Fuzzy linear regression

Linear Programming (LP) methods are commonly used to construct Fuzzy Linear Regression (FLR) models. Probabilistic Fuzzy Linear Regression (PFLR) (Tanaka, 1989) and Unrestricted Fuzzy Linear Regression (UFLR) (Lee and Chang, 1994) are two of the mostly applied models that employ LP methods. In this study, commonly used models which employ LP methods are given. Also a new modified fuzzy linear regression model which use LP methods is proposed. Proposed model divides total vagueness into two parts as explained and unexplained. It tries to minimize only the explained vagueness not the unexplained one. Four numerical applications with four different data sets were performed in which PFLR, UFLR and proposed model were compared in terms of mean squared error (MSE) and total fuzziness and it is concluded the proposed model is acceptable.