RT Journal Article
T1 Computing a T-transitive lower approximation or opening of a proximity relation
A1 Garmendia Salvador, Luis
A1 Salvador Alcaide, Adela
A1 Montero De Juan, Francisco Javier
AB 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 higher the number of elicitations, the more probable is inconsistency. This is mostly the case within a fuzzy framework, even when the number of alternatives or objects 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, T being any left-continuous t-norm. The computed approximation we propose will have 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 is no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties.
PB Elsevier Science Bv
SN 0165-0114
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/50075
UL https://hdl.handle.net/20.500.14352/50075
LA eng
NO Garmendia, L., Salvador, A., Montero, J.: Computing a T-transitive lower approximation or opening of a proximity relation. Fuzzy Sets and Systems. 160, 2097-2105 (2009). https://doi.org/10.1016/j.fss.2009.01.015
DS Docta Complutense
RD 6 abr 2025