Efficiency Comparison of the Parameters Estimation by a Fuzzy Linear Regression Model

Abstract

The fuzzy regression method can be used for fitting the fuzzy data for the construction of the simple linear regression model. This paper aims to study the performance and compare the adaptive fuzzy method and traditional fuzzy method by using the criteria of mean square error (MSE) and the coefficient of determine R 2. A Monte Carlo simulation with 5,000 iterations was performed to achieve the objective of research. In simulations, the independent variable has a gamma distribution with the parameters are α = 4, 5, 6 and β = 1. We carried out simulations to examine the performance of MSE from the adaptive fuzzy regression model and the traditional fuzzy regression model. The results showed that the transformation of independent variable with gamma distribution to be a normal distribution make the simple linear regression by the adaptive fuzzy method outperforms the traditional fuzzy method. In terms of MSE, the adaptive fuzzy method performed better than the traditional fuzzy method. In addition, the values of coefficient of determine from the adaptive fuzzy method and the traditional fuzzy method are slightly different.