A simple linear regression analysis for fuzzy input-output data and its application to psychological study

A simple linear regression analysis using the least squares method under some constraints, where both input data and output data are represented by triangular fuzzy numbers, is proposed and then compared to the possibilistic linear regression analysis proposed by Sakawa and Yano (1992) using fuzzy rating data in a psychological study. The major findings of the comparison were as follows: under the proposed analysis, the width between the upper and lower values of the predicted model was nearer to the width of the dependent variable than that of the possibilistic linear regression analysis. Also, the representative value of the predicted value by the proposed analysis was also nearer to that of the dependent variable, compared with that of the possibilistic linear regression analysis.