Axiomatization of an Importance Index for Generalized Additive Independence Models

  • Mustapha Ridaoui
  • Michel Grabisch
  • Christophe Labreuche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)

Abstract

We consider MultiCriteria Decision Analysis models which are defined over discrete attributes, taking a finite number of values. We do not assume that the model is monotonically increasing with respect to the attributes values. Our aim is to define an importance index for such general models, encompassing Generalized-Additive Independence models as particular cases. They can be seen as being equivalent to k-ary games (multichoice games). We show that classical solutions like the Shapley value are not suitable for such models, essentially because of the efficiency axiom which does not make sense in this context. We propose an importance index which is a kind of average variation of the model along the attributes. We give an axiomatic characterization of it.

Keywords

MultiCriteria decision analysis k-ary game Shapley value 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mustapha Ridaoui
    • 1
  • Michel Grabisch
    • 1
  • Christophe Labreuche
    • 2
  1. 1.Paris School of EconomicsUniversité Paris I - Panthéon-SorbonneParisFrance
  2. 2.Thales Research and TechnologyPalaiseauFrance

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