Entropy of capacities on lattices and set systems

@article{Honda2006EntropyOC,
  title={Entropy of capacities on lattices and set systems},
  author={Aoi Honda and Michel Grabisch},
  journal={Inf. Sci.},
  year={2006},
  volume={176},
  pages={3472-3489}
}
We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability measures, as well as the entropy of Marichal defined for classical capacities. Some properties and… CONTINUE READING

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SHOWING 1-10 OF 23 REFERENCES

General Entropy of General Measures

  • International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
  • 2002
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Entropy of discrete Choquet capacities

  • European Journal of Operational Research
  • 2002
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Entropy of a choquet capacity

  • EUSFLAT-ESTYLF Joint Conf.
  • 1999
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

A mathematical theory of communication

C. E. Shannon
  • Bell System Tech. Journ. 27
  • 1948
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

R

E. Algaba, J. M. Bilbao
  • van den Brink and A. Jiménez-Losada, Cooperative games on antimatroids, Discrete Mathematics 282
  • 2004
VIEW 1 EXCERPT