A reduction of the complexity of inconsistencies test in the MACBETH 2-additive methodology

Authors:
Brice Mayag;Michel Grabisch;Christophe Labreuche
Affiliations:
Laboratoire Génie industriel, École Centrale Paris, Châtenay-Malabry Cedex, France;University of Paris 1, Paris, France;T.R.T France, Palaiseau Cedex, France
Venue:
ADT'11 Proceedings of the Second international conference on Algorithmic decision theory
Year:
2011

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Abstract

MACBETH 2-additive is the generalization of the Choquet integral to the MACBETH approach, a MultiCriteria Decision Aid method. In the elicitation of a 2-additive capacity step, the inconsistencies of the preferential information, given by the Decision Maker on the set of binary alternatives, is tested by using the MOPI conditions. Since a 2-additive capacity is related to all binary alternatives, this inconsistencies checking can be more complex if the set of alternatives is very large. In this paper, we show that it is possible to limited the test of MOPI conditions to the only alternatives used in the preferential information.