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)


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.


Distributive Lattice Belief Function Boolean Lattice Finite Lattice Focal Element 
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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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