Monotone Functions on Finite Lattices: An Ordinal Approach to Capacities, Belief and Necessity Functions
Jean‐Pierre Barthélemy · Studies in fuzziness and soft computing · 2000
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.