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A method for obtaining transitive approximations of a binary relation

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  • Jacinto González-Pachón
  • Carlos Romero

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

Suggested Citation

  • Jacinto González-Pachón & Carlos Romero, 2008. "A method for obtaining transitive approximations of a binary relation," Annals of Operations Research, Springer, vol. 163(1), pages 197-208, October.
    • Handle: RePEc:spr:annopr:v:163:y:2008:i:1:p:197-208:10.1007/s10479-008-0324-3
    DOI: 10.1007/s10479-008-0324-3
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    References listed on IDEAS

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    1. González-Pachøn, Jacinto & Romero, Carlos, 1999. "Distance-based consensus methods: a goal programming approach," Omega, Elsevier, vol. 27(3), pages 341-347, June.
    2. Fodor, Janos C. & Roubens, Marc, 1995. "Structure of transitive valued binary relations," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 71-94, August.
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    Cited by:

    1. González-Pachón, Jacinto & Romero, Carlos, 2011. "The design of socially optimal decisions in a consensus scenario," Omega, Elsevier, vol. 39(2), pages 179-185, April.

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