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Finding the Set of k-additive Dominating Measures Viewed as a Flow Problem

  • Pedro MirandaEmail author
  • Michel Grabisch
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 610)

Abstract

In this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.

Keywords

Fuzzy measures Dominance k-additivity 

Notes

Acknowledgements

This research has been partially supported by Spanish Grant MTM2012-33740 and MTM-2015-67057.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Universidad Complutense de MadridMadridSpain
  2. 2.Paris School of EconomicsUniversité Paris I-Panthéon-SorbonneParisFrance

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