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How to make T-transitive a proximity relation

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10.1109/TFUZZ.2008.2003128
 
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Garmendia Salvador, Luis
Recasens Ferrés, JorgeMés informacióMés informacióMés informació
Document typeArticle
Defense date2009-02
Rights accessRestricted access - publisher's policy
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
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.
CitationGarmendia, 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. 
URIhttp://hdl.handle.net/2117/19223
DOI10.1109/TFUZZ.2008.2003128
ISSN1063-6706
Publisher versionhttp://ieeexplore.ieee.org/xpl/aboutJournal.jsp?punumber=91
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