A fuzzy linear regression model with autoregressive fuzzy errors based on exact predictors and fuzzy responses

This paper is an attempt to develop a novel linear regression model with autocorrelated fuzzy error terms and exact predictors and fuzzy responses. The conventional Durbin-Watson test was utilized to investigate the non-zero correlation assumptions between fuzzy error terms. A hybrid procedure was adopted with a weighted mean square error and cross-validation criterion to estimate the unknown autocorrelation criteria and fuzzy coefficients. The performance of the proposed method was illustrated relative to some commonly used fuzzy linear regression methods through three practical examples based on real-world data. For this purpose, several goodness-of-fit criteria were used to evaluate the performance of the proposed method compared to the other methods. The proposed algorithm improved the effect of correlated fuzzy error terms on the model fit considering the role of the autocorrelation parameter. The results revealed the higher relative performance of fuzzy linear regression techniques compared to the conventional fuzzy linear regression techniques in dealing with correlated fuzzy error terms.