Theil방법을 이용한 퍼지회귀모형

국문 초록 (Abstract)

설명변수와 반응변수 사이의 통계적 관계를 설명하기 위해 사용되는 회귀모형을 분석하는 방법을 회귀분석이라 한다. 본 논문에서는 독립변수와 종속변수에 대한 퍼지관계를 표현하는 퍼지회귀모형를 추정하기 위하여 이상치에 민감하지 않은 로버스트한 추정량인 Theil방법을 소개한다. Theil방법은 설명변수와 반응변수의  -수준집합의 각 성분으로 구성된 집합에서 선택한 임의의 두 쌍 자료로부터 계산된 변화율의 중위수를 두 변수에 대한 변화량의 추정량으로 간주한다. 본 논문에서 제안된 Theil방법이 최소자승법을 이용하여 추정된 퍼지회귀모형보다 더 정확할 수 있음을 예제를 통하여 확인한다.

다국어 초록 (Multilingual Abstract)

Regression Analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variable and response variables. This paper introduce Theil’s method to find a fuzzy regression model which explain the relationship between explanatory variable and response variables. Theil’s method is a robust method which is not sensive to outliers. Theil’s method use medians of rate of increment based on randomly chosen pairs of each components of α-level sets of fuzzy data in order to estimate the coefficients of fuzzy regression model. We propose an example to show Theil’s estimator is robust than the Least squares estimator.

목차 (Table of Contents)

• 요약
• Abstract
• 1. 서론
• 2. 퍼지회귀모형
• 3. 예제
• 4. 결론
• References

참고문헌 (Reference)

1 H. Tanaka, "Watada, Possibilistic linear regression analysis for fuzzy data" 40 : 389-396, 1989

2 L. A. Zadeh, "The concept of linguistic variable and its application to approximate reasoning I" 8 : 199-249, 1975

3 S. S. Hussain, "Non-parametric regression" 146 : 182-191, 1983

4 H. Tanaka, "Linear regression analysis with fuzzy model" 12 : 903-907, 1982

5 C. Kao, "Least-squares estimates in fuzzy regression analysis" 148 : 426-435, 2003

6 S. H. Choi, "General fuzzy regression using least squares method" 41 : 477-485, 2010

7 L. A. Zadeh, "Fuzzy sets" 8 : 338-353, 1965

8 S. H. Choi, "Fuzzy regression using least absolute deviation estimators" 12 : 257-263, 2008

9 L. H. Chen, "Fuzzy regression models using the least-squares method based on the concept of distance" 17 : 1259-1272, 2009

10 P. Diamond, "Fuzzy regression analysis, In Fuzzy sets in decision analysis, operations research and statistics" Kluwer Academic Publishers 349-387, 1998

11 P. Diamond, "Fuzzy Least Squares" 46 : 141-157, 1988

12 B. Kim, "Evaluation of fuzzy linear regression models by comparing membership functions" 100 : 343-352, 1998

13 D. Savic, "Evaluation of fuzzy linear regression models" 39 : 51-63, 1991

14 J. H. Yoon, "Componentwise Fuzzy Linear Regression Using Least Squares Estimation" 15 : 137-153, 2009

15 H. K. Kim, "Asymptotic properties of least squares estimation with fuzzy observations" 178 : 439-451, 2008

16 H. Theil, "A rank invariant of linear and polynomial regression analysis" 53 : 386-392, 1950