Computationally efficient sup-t transitive closure for sparse fuzzy binary relations

Wallace, M; Avrithis, Y; Kollias, S

dc.contributor.author	Wallace, M	en
dc.contributor.author	Avrithis, Y	en
dc.contributor.author	Kollias, S	en
dc.date.accessioned	2014-03-01T01:23:43Z
dc.date.available	2014-03-01T01:23:43Z
dc.date.issued	2006	en
dc.identifier.issn	0165-0114	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17115
dc.subject	Complexity	en
dc.subject	Fuzzy partial ordering relations	en
dc.subject	Sparse matrix	en
dc.subject	Transitive closure	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Statistics & Probability	en
dc.subject.other	Algorithms	en
dc.subject.other	Computation theory	en
dc.subject.other	Computational complexity	en
dc.subject.other	Information theory	en
dc.subject.other	Complexity	en
dc.subject.other	Fuzzy partial ordering relations	en
dc.subject.other	Sparse matrix	en
dc.subject.other	Transitive closure	en
dc.subject.other	Fuzzy sets	en
dc.title	Computationally efficient sup-t transitive closure for sparse fuzzy binary relations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.fss.2005.06.005	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.fss.2005.06.005	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real-life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little attention to the case of general fuzzy binary relations. Most works that deal with the algorithmic part of the transitive closure of fuzzy relations focus only on the case of max-min transitivity, disregarding other types of transitivity. In this paper, after formalizing the notion of sparseness and providing a representation model for sparse relations that displays both computational and storage merits, we propose an algorithm for the incremental update of fuzzy sup-t transitive relations. The incremental transitive update (ITU) algorithm achieves the re-establishment of transitivity when an already transitive relation is only locally disturbed. Based on this algorithm, we propose an extension to handle the sup-t transitive closure of any fuzzy binary relation, through a novel incremental transitive closure (ITC) algorithm. The ITU and ITC algorithms can be applied on any fuzzy binary relation and t-norm; properties such as reflexivity, symmetricity and idempotency are not a requirement. Under the specified assumptions for the average sparse relation, both of the proposed algorithms have considerably smaller computational complexity than the conventional approach; this is established both theoretically and verified via appropriate computing experiments. (c) 2005 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Fuzzy Sets and Systems	en
dc.identifier.doi	10.1016/j.fss.2005.06.005	en
dc.identifier.isi	ISI:000233696300002	en
dc.identifier.volume	157	en
dc.identifier.issue	3	en
dc.identifier.spage	341	en
dc.identifier.epage	372	en