remaining rules are much more general

10. Rule extraction: algorithm
For each pair of rule nodes, find the Euclidean distance between their weight vectors
If the distance is under a certain threshold, merge the two rule nodes by taking the average weight vector
Repeat until no more merging occurs

11. Supervised learning The rules can still be refined further
Given the training inputs, the actual outputs will still have some error
Use this error to adjust the weights and widths
LMS algorithm

12. Supervised learning formulae

13. Final result In the end, each rule node represents one rule
Each rule is of the form: “IF input1 is catagory1 AND input2 is catagory2 AND...THEN the outputs should be [whatever]”
Whether or not inputx is of catagoryx is up to a membership function with known parameters

14. Example application Steering a remote control car around corners
Inputs = various distances to the walls, current steering angle
Output = next steering angle
Numerical data: collected while car was correctly run by a human operator

15. Remote control car: diagram

16. Remote control car: results
32 rules were found