A Fuzzy Linear Regression Analysis for Fuzzy Input-Output Data Using the Least Squares Method under Linear Constraints and Its Application to Fuzzy Rating Data

Abstract

Fuzzy linear regression analysis using the least squares method under linear constraint, where input data, output data, and coefficients are represented by triangular fuzzy numbers, was proposed and compared to possibilistic linear regression analysis proposed by Sakawa and Yano (1992) using fuzzy rating data in a psychological study. Major findings of the comparison were as follows: (1) Under the proposed analysis, the width between the maximum and minimum of the predicted model was nearer to the width of the dependent variable than that of possibilistic linear regression analysis, (2) the representative prediction by the proposed analysis was also nearer to that of the dependent variable, compared to that of possibilistic linear regression analysis.