On the effect of membership function in a high-order fuzzy time series

In view of the model of Song and Chissom (1993), their first-order model is effective to analysis historical data with linguistic variables, but the other membership function effects are still unknown. In this study, authors consider various membership functions, and make the results more accurate. The membership functions include unit step function, linear function, and polynomial function with various degrees. To illustrate the effect of the membership function, the forecasting enrollments at the University of Alabama are carried out. It is found that the second-degree polynomial has the best effect to the first-order model, but the unit step function has the best effect to second and third order models.