Imprecise Temporal Interval Relations

When the time span of an event is imprecise, it can be represented by a fuzzy set, called a fuzzy time interval. In this paper we propose a representation for 13 relations that can hold between intervals. Since our model is based on fuzzy orderings of time points, it is not only suitable to express precise relationships between imprecise events (“the mid 1930’s came before the late 1930’s) but also imprecise relationships (“the late 1930’s came long before the early 1990’s). Furthermore we show that our model preserves many of the properties of the 13 relations Allen introduced for crisp time intervals.