Identification of non-additive measures from sample data

  • Pedro Miranda
  • Michel Grabisch
  • Pedro Gil
Part of the International Centre for Mechanical Sciences book series (CISM, volume 472)


Non-additive measures have become a powerful tool in Decision Making. Therefore, a lot of problems can be solved through the use of Choquet integral with respect to a non-additive measure. Once the decision maker decides to use this criterion in his decision process, next step is to build the non-additive measure up. In this paper we solve the problem of learning the measure from sample data by minimizing the squared error. We study the conditions for the unicity of solution, as well as the set of solutions. A particular family of non-additive measures, the so-called k-additive measures, are specially appealing due to their simplicity and richness. We will use 2-additive measures in a practical case to show that k-additive measures can be considered as a good approximation of general measures.


Extreme Point Convex Combination Fuzzy Measure Quadratic Problem Quadratic Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • Pedro Miranda
    • 1
  • Michel Grabisch
    • 2
  • Pedro Gil
    • 1
  1. 1.Department of Statistics and Operations ResearchUniversity of OviedoSpain
  2. 2.Université Paris I- Panthéon- SorbonneParisFrance

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