Computing a T-transitive lower approximation or opening of a proximity relation

Garmendia Salvador, Luis and Salvador Alcaide, Adela and Montero de Juan, Javier (2008). Computing a T-transitive lower approximation or opening of a proximity relation. "Fuzzy Sets and Systems", v. 160 (n. 14); pp. 2097-2105. ISSN 0165-0114. https://doi.org/10.1016/j.fss.2009.01.015.

Description

Title: Computing a T-transitive lower approximation or opening of a proximity relation
Author/s:
  • Garmendia Salvador, Luis
  • Salvador Alcaide, Adela
  • Montero de Juan, Javier
Item Type: Article
Título de Revista/Publicación: Fuzzy Sets and Systems
Date: July 2008
ISSN: 0165-0114
Volume: 160
Subjects:
Faculty: E.T.S.I. Caminos, Canales y Puertos (UPM)
Department: Matemática e Informática Aplicadas a la Ingeniería Civil [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

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.

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