1. Chapter 6 FUZZY FUNCTION Chi-Yuan Yeh

2. Kinds of fuzzy function Crisp function with fuzzy constraint Fuzzy extension function which propagates the fuzziness of independent variable to dependent variable Fuzzifying function which blurs the image of a crisp independent variable 2

3. Function with fuzzy constraint 3

4. Fuzzy extension function 4 tes

5. Fuzzy extension function 5

6. Single fuzzifying function 6

7. 7

8. 8

9. Fuzzy bunch of functions 9

10. 10

11. Fuzzy bunch of functions 11

12. Fuzzy bunch of functions 12

13. Fuzzy bunch of functions 13

14. Maximizing set 14

15. Minimizing set Minimizing set of f is defined as the maximizing set of -f 15

16. Maximizing set 16

17. Maximizing set 17

18. Maximizing set 18

19. Maximum value in crisp domain 19

20. Maximum value in crisp domain 20

21. Maximum value in crisp domain 21

22. Maximum value in fuzzy domain 22

23. Maximum value in fuzzy domain 23

24. Maximum value in fuzzy domain 24

25. Maximum value in fuzzy domain 25

26. Maximum value in fuzzy domain 26

27. Integration of fuzzying function 27

28. Integration of fuzzying function 28

29. Integration of fuzzying function 29

30. Integration of fuzzying function 30

31. Integration in fuzzy interval 31

32. Integration in fuzzy interval 32

33. 33

34. Differentiation of crisp function in fuzzy interval 34

35. Differentiation of crisp function in fuzzy interval 35

36. 36 Differentiation of fuzzifying function function

37. 37 Thanks for your attention!