Two algorithms for fast incremental transitive closure of sparse fuzzy binary relations

Wallace, M; Kollias, S

dc.contributor.author	Wallace, M	en
dc.contributor.author	Kollias, S	en
dc.date.accessioned	2014-03-01T01:27:31Z
dc.date.available	2014-03-01T01:27:31Z
dc.date.issued	2007	en
dc.identifier.issn	0219-8762	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18485
dc.subject	Complexity	en
dc.subject	Partial ordering relations	en
dc.subject	Sparse matrix	en
dc.subject	Transitive closure	en
dc.subject.other	Algorithms	en
dc.subject.other	Computational complexity	en
dc.subject.other	Computational methods	en
dc.subject.other	Fuzzy sets	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Partial ordering relations	en
dc.subject.other	Sparse fuzzy ordering	en
dc.subject.other	Sparse matrix	en
dc.subject.other	Transitive closure	en
dc.subject.other	Knowledge based systems	en
dc.title	Two algorithms for fast incremental transitive closure of sparse fuzzy binary relations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1142/S0219876207001102	en
heal.identifier.secondary	http://dx.doi.org/10.1142/S0219876207001102	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	Sparse fuzzy ordering and partial ordering relations have recently become of great importance in the field of knowledge systems. As the size of the relations utilized in such a framework is extremely large, efficient algorithms are needed for their handling. More specifically, when a part of such a relation is updated, the property of transitivity needs to be re-established in timely manner, as the knowledge system often becomes unusable until this process is completed. In this paper we propose two algorithms for the incremental update of fuzzy transitive relations. The first one focuses on the incremental update of a part of an already transitive relation, while the other tackles the complete transitive closure of any relation. For the average sparse relation, both of the proposed algorithms have considerably smaller computational complexity than the classical approach, which we also prove experimentally via application to real life relations of this type. © 2007 World Scientific Publishing Company.	en
heal.publisher	WORLD SCIENTIFIC PUBL CO PTE LTD	en
heal.journalName	International Journal of Computational Methods	en
dc.identifier.doi	10.1142/S0219876207001102	en
dc.identifier.isi	ISI:000207553300001	en
dc.identifier.volume	4	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	13	en