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Supporting decisions by unleashing multiple mindsets using pairwise comparisons method

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  • Salvatore Greco
  • Sajid Siraj
  • Michele Lundy

Abstract

Inconsistency in pairwise comparison judgements is often perceived as an unwanted phenomenon and researchers have proposed a number of techniques to either reduce it or to correct it. We take a viewpoint that this inconsistency unleashes different mindsets of the decision maker(s) that should be taken into account when generating recommendations as decision support. With this aim we consider the spanning trees analysis which is a recently emerging idea for use with the pairwise comparison approach that represents the plurality of mindsets (in terms of a plurality of vectors corresponding to different spanning trees). Until now, the multiplicity of the vectors supplied by the spanning trees approach have been amalgamated into a single preference vector, losing the information about the plurality of mindsets. To preserve this information, we propose a novel methodology taking an approach similar to Stochastic Multi-criteria Acceptability Analysis. Considering all the rankings of alternatives corresponding to the different mindsets, our methodology gives the probability that an alternative attains a given ranking position as well as the probability that an alternative is preferred to another one. Since the exponential number of spanning trees makes their enumeration prohibitive, we propose computing approximate probabilities using statistical sampling of the spanning trees. Our approach is also appealing because it can be applied also to incomplete sets of pairwise comparisons. We demonstrate its usefulness with a didactic example as well as with an application to a real-life case of selecting a Telecom backbone infrastructure for rural areas.

Suggested Citation

  • Salvatore Greco & Sajid Siraj & Michele Lundy, 2021. "Supporting decisions by unleashing multiple mindsets using pairwise comparisons method," Papers 2107.01731, arXiv.org.
  • Handle: RePEc:arx:papers:2107.01731
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    File URL: http://arxiv.org/pdf/2107.01731
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    References listed on IDEAS

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    1. Lundy, Michele & Siraj, Sajid & Greco, Salvatore, 2017. "The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis," European Journal of Operational Research, Elsevier, vol. 257(1), pages 197-208.
    2. Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
    3. Fedrizzi, Michele & Giove, Silvio, 2007. "Incomplete pairwise comparison and consistency optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 303-313, November.
    4. Lahdelma, Risto & Hokkanen, Joonas & Salminen, Pekka, 1998. "SMAA - Stochastic multiobjective acceptability analysis," European Journal of Operational Research, Elsevier, vol. 106(1), pages 137-143, April.
    5. Risto Lahdelma & Pekka Salminen, 2001. "SMAA-2: Stochastic Multicriteria Acceptability Analysis for Group Decision Making," Operations Research, INFORMS, vol. 49(3), pages 444-454, June.
    6. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2019. "Sigma-Mu efficiency analysis: A methodology for evaluating units through composite indicators," European Journal of Operational Research, Elsevier, vol. 278(3), pages 942-960.
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