Abstract
ABSTRACT Fuzzy regression was first introduced by Tanaka et al [30] in 1982 to be an alternative to evaluate the relation between input variables and output variable. According to the simulation results proposed by Kim, Moskowitz and Koksalan showed that the predicted performance in statistical regression is better than fuzzy regression when the collected data is large. However, fuzzy regression performance becomes relative better as the size of data set diminished and the aptness of the regression model deteriorated. Since fuzzy regression plays the positive role in performance when the collected data is small and the relation between input variables and output variable is vague. Based on the motivation to research a new predicted tool, in this thesis, we will major in Tanaka's fuzzy regression model. Although, fuzzy regression provides the information for prediction when the systems are indefinite, it has been criticized by the following problems classified into three categories: I. Data Analysis (1) Proper interpretation about the fuzzy regression interval is not discussed [14]. (2) Tanaka's model only considers the linear model but not intrinsically linear models [36]. (3) Variable selection method is still lack of discussion [36] II. Modeling (4) What is the difference between Tanaka's model and the fuzzy least square model [38] ? (5) The confidence level h is hard to decide for deriving a fuzzy regression interval [20][40]. III. Applications (6) The original Tanaka's model was extremely sensitive to the outliers [5][23][41]. (7) Issues of forecasting have never been addressed [39]. In our study, we tried to overcome these problems and presented the results in this thesis with the following structure. In Chapter 3 based on the viewpoint of data analysis, we try to find the best estimated value in a fuzzy regression interval to overcome the problem (1). For problem (2), the properties of an intrinsically linear function were considered. By applying residual analysis, the validity of a transformed the transferred nonlinear fuzzy regression model can be checked. Furthermore, for problem (3), for a fuzzy regression equation with fuzzy relation between input and output variable was first considered. By the concept of Error Sum of Square, we defined an Index of IC to select input variables to the fuzzy regression equation. For the crisp-input and fuzzy-output fuzzy regression, we applied Error Sum of Square and Regression Sum of Square to be two criteria and applied Branch-and-Bound algorithm to select input variables. For Modeling problems, in Chapter 4, we derived a more efficient and better predictability fuzzy regression model by combining Tanaka's model and fuzzy least square model. Besides, from the concept of fuzzy goal programming, we construct a fuzzy regression model which provides the best satisfactory level h by trading off all of the collected data. For Application issues, in Chapter 5, we proposed a method to identify an outliers in the collected data and applied fuzzy linear programming model to reduce the effect of outliers. Finally, in Chapter 6, we proposed a fuzzy linear programming model to enlarge the feasible region in order to find the best satisfactory solution in prediction and forecasting.