2026-04-17T12:40:25Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/192232026-02-01T06:08:34Zcom_2072_1033col_2072_452950

How to make T-transitive a proximity relation Garmendia Salvador, Luis Recasens Ferrés, Jorge Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica Fuzzy logic Lògica difusa Three ways to approximate a proximity relation R (i.e., a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous Archimedean t-norm are given. The first one aggregates the transitive closure R macr of R with a (maximal) T-transitive relation B contained in R . The second one computes the closest homotecy of R macr or B to better fit their entries with the ones of R. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for T the Lukasiewicz or the product t-norm. The previous methods do not apply for the minimum t-norm. An algorithm to approximate a given proximity relation by a min-transitive relation (a similarity) is given in the last section of the paper. Peer Reviewed Postprint (published version) 2009-02 Article http://ieeexplore.ieee.org/xpl/aboutJournal.jsp?punumber=91 Restricted access - publisher's policy