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A tutorial for Fuzzy Prediction

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A tutorial for Fuzzy Prediction

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  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