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Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process

Author

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  • Silvia Bortot
  • Ricardo Alberto Marques Pereira

Abstract

We propose to extend the aggregation scheme of Saaty's AHP, from the standard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the consistency case. In the general inconsistency case, however, the new aggregation scheme based on Choquet integration tends to attenuate (resp. emphasize) the priority values of the criteria with higher (resp. lower) average inconsistency with the remaining criteria.

Suggested Citation

  • Silvia Bortot & Ricardo Alberto Marques Pereira, 2011. "Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process," DISA Working Papers 2011/06, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
  • Handle: RePEc:trt:disawp:2011/06
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    References listed on IDEAS

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    1. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445132, HAL.
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    5. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
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    Keywords

    Aggregation Functions; Multiple Criteria Analysis; AHP; Inconsintency; non-additive measures; Choquet integral; and Shapley values.;

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