Computational Complexity Study of Fuzzy Qualitative Temporal Algebra

Starting from the complexity classification of qualitative algebra recently proposed by Jonsson and Krokhin, we study the tractable fragments of fuzzy qualitative algebra QA^fuz, an integrated framework able to deal with qualitative temporal constraints between points and intervals affected by vagueness and uncertainty. To do this we generalize the results obtained for the classical case exploiting the notion of alpha-cut in relating the QA^fuz tractable fragments to their QA classical counterparts. In order to guarantee the applicability of Path-Consistency algorithm, we prove that the identified fragments are algebras. Besides, we also prove that the set of the identified tractable fuzzy fragments is maximal.