An omission approach for detecting outliers in fuzzy regression models

Since Tanaka et al. in 1982 proposed a study in linear regression with a fuzzy model, fuzzy regression analysis has been widely studied and applied in various areas. However, Tanaka's approach may give an incorrect interpretation of the fuzzy linear regression results when outliers are present in the data set. To handle the outlier problem, we propose an omission approach for Tanaka's linear programming method. This approach has the capability to examine the behavior of value changes in the objective function of fuzzy regression models when observations are omitted. Furthermore, we use a simple visual display—box plot—to define the cutoffs for outliers. Some numerical experiments are performed to assess the performance of the proposed approach. Numerical results clearly indicate our approach performed well.