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Capacities and Games on Lattices: A Survey of Results

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3558))

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Abstract

Capacities, introduced by Choquet [3], or fuzzy measures, introduced by Sugeno [20], are set functions vanishing on the empty set and being monotone w.r.t. set inclusion. They have been widely used in decision making and related areas, e.g., pattern recognition (see a compilation of applications in the monograph [17]). Cooperative games in characteristic form are set functions vanishing on the empty set, but not requiring monotonicity; they are sometimes called non monotonic fuzzy measures. They model the power or worth of coalitions of players.

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Author information

Authors and Affiliations

  1. Université Paris I – Panthéon-Sorbonne, LIP6, 8 rue du Capitaine Scott, 75015, Paris, France

    Michel Grabisch

Authors
  1. Michel Grabisch
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Editor information

Editors and Affiliations

  1. IIIA, Artificial Intelligence Research Institute CSIC, Spanish National Research Council, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10 Naka, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

  3. Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba, 305-8573, Ibaraki, Japan

    Sadaaki Miyamoto

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Grabisch, M. (2005). Capacities and Games on Lattices: A Survey of Results. In: Torra, V., Narukawa, Y., Miyamoto, S. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2005. Lecture Notes in Computer Science(), vol 3558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526018_2

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  • DOI: https://doi.org/10.1007/11526018_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27871-9

  • Online ISBN: 978-3-540-31883-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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