The idea of using the Choquet integral as an aggregation operator in machine learning has gained increasing attention in recent years, and a number of corresponding methods have already been proposed. Complementing these contributions from a more theoretical perspective, this paper addresses the following question: What is the VC dimension of the (discrete) Choquet integral when being used as a binary classifier? The VC dimension is a key notion in statistical learning theory and plays an important role in estimating the generalization performance of a learning method. Although we cannot answer the above question exactly, we provide a first interesting result in the form of (relatively tight) lower and upper bounds.


Model Class Decision Boundary Generalization Performance Aggregation Operator Fuzzy Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eyke Hüllermeier
    • 1
  • Ali Fallah Tehrani
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of MarburgGermany

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