On the robustness of the sign of nonadditivity index in a Choquet integral model

Paul Kaldjob Kaldjob, Brice Mayag () and Denis Bouyssou
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Paul Kaldjob Kaldjob: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Brice Mayag: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: In the context of Multiple Criteria Decision Making, this paper studies the robustness of the sign of nonadditivity index for subset of criteria in a Choquet integral model. In the case where the set of alternatives is discrete, the use of the nonadditivity index proposed in the literature often leads to interpretations which are not always robust. Indeed, the sign of this nonadditivity index can depend on the arbitrary choice of a numerical representation in the set of all numerical representations compatible with the ordinal preferential information given by the Decision Maker. We characterize the ordinal preferential information for which the problem appears. We also propose a linear program allowing to test the non robustness of the sign of nonadditivity index for subset of criteria.

Keywords: Robustness Nonadditivity index Binary alternatives Choquet integral model Numerical representation; Robustness; Nonadditivity index; Binary alternatives; Choquet integral model; Numerical representation (search for similar items in EconPapers)
Date: 2022
Note: View the original document on HAL open archive server: https://hal.science/hal-03904424v1
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Published in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, inPress

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03904424

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