Study of the Instability of the Sign of the Nonadditivity Index in a Choquet Integral Model

Paul Alain Kaldjob Kaldjob,Brice Mayag,Denis Bouyssou

doi:10.1007/978-3-031-08974-9_16

Paul Alain Kaldjob Kaldjob, Brice Mayag + Show 1 more

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https://doi.org/10.1007/978-3-031-08974-9_16

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Abstract

AbstractThis paper studies the instability of the sign of the nonadditivity index between criteria in a Choquet integral model. Nonadditivity is an essential property of capacities defined on the sets of decision criteria and allows one to flexibly represent the phenomenon of interaction between criteria. In some cases, we show that the sign of the nonadditivity index proposed in the literature depends on arbitrary choice of a numerical representation in the set of all numerical representations compatible with the strict preferential information given by the Decision Maker(DM). This makes its interpretation difficult. We illustrate our results with examples.KeywordsInstabilityNonadditivity indexChoquet integral modelNumerical representationStrict preferential information

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