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How to make T-transitive a proximity relation Garmendia Salvador, Luis Recasens Ferrés, Jorge Universitat Politècnica de Catalunya. Departament d'Estructures a l'Arquitectura Universitat Politècnica de Catalunya. FIA - Modelització Matemàtica Funcional i Aplicacions 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 Garmendia, L.; Recasens, J. How to make T-transitive a proximity relation. "IEEE transactions on fuzzy systems", Febrer 2009, vol. 17, núm. 1, p. 200-207. 1063-6706 https://hdl.handle.net/2117/19223 10.1109/TFUZZ.2008.2003128 eng http://ieeexplore.ieee.org/xpl/aboutJournal.jsp?punumber=91 Restricted access - publisher's policy 8 p. application/pdf