Resolution of composite fuzzy relation equations based on Archimedean triangular norms

Stamou, GB; Tzafestas, SG

dc.contributor.author	Stamou, GB	en
dc.contributor.author	Tzafestas, SG	en
dc.date.accessioned	2014-03-01T01:17:01Z
dc.date.available	2014-03-01T01:17:01Z
dc.date.issued	2001	en
dc.identifier.issn	0165-0114	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14330
dc.subject	Archimedean t-norms	en
dc.subject	Fuzzy inference systems	en
dc.subject	Fuzzy relation equations	en
dc.subject	Sup-t-norm compositions of fuzzy relations	en
dc.subject	t-norms	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Statistics & Probability	en
dc.subject.other	INVERSE PROBLEM	en
dc.subject.other	APPROXIMATION-THEORY	en
dc.subject.other	LINEAR-SYSTEMS	en
dc.subject.other	ALGORITHMS	en
dc.subject.other	INFERENCE	en
dc.subject.other	MATRIX	en
dc.title	Resolution of composite fuzzy relation equations based on Archimedean triangular norms	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0165-0114(99)00117-7	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0165-0114(99)00117-7	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	Lately, the sup-t-norm composition of fuzzy relations has been used instead of the well-known max-min. Thus, there is a need for methods of studying and solving sup-t-norm fuzzy relation equations (t is any t-norm). In this paper, the solution existence problem is first studied and solvability criteria for composite fuzzy relation equations of any t-norm are given. Then, a methodology for solving fuzzy relation equations based on sup-t composition, where t is an Archimedean t-norm, is proposed. This resolution method is simpler and faster than those proposed for covering all the continuous t-norms. The result is important, since, as is shown in the paper, the only continuous t-norm. that is not Archimedean is the "minimum". (C) 2001 Elsevier Science B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Fuzzy Sets and Systems	en
dc.identifier.doi	10.1016/S0165-0114(99)00117-7	en
dc.identifier.isi	ISI:000170158400003	en
dc.identifier.volume	120	en
dc.identifier.issue	2	en
dc.identifier.spage	395	en
dc.identifier.epage	407	en