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The Polytope of Fuzzy Measures and Its Adjacency Graph

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5285))

Abstract

In this paper we deal with the problem of studying the structure of the polytope of fuzzy measures for finite referential sets. We prove that the diameter of the polytope of fuzzy measures is 3 for referentials of 3 elements or more. We also show that the polytope is combinatorial, whence we deduce that the adjacency graph of fuzzy measures is Hamilton connected if the cardinality of the referential set is not 2. We also give some results about the facets and edges of this polytope. Finally, we treat the corresponding results for the polytope given by the convex hull of monotone boolean functions.

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Author information

Authors and Affiliations

  1. Artificial Intelligence Center, University of Oviedo, Spain

    Elías F. Combarro

  2. Department of Statistics and O.R., Complutense University of Madrid, Spain

    Pedro Miranda

Authors
  1. Elías F. Combarro
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  2. Pedro Miranda
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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

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© 2008 Springer-Verlag Berlin Heidelberg

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Combarro, E.F., Miranda, P. (2008). The Polytope of Fuzzy Measures and Its Adjacency Graph. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2008. Lecture Notes in Computer Science(), vol 5285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88269-5_8

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  • DOI: https://doi.org/10.1007/978-3-540-88269-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88268-8

  • Online ISBN: 978-3-540-88269-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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