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A Comparison of the GAI Model and the Choquet Integral w.r.t. a k-ary Capacity

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Book cover Modeling Decisions for Artificial Intelligence (MDAI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9321))

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Abstract

This paper proposes a comparison between a GAI model and the Choquet integral w.r.t. a k-ary capacity. We show that these two models are much closer than one would expect. Based on this comparison, we show a new result on the GAI models: any 2-additive GAI model can be rewritten in such a way that all utility terms in the GAI decomposition are non-negative and monotone. This is very important in practice since it allows reducing the number of monotonicity constraints to be enforced in the elicitation process, from an exponential number (of the number of attributes) to a quadratic number.

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Author information

Authors and Affiliations

  1. Thales Research and Technology, Palaiseau, France

    Christophe Labreuche

  2. Paris School of Economics, Université Paris I - Panthéon-Sorbonne, Paris, France

    Michel Grabisch

Authors
  1. Christophe Labreuche
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  2. Michel Grabisch
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Corresponding author

Correspondence to Christophe Labreuche .

Editor information

Editors and Affiliations

  1. University of Skövde, Skövde, Sweden

    Vicenc Torra

  2. Toho Gakuen, Tokyo, Japan

    Torra Narukawa

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Labreuche, C., Grabisch, M. (2015). A Comparison of the GAI Model and the Choquet Integral w.r.t. a k-ary Capacity. In: Torra, V., Narukawa, T. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2015. Lecture Notes in Computer Science(), vol 9321. Springer, Cham. https://doi.org/10.1007/978-3-319-23240-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-23240-9_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23239-3

  • Online ISBN: 978-3-319-23240-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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