Univariate fuzzy time series approaches which have been widely used in recent years can be divided into two classes, which are called first order and high order models. In the literature, it has been shown that high order fuzzy time series approaches improve the forecasting accuracy. One of the important parts of obtaining high accuracy forecasts in fuzzy time series is that the length of interval is very vital. As mentioned in the first-order models by Egrioglu, Aladag, Basaran, Uslu, and Yolcu (2009), the length of interval also plays very important role in high order models too. In this study, a new approach which uses an optimization technique with a single-variable constraint is proposed to determine an optimal interval length in high order fuzzy time series models. An optimization procedure is used in order to determine optimum length of interval for the best forecasting accuracy, we used optimization procedure. In the optimization process, we used a MATLAB function employing an algorithm based on golden section search and parabolic interpolation. The proposed method was employed to forecast the enrollments of the University of Alabama to show the considerable outperforming results.