Fuzzy Ridge Linear Regression Analysis for Fuzzy Input– Output Data

In this paper, we propose a new weighted fuzzy ridge regression model for a given set of fuzzy inputs and their corresponding triangular fuzzy outputs. Coefficients are also considered to be fuzzy. First, some approximations for multiplication of two triangular fuzzy numbers are introduced. Then, respective definitions of fuzzy weighted arithmetic (FWA) are given. Followingly, a method for fuzzy least-squares ridge regression based on FWA is developed. To obtain the ridge tunning parameter an objective function is optimized. Lastly, for the illustration propose, a real example is analyzed, which indicates the superior performance of the proposed method.