In the development of the social-economics of countries, time series is a data type stored commonly nowadays. For these data, forecasting has always received the attention of statisticians and managers because it brings to great advantages. Currently, most studies focus on forecasting for the point time series and pay less attention to the interval data series. This paper proposes a forecasting model for interval time series based on the established fuzzy relationship for the elements in the series. Specifically, the study uses the variation of two consecutive intervals as the universal set and the overlap distance of two intervals to evaluate the similarity of elements in the series. This measure is not only used to divide the series into groups with the appropriate numbers but also to establish the relationship between the elements in the series with the divided groups through a proposed algorithm. From these relationships, an interpolating rule for interval time series has been established. Compared with many benchmark data sets, the proposed model has shown the outstanding advantages. With the established Matlab procedure, the proposed model can be applied well to real problems. The comparisons and applications have shown potential in forecasting the interval time series of this study.