Neural-Network-Based Fuzzy Logical Control and Decision System

1. Neural-Network-Based Fuzzy Logical Control and Decision System 主講人 虞台文

2. Content • Introduction • Basic Structure of Fuzzy Systems • Connectionist Fuzzy Logic Control and Decision Systems • Hybrid Learning Algorithm • Example: Fuzzy Control of Unmanned Vehicle

3. Neural-Network-Based Fuzzy Logical Control and Decision System Introduction

4. Reference Chin-Teng Lin and C. S. George Lee, “Neural-network-based fuzzy logic control and decision system,” IEEE Transactions on Computers, Volume: 40 , Issue: 12 , Dec. 1991, Pages:1320 – 1336.

5. Neural-Network & Fuzzy-Logic Systems • Neural-Network Systems • Highly connected PE’s (distributive representation) • Learning capability (Learning from examples) • Learning result is hardly interpretable • Efficient in pattern matching, but inefficient in computation • Fuzzy-Logic Systems • Inference based on human readable fuzzy rules • Linguistic-variable based fuzzy rules • Fuzzy rules from experienced engineers • Fuzzification before inference • Inference using compositional rule • Defuzzification before output

6. Neural-Network & Fuzzy-Logic Systems • Neural-Network Systems • Highly connected PE’s (distributive representation) • Learning capability (Learning from examples) • Learning result is hardly interpretable • Efficient in pattern matching, but inefficient in computation • Fuzzy-Logic Systems • Inference based on human readable fuzzy rules • Linguistic-variable based fuzzy rules • Fuzzy rules from experienced engineers • Fuzzification before inference • Inference using compositional rule • Defuzzification before output Back-propagation learning algorithm is efficient if the appropriate network structure is used. However, the determination of the appropriate network structure is difficult. The construction of fuzzy rule base & the determination of membership functions are subjective.

7. Neuro-Fuzzy Systems Neural Network Fuzzy Logic + Good for learning. Human reasoning scheme. • Supervised leaning • Unsupervised learning • Reinforcement learning • Readable Fuzzy rules • Interpretable Fuzzy rules and membership functions are subjective. Not good for human to interpret its internal representation.

8. Neuro-Fuzzy Systems Neural Network Fuzzy Logic + Good for learning. A neuro-fuzzy system is a fuzzy system that uses a learning algorithm derived from or inspired by neural network theory to determine its parameters by processing data samples. Human reasoning scheme. • Supervised leaning • Unsupervised learning • Reinforcement learning • Readable Fuzzy rules • Interpretable Fuzzy rules and membership functions are subjective. Not good for human to interpret its internal representation.

9. Neuro-Fuzzy Systems Neural Network Fuzzy Logic + fuzzy sets and fuzzy rules A neuro-fuzzy system is a fuzzy system that uses a learning algorithm derived from or inspired by neural network theory to determine its parameters by processing data samples.

10. Neural-Network-Based Fuzzy Logical Control and Decision System Basic Structure of Fuzzy Systems

11. Fuzzifier Inference Engine Defuzzifier Fuzzy Knowledge Base Basic Structure of Fuzzy Systems X Y

12. Fuzzifier Inference Engine Defuzzifier Fuzzy Knowledge Base Fuzzifier Fuzzifier X Y Converts the crisp input to a linguistic variable using the membership functions stored in the fuzzy knowledge base.

13. Fuzzifier Inference Engine Defuzzifier Fuzzy Knowledge Base Inference Engine Inference Engine X Y Using If-Then type fuzzy rules converts the fuzzy input to the fuzzy output.

14. Fuzzifier Inference Engine Defuzzifier Fuzzy Knowledge Base Defuzzifier Defuzzifier X Y Converts the fuzzy output of the inference engine to crisp using membership functions analogous to the ones used by the fuzzifier.

15. Fuzzy Knowledge Base Fuzzifier Inference Engine Defuzzifier X Y Fuzzy Knowledge Base Fuzzy Knowledge Base • Information storage for • Linguistic variables definitions. • Fuzzy rules.

16. Fuzzifier Inference Engine Defuzzifier Fuzzy Knowledge Base Input/Output Vectors X Y

17. MIMO: multiinput and multioutput. Fuzzy Rules

18. MIMO: multiinput and multioutput. Fuzzy Rules MIMO MISO

19. Deffuzzifier y X Fuzzy Reasoning

20. Deffuzzifier  y X Fuzzy Reasoning

21. Deffuzzifier  y X Rule Firing Strengths  1 =  2 = 3 =   4 =

22. Deffuzzifier  y X Fuzzy Sets of Decisions   1 1 =   2 2 = 3 =   3  4 =  4

23. Deffuzzifier  y X Fuzzy Sets of Decisions   1 1 =   2 2 = 3 =   3  4 =  4

24. Deffuzzifier  y X Fuzzy Sets of Decisions

25. Defuzzification  Decision Output Deffuzzifier  Deffuzzifier y X

26. General Model of Fuzzy Controller and Decision Making System

27. Neural-Network-Based Fuzzy Logical Control and Decision System Connectionist Fuzzy Logic Control and Decision Systems

28. output linguistic nodes Layer 5 Output term node Layer 4 rule nodes Layer 3 input term nodes Layer 2 input linguistic nodes Layer 1 The Architecture

29. output linguistic nodes Layer 5 Output term node Layer 4 rule nodes Layer 3 input term nodes Layer 2 input linguistic nodes Layer 1 The Architecture Defuzzifier Inference Engine Fuzzifier

30. output linguistic nodes Layer 5 Output term node Layer 4 rule nodes Layer 3 input term nodes Layer 2 input linguistic nodes Layer 1 The Architecture Fully Connected Fully Connected

31. output linguistic nodes Layer 5 Output term node Layer 4 rule nodes Layer 3 input term nodes Layer 2 input linguistic nodes Layer 1 The Architecture consquent antecedent

32. Basic Structure of Neurons Layer k

33. Layer 1 Neurons

34. width center Layer 2 Neurons

35. Layer 3 Neurons

36. {0, 1} Layer 4 Neurons Down-Up Mode

37. width center Layer 4 Neurons Up-Down Mode

38. Layer 5 Neurons Up-Down Mode

39. Layer 5 Neurons Down-Up Mode

40. Neural-Network-Based Fuzzy Logical Control and Decision System Hybrid Learning Algorithm

41. rule nodes Initialization

42. rule nodes Initialization

43. Two-Phase Learning Scheme • Self-Organized Learning Phase • Unsupervised learning of the membership functions. • Unsupervised learning of the rulebase. • Supervised Learning Phase • Error back-propagation for optimization of the membership functions.

44. Note that the membership functions calculated are far from ideal but this is only a pre-estimation in order to create the rulebase. Unsupervised Learning of the Membership Functions • Step 1: First estimation of the membership function’s centers using Kohonen’s learning rule. • Step 2: The widths of the membership functions are estimated from the widths using a simple mathematical formula.

45. Note that the membership functions calculated are far from ideal but this is only a pre-estimation in order to create the rulebase. Unsupervised Learning of the Membership Functions • Step 1: First estimation of the membership function’s centers using Kohonen’s learning rule. • Step 2: The widths of the membership functions are estimated from the widths using a simple mathematical formula. Winner-take-all:

46. Note that the membership functions calculated are far from ideal but this is only a pre-estimation in order to create the rulebase. Unsupervised Learning of the Membership Functions N-nearest-neighbors • Step 1: First estimation of the membership function’s centers using Kohonen’s learning rule. • Step 2: The widths of the membership functions are estimated from the widths using a simple mathematical formula. Minimize 1-nearest-neighbors r : overlay parameter

47. Method: • Competitive Learning + Learn-if-win • Deletion of rule nodes • Combination of rule nodes Unsupervised Learning of the Rulebase Learn-if-win:

48. Example of Combination of Rule Nodes

49. Learning Rate Error back-propagation for optimization of the membership functions. Supervise Learning Phase

50. How w effects f? w How f effects E? How w effects E? Error back-propagation for optimization of the membership functions. Supervise Learning Phase