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Chapter 5 FUZZY NUMBER

Chapter 5 FUZZY NUMBER. Chi-Yuan Yeh. Outline. Interval and Fuzzy number Operations of interval Operations of fuzzy number α -cut extension principle Triangular fuzzy number Trapezoidal fuzzy number. Interval. α -cut. α -cut. α -cut. Fuzzy number.

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Chapter 5 FUZZY NUMBER

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  1. Chapter 5 FUZZY NUMBER Chi-Yuan Yeh

  2. Outline • Interval and Fuzzy number • Operations of interval • Operations of fuzzy number • α-cut • extension principle • Triangular fuzzy number • Trapezoidal fuzzy number

  3. Interval

  4. α-cut

  5. α-cut

  6. α-cut

  7. Fuzzy number • Definition: a fuzzy set A on R must posses at least the following three properties • A must be a normal fuzzy set • must be a closed interval for every (convex) • the support of fuzzy set A, , must be bounded

  8. Operations of Interval

  9. Operations of Interval

  10. Operations of Interval

  11. Operations of Interval

  12. Operations of Interval

  13. Operations of Fuzzy Number • α-cut • Addition:

  14. Operations of Fuzzy Number • α-cut • Subtraction: • Multiplication: • Division: • Minimum: • Maximum:

  15. Operations of Fuzzy Number

  16. Operations of Fuzzy Number • α-cut • α = 0.5 • α = 1.0

  17. Operations of Fuzzy Number • Extension principle • Addition: • Subtraction: • Multiplication: • Division: • Minimum: • Maximum:

  18. Operations of Fuzzy Number

  19. Operations of Fuzzy Number

  20. Operations of Fuzzy Number

  21. Operations of Fuzzy Number

  22. Operations of Fuzzy Number

  23. Operations of Fuzzy Number

  24. Operations of Fuzzy Number

  25. Operations of Fuzzy Number

  26. Triangular fuzzy number

  27. Triangular fuzzy number

  28. Triangular fuzzy number

  29. Triangular fuzzy number

  30. Operations of triangular fuzzy number

  31. Operations of triangular fuzzy number

  32. Operations of triangular fuzzy number

  33. Operations of triangular fuzzy number

  34. Operations of triangular fuzzy number

  35. Operations of triangular fuzzy number

  36. Operations of triangular fuzzy number

  37. Operations of triangular fuzzy number

  38. Operations of triangular fuzzy number

  39. Operations of triangular fuzzy number

  40. Operations of triangular fuzzy number

  41. Operations of triangular fuzzy number

  42. Operations of triangular fuzzy number

  43. Operations of triangular fuzzy number

  44. Approximation of Triangular Fuzzy Number

  45. Approximation of Triangular Fuzzy Number

  46. Approximation of Triangular Fuzzy Number

  47. Operations of triangular fuzzy number

  48. Operations of triangular fuzzy number 4

  49. Approximation of Triangular Fuzzy Number 4

  50. Approximation of Triangular Fuzzy Number

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