A method for obtaining transitive approximations of a binary relation

Jacinto González-Pachón () and Carlos Romero ()

Annals of Operations Research, 2008, vol. 163, issue 1, 197-208

Abstract: A binary relation R does not always possess the desirable property of transitivity. Consequently, this needs to be imposed artificially by deviating as little as possible from R. In this paper, three approaches to transitive approximation are analyzed within a common distance-based framework: exterior (transitive closure), interior (openings or maximal transitive sub-relations contained in R) and mixed (transitive fittings) approximation. Additionally, we propose a method for obtaining all these transitive approximations. The method is based on a distance function optimization framework that leads to straightforward goal programming models. Copyright Springer Science+Business Media, LLC 2008

Keywords: Binary relation; Transitive approximation; Transitive closure; Maximal transitive sub-relation; Transitive opening; Goal programming (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10479-008-0324-3

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