حداقل مربعات تجزیه و تحلیل رگرسیون خطی فازی برای داده های ورودی و خروجی فازی

A fuzzy regression model is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment. Most fuzzy regression models are considered to be fuzzy outputs and parameters but non-fuzzy (crisp) inputs. In general, there are two approaches in the analysis of fuzzy regression models: linear-programming-based methods and fuzzy least-squares methods. In 1992, Sakawa and Yano considered fuzzy linear regression models with fuzzy outputs, fuzzy parameters and also fuzzy inputs. They formulated multiobjective programming methods for the model estimation along with a linear-programming-based approach. In this paper, two estimation methods along with a fuzzy least-squares approach are proposed. These proposed methods can be effectively used for the parameter estimation. Comparisons are also made between them.