Error measures for fuzzy linear regression: Monte Carlo simulation approach

• The study covers different error measures that have not previously calculated for Monte Carlo study in fuzzy linear regression models.
• We obtain the most useful and the worst error measures to estimate fuzzy regression parameters without using any mathematical programming or heavy fuzzy arithmetic operations.

The focus of this study is to use Monte Carlo method in fuzzy linear regression. The purpose of the study is to figure out the appropriate error measures for the estimation of fuzzy linear regression model parameters with Monte Carlo method. Since model parameters are estimated without any mathematical programming or heavy fuzzy arithmetic operations in fuzzy linear regression with Monte Carlo method. In the literature, only two error measures (E1 and E2) are available for the estimation of fuzzy linear regression model parameters. Additionally, accuracy of available error measures under the Monte Carlo procedure has not been evaluated. In this article, mean square error, mean percentage error, mean absolute percentage error, and symmetric mean absolute percentage error are proposed for the estimation of fuzzy linear regression model parameters with Monte Carlo method. Moreover, estimation accuracies of existing and proposed error measures are explored. Error measures are compared to each other in terms of estimation accuracy; hence, this study demonstrates that the best error measures to estimate fuzzy linear regression model parameters with Monte Carlo method are proved to be E1, E2, and the mean square error. One the other hand, the worst one can be given as the mean percentage error. These results would be useful to enrich the studies that have already focused on fuzzy linear regression models.