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A method for obtaining transitive approximations of a binary relation

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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.

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Authors and Affiliations

  1. Dept. Inteligencia Artificial, Facultad de Informática, Univ. Politecn. Madrid, Campus de Montegancedo s/n 28660-Boadilla del Monte, Madrid, Spain

    Jacinto González-Pachón

  2. Dept. Economía y Gestión Forestal, Escuela Tecn. Super Ingn. Montes, Univ. Politecn. Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain

    Carlos Romero

Authors
  1. Jacinto González-Pachón
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  2. Carlos Romero
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Correspondence to Jacinto González-Pachón.

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González-Pachón, J., Romero, C. A method for obtaining transitive approximations of a binary relation. Ann Oper Res 163, 197–208 (2008). https://doi.org/10.1007/s10479-008-0324-3

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  • DOI: https://doi.org/10.1007/s10479-008-0324-3

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