A fuzzy Bayesian regression model with Gaussian process prior based on exact predictors and fuzzy responses

The purpose of this study is to develop a new fuzzy regression model based on a common Bayesian nonparametric-based method with exact predictors and fuzzy responses. To this end, the left, center, and right values of the unknown fuzzy smooth function were evaluated based on the conventional kernel-based Bayesian method adopted with Gaussian kernel and a multivariate normal distribution as a prior distribution function in the cases where the residuals were assumed to be observed values of a normal distribution function. The unknown components of the model including bandwidth and variance were estimated via a hybrid algorithm. In this regard, a generalized cross-validation and similarity measure between two LR-fuzzy numbers were applied. The mean similarity measure criterion and a mean square error were utilized to assess the performance of the proposed method. Some applied examples and comparison studies were considered to clarify the proposed method and illustrate its performance relative to some common fuzzy nonlinear methods. The results indicated the superior performance of the proposed method over other nonlinear methods. Further, two essential assumptions associated with proposed regression models including homoscedasticity and normality of residuals were also analyzed in each example based on some common scatter plots and a well-established hypothesis test.