Tractable Fragments of Fuzzy Qualitative Algebra

Abstract

In this paper we study the computational complexity of Fuzzy Qualitative Temporal Algebra (QA ^fuz ), a framework that combines qualitative temporal constraints between points and intervals, and allows modelling vagueness and uncertainty. Its tractable fragments can be identified by generalizing the results obtained for crisp Constraint Satisfaction Problems (CSPs) to fuzzy CSPs (FCSPs); to do this, we apply a general methodology based on the notion of α-cut. In particular, the results concerning the tractability of Qualitative Algebra QA, obtained in a recent study by different authors, can be extended to identify the tractable algebras of the fuzzy Qualitative Algebra QA ^fuz in such a way that the obtained set is maximal, namely any maximal tractable fuzzy algebra belongs to this set.