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 number4

49. Approximation of Triangular Fuzzy Number4

50. Approximation of Triangular Fuzzy Number

51. Trapezoidal fuzzy number

52. Operations of Trapezoidal Fuzzy Number

53. Operations of Trapezoidal Fuzzy Number

54. Operations of Trapezoidal Fuzzy Number

55. Approximation of Trapezoidal Fuzzy Number

56. Operations of Trapezoidal Fuzzy Number

57. Exercise
Is B a convex fuzzy set?
Is B a fuzzy number?

58. Exercise

59. Thanks for your attention!