%0 Journal Article
%@ 0165-0114
%A Garmendia Salvador, Luis
%A Salvador Alcaide, Adela
%A Montero de Juan, Javier
%D 2008
%F upm:3055
%I Elsevier
%J Fuzzy Sets and Systems
%N 14
%P 2097-2105
%T Computing a T-transitive lower approximation or opening of a proximity relation
%U http://oa.upm.es/3055/
%V 160
%X 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.