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.
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Barthélemy, JP. (2000). Monotone Functions on Finite Lattices: An Ordinal Approach to Capacities, Belief and Necessity Functions. In: Fodor, J., De Baets, B., Perny, P. (eds) Preferences and Decisions under Incomplete Knowledge. Studies in Fuzziness and Soft Computing, vol 51. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1848-2_11
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DOI: https://doi.org/10.1007/978-3-7908-1848-2_11
Publisher Name: Physica, Heidelberg
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