Computationally efficient incremental transitive closure of sparse fuzzy binary relations

Existing literature in the field of transitive relations focuses mainly on dense, Boolean, undirected relations. With the emergence of a new area of intelligent retrieval, where sparse transitive fuzzy ordering relations are utilized, existing theory and methodologies need to be extended, as to cover the new needs. This work discusses the incremental update of such fuzzy binary relations, while focusing on both storage and computational complexity issues. Moreover, it proposes a novel transitive closure algorithm that has a remarkably low computational complexity (below O(n²)) for the average sparse relation; such are the relations encountered in intelligent retrieval.