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

Silvia Bortot and Ricardo Alberto Marques Pereira

No 2011/06, DISA Working Papers from Department of Computer and Management Sciences, University of Trento, Italy

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.

Keywords: Aggregation Functions; Multiple Criteria Analysis; AHP; Inconsintency; non-additive measures; Choquet integral; and Shapley values. (search for similar items in EconPapers)
Pages: 32 pages
Date: 2011-06, Revised 2011-07-29
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