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INVE_MEM_2008_61819.pdf
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Garmendia Salvador
Luis

Salvador Alcaide
Adela

Montero de Juan
Javier
Computing a Ttransitive lower approximation or opening of a proximity relation
Elsevier
byncnd
pub
 matematicas
public
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 Tindistinguishability from a reflexive and symmetric fuzzy relation, being T any leftcontinuous tnorm. 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 Ttransitive opening. To the authors¿ knowledge, there are no other proposed algorithm that computes Ttransitive lower approximations or openings while preserving the reflexivity and symmetry properties.
published
200807
Fuzzy Sets and Systems
160
14
20972105
10.1016/j.fss.2009.01.015
Caminos
Matematica_Aplicada11
TRUE
01650114
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V054VKP3T011&_cdi=5637&_user=885385&_pii=S0165011409000554&_orig=browse&_coverDate=07/16/2009&_sk=998399985&view=c&wchp=dGLbVzzzSkWA&md5=b1660ae3af7b2354627fce2a36e61f35&ie=/sdarticle.pdf