title: Computing a T-transitive lower approximation or opening of a proximity relation
creator: Garmendia Salvador, Luis
creator: Salvador Alcaide, Adela
creator: Montero de Juan, Javier
subject: Mathematics
description: Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors¿ knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties.
publisher: E.T.S.I. Caminos, Canales y Puertos (UPM)
rights: http://creativecommons.org/licenses/by-nc-nd/3.0/es/
date: 2008-07
type: info:eu-repo/semantics/article
type: Article
source: Fuzzy Sets and Systems, ISSN 0165-0114, 2008-07, Vol. 160, No. 14
type: PeerReviewed
format: application/pdf
language: eng
relation: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V05-4VKP3T0-1-1&_cdi=5637&_user=885385&_pii=S0165011409000554&_orig=browse&_coverDate=07/16/2009&_sk=998399985&view=c&wchp=dGLbVzz-zSkWA&md5=b1660ae3af7b2354627fce2a36e61f35&ie=/sdarticle.pdf
rights: info:eu-repo/semantics/openAccess
relation: info:eu-repo/semantics/altIdentifier/doi/10.1016/j.fss.2009.01.015
identifier: http://oa.upm.es/3055/