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Transitive approximation to pairwise comparison matrices by using interval goal programming

Author

Listed:
  • J González-Pachón

    (Technical University of Madrid)

  • M I Rodríguez-Galiano

    (Technical University of Madrid)

  • C Romero

    (Technical University of Madrid)

Abstract

Paired comparison is a very popular method for establishing the relative importance of n objects, when they cannot be directly rated. The challenge faced by the pairwise comparison method stems from some missing properties in its associated matrix. In this paper, we focus on the following general problem: given a non-reciprocal and inconsistent matrix computing intransitivities, what is its associated ranking (defined by importance values)? We propose to use inconsistencies as a source of information for obtaining importance values. For this purpose, a methodology with a decomposition and aggregation phase is proposed. Interval Goal Programming will be a useful tool for implementing the aggregation process defined in the second phase.

Suggested Citation

  • J González-Pachón & M I Rodríguez-Galiano & C Romero, 2003. "Transitive approximation to pairwise comparison matrices by using interval goal programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 532-538, May.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:5:d:10.1057_palgrave.jors.2601542
    DOI: 10.1057/palgrave.jors.2601542
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    References listed on IDEAS

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    1. Mass A. & Bezembinder, T. & Wakker, P., 1996. "On solving intansitivities in repeated pairwise choices," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 53-53, February.
    2. González-Pachøn, Jacinto & Romero, Carlos, 1999. "Distance-based consensus methods: a goal programming approach," Omega, Elsevier, vol. 27(3), pages 341-347, June.
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