Fuzziness and Uncertainty in Temporal Reasoning

This paper proposes a general discussion of the handling of imprecise and uncertain information in temporal reasoning in the framework of fuzzy sets and possibility theory. The introduction of fuzzy features in temporal reasoning can be related to different issues. First, it can be motivated by the need of a gradual, linguistic-like description of temporal relations even in the face of complete information. An extension of Allen relational calculus is proposed, based on fuzzy comparators expressing linguistic tolerance. Fuzzy Allen relations are defined from a fuzzy partition made by three possible fuzzy relations between dates (approximately equal, clearly smaller, and clearly greater). Second, the handling of fuzzy or incomplete information leads to pervade classical Allen relations, and more generally fuzzy Allen relations, with uncertainty. The paper provides a detailed presentation of the calculus of fuzzy Allen relations (including the composition table of these relations). Moreover, the paper discusses the patterns for propagating uncertainty about (fuzzy) Allen relations in a possibilistic way.