 Download Download Presentation A tutorial for Fuzzy Prediction

# A tutorial for Fuzzy Prediction

Télécharger la présentation ## A tutorial for Fuzzy Prediction

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. A tutorial for Fuzzy Regression Regression A tutorial for Fuzzy Prediction Jin Hee Yoon Yonsei University, South Korea MAR. 1, 2013

2. A tutorial for Fuzzy Regression Regression 1. Introduction (Regression) Dependent variable Independent variable (x) Regression is the attempt to explain the variation in a dependent variable using the variation in independent variables. Regression is thus an explanation of causation. If the independent variable(s) sufficiently explain the variation in the dependent variable, the model can be used for prediction.

3. A tutorial for Fuzzy Regression Simple Linear Regression Regression 1. Introduction (Simple Regression) є Dependent variable (y) Independent variable (x) LSE (Least squares estimation) LAD (Least absolute deviation) ( Estimated regression model)

4. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 1. Introduction (Multiple Regression) More than one independent variable can be used to explain variance in the dependent variable, as long as they are not linearly related. A multiple regression takes the form: LSE (Least squares estimation) LAD (Least absolute deviation)

5. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression Analysis

6. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression Analysis

7. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression Analysis • Triangular fuzzy number • Triangular fuzzy number 1 mode spread

8. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression Analysis • Alpha-level set

9. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression Analysis • LR- fuzzy number 1 Lx Rx

10. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression Analysis

11. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression Analysis

12. A tutorial for Fuzzy Regression Regression 2. Fuzzy Regression Analysis • Fuzzy Regression Analysis • Number of independent variables • Fuzzy simple regression • Fuzzy multiple regression • Function shape • Fuzzy Linear regression • Fuzzy Nonlinear regression (logistric, quadratic, cubic) • Minimizing methods • Fuzzy Least squares estimation (FLSE) • Fuzzy Least absolute deviation estimation (FLAD) • Fuzzy Maximum Likelihood Estimation (FMSE) • Error assumption • Fuzzy Parametric regression • Fuzzy Nonparametric regression (Rank transform, Theil’s,…) • Estimation methods • Numerical method • Statistical method Robust method

13. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 2. Fuzzy Regression analysis (Metric for Fuzzy numbers) • For LSE • For LAD

14. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 3. Nonparametric Fuzzy Regression Method (Theil’s)

15. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 3. Nonparametric Fuzzy Regression Method

16. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 3. Nonparametric Fuzzy Regression Method (Theil’s)

17. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 3. Nonparametric Fuzzy Regression Method (Theil’s)

18. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 3. Nonparametric Fuzzy Regression Method (Theil’s)

19. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 3. Nonparametric Fuzzy Regression Method (Theil’s)

20. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 3. Nonparametric Fuzzy Regression Method (Theil’s) • Example

21. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

22. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

23. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

24. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

25. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

26. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

27. A tutorial for Fuzzy Regression Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

28. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation Example 4.1 ( by Diamond(1997)) (by Kao and Chyu (2002))

29. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation • Example 4.1 Sakawa and Yano (1992)

30. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

31. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation • Example 4.2 Wu (2003)

32. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 4. Fuzzy Least Squares Estimation

33. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

34. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

35. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

36. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

37. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

38. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

39. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

40. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

41. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

42. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

43. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

44. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

45. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

46. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

47. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

48. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

49. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series

50. An asymptotic approach of Fuzzy Least Squares Estimation A tutorial for Fuzzy Regression Fuzzy least squares estimation with new fuzzy operations Multiple Linear Regression Regression 5. Fuzzy Time Series