Fuzzifying Allen's Temporal Interval Relations

Abstract

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 framework to represent, compute, and reason about temporal relationships between such events. Since our model is based on fuzzy orderings of time points, it is not only suitable to express precise relationships between imprecise events (ldquoRoosevelt died before the beginning of the Cold Warrdquo) but also imprecise relationships (ldquoRoosevelt died just before the beginning of the Cold Warrdquo). We show that, unlike previous models, our model is a generalization that preserves many of the properties of the 13 relations Allen introduced for crisp time intervals. Furthermore, we show how our model can be used for efficient fuzzy temporal reasoning by means of a transitivity table. Finally, we illustrate its use in the context of question answering systems.