Fuzzy Temporal Logic on Fuzzy Temporal Constraint Networks

The aim of this work is to integrate the ideas of flexibility and uncertainty into Allen´s interval-based temporal logic, defining a new formalism which extends classical interval Algebra. We refer to fuzzy temporal constraint satisfaction problem, in which constraints are satisfied to a degree, which is based on fuzzy sets. The main objective of this research is the development of a temporal reasoning system able to manage qualitative and quantitative information also affected by vagueness and uncertainty about the external reality reaches. This paper proposes a fuzzy temporal reasoner based on an interval constraint network. We generalize some earlier definitions for fuzzy temporal constraint networks, we identify and define fuzzy temporal queries in a fuzzy temporal constraint network, and explore a method for efficiently computing them in a specific case. Further analysis of some measures on fuzzy degrees turns out to be fundamental in order to precisely determine some of these queries. The results presented in this paper can be useful in the design of a system for fuzzy temporal reasoning under uncertainty.