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Monotone Functions on Finite Lattices: An Ordinal Approach to Capacities, Belief and Necessity Functions

  • Jean-Pierre Barthélemy
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 51)

Summary

In this paper we investigate the theoretical possibility to extend Choquet monotonicity, Dempster-Shafer belief functions as well as necessity functions to arbitrary lattices. We show, in particular, that every finite lattice admits a belief function (while the existence of a probability measure on a lattice characterizes its distributivity). Thus belief functions appear as a good substitute to probabilities in the framework of a non-classical propositional calculus.

Keywords

Distributive Lattice Belief Function Boolean Lattice Finite Lattice Focal Element 
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 Berlin Heidelberg 2000

Authors and Affiliations

  • Jean-Pierre Barthélemy
    • 1
  1. 1.Ecole Nationale Supérieure des Télécommunications de BretagneBrest (Breizh)France

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