Fuzzy linear regression model based on fuzzy scalar product

摘要

The new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed in this paper. We introduce the fuzzy scalar (inner) product to formulate the fuzzy linear regression model. In order to invoke the conventional approach of linear regression analysis for real-valued data, we transact the alpha-level linear regression models of the fuzzy linear regression model. We construct the membership functions of fuzzy least squares estimators via the form of "Resolution Identity" which is a well-known formula in fuzzy sets theory. In order to obtain the membership value of any given least squares estimate taken from the fuzzy least squares estimator, we transform the original problem into the optimization problems. We also provide two computational procedures to solve the optimization problems.