The Choquet integral as a linear interpolator

@inproceedings{Grabisch2004TheCI,
  title={The Choquet integral as a linear interpolator},
  author={Michel Grabisch},
  year={2004}
}
We show that the Choquet integral is the unique linear interpolator between vertices of the [0, 1] hypercube, using the least possible number of vertices. Related results by Lovász and Singer are discussed, as well as other interpolations. We show that the Choquet integral for bi-capacities can be also casted into this framework. Lastly, we discuss the case of Sugeno integral. 

From This Paper

Figures, tables, and topics from this paper.
21 Citations
17 References
Similar Papers

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 17 references

Submodular function and convexity

  • L. Lovász
  • Mathematical programming. The state of the art,
  • 1983
Highly Influential
4 Excerpts

Vansnick. On the extension of pseudo- Boolean functions for the aggregation of interacting bipolar criteria

  • M. Grabisch, Ch. Labreuche, J.C
  • Eur. J. of Operational Research,
  • 2003
2 Excerpts

Choquet expected utility model: a new approach to individual behavior under uncertainty and to social welfare

  • A. Chateauneuf, M. Cohen
  • Fuzzy Measures and Integrals — Theory and…
  • 2000
1 Excerpt

Generalized Expected Utility Theory: the rank-dependent model

  • J. Quiggin
  • Kluwer Academic,
  • 1993
1 Excerpt

Similar Papers

Loading similar papers…