Many fuzzy time series approaches have been proposed in recent years. These methods include three main phases such as fuzzification. defining fuzzy relationships and, defuzzification. Aladag et al.  improved the forecasting accuracy by utilizing feed forward neural networks to determine fuzzy relationships in high order fuzzy time series. Another study for increasing forecasting accuracy was made by Cheng et al. . In their study, they employ adaptive expectation model to adopt forecasts obtained from first order fuzzy time series forecasting model. In this study, we propose a novel high order fuzzy time series method in order to obtain more accurate forecasts. In the proposed method, fuzzy relationships are defined by feed forward neural networks and adaptive expectation model is used for adjusting forecasted values. Unlike the papers of Cheng et al.  and Liu et al. , forecast adjusting is done by using constraint optimization for weighted parameter. The proposed method is applied to the enrollments of the University of Alabama and the obtained forecasting results compared to those obtained from other approaches are available in the literature. As a result of comparison, it is clearly seen that the proposed method significantly increases the forecasting accuracy. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.