| Fuzzy linear regression was introduced by H. Tanaka, S. Uegima, and K. Asai to model linear relationships between an inaccurately measured dependent variable and accurately measured independent variables. The formulations of fuzzy linear regression, which are predominately referred to as the minimization, maximization, and conjunction problems are herein reviewed. The properties of the original minimization problem, herein referred to as Method 1, presented by Tanaka, Uegima, and Asai, are examined as well as the properties of the second minimization problem, proposed by Tanaka and herein referred to as Method 2. Properties of the minimization problem proposed by Tanaka and Ishibuchi to obtain interactive fuzzy coefficients are also studied. This problem is herein referred to as Method 3. A detailed comparison of Method 1 and Method 2 to ordinary least squares regression is given.;Sakawa and Yano introduced another formulation of fuzzy linear regression to model linear relationships between an inaccurately measured dependent variable and inaccurately measured independent variables. The properties of the minimization problem developed by Sakawa and Yano are also investigated. A detailed comparison of the methodology of Sakawa and Yano and the measurement error model is given. |
