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Chapter 9 FUZZY INFERENCE

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  1. Chapter 9FUZZY INFERENCE Chi-Yuan Yeh

  2. GMP and GMT

  3. Fuzzy rule as a relation

  4. Fuzzy implications

  5. Example of Fuzzy implications

  6. Example of Fuzzy implications

  7. Example of Fuzzy implications

  8. Compositional rule of inference The inference procedure is called as the “compositional rule of inference”. The inference is determined by two factors : “implication operator” and “composition operator”. For the implication, the two operators are often used: For the composition, the two operators are often used:

  9. Representation of Fuzzy Rule Single input and single output Multiple inputs and single output Multiple inputs and Multiple outputs

  10. Representation of Fuzzy Rule Multiple rules

  11. Representation of Fuzzy Rule

  12. Representation of Fuzzy Rule Consequence:

  13. Representation of Fuzzy Rule Max-min composition operator Mamdani: min operator for the implication Larsen: product operator for the implication

  14. One singleton input and one fuzzy output Mamdani

  15. One singleton input and one fuzzy output Mamdani

  16. One singleton input and one fuzzy output Larsen

  17. One singleton input and one fuzzy output Larsen

  18. One fuzzy input and one fuzzy output Mamdani

  19. One fuzzy input and one fuzzy output Mamdani

  20. MIMO to MISO

  21. Ri consists of R1 and R2

  22. Example

  23. Two singleton inputs and one fuzzy output Mamdani

  24. Two singleton inputs and one fuzzy output Mamdani

  25. Example

  26. Two fuzzy inputs and one fuzzy output Mamdani

  27. Two fuzzy inputs and one fuzzy output Mamdani

  28. Two fuzzy inputs and one fuzzy output Mamdani

  29. Example

  30. Multiple rules

  31. Multiple rules

  32. Multiple rules

  33. Example

  34. Mamdani method

  35. Mamdani method

  36. Mamdani method

  37. Mamdani method

  38. Larsen method

  39. Larsen method

  40. Larsen method

  41. Larsen method

  42. Tsukamoto method

  43. Tsukamoto method

  44. TSK method

  45. TSK method

  46. Thanks for your attention!

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