✦ LIBER ✦

Belief functions on lattices

✍ Scribed by Michel Grabisch

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 162 KB
Volume: 24
Category: Article
ISSN: 0884-8173
DOI: 10.1002/int.20321

No coin nor oath required. For personal study only.

✦ Synopsis

We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set of properties according to our needs. We show that all classical constructions and definitions (e.g., mass allocation, commonality function, plausibility functions, necessity measures with nested focal elements, possibility distributions, Dempster rule of combination, decomposition with regard to simple support functions, etc.) remain valid in this general setting. Moreover, our proof of decomposition of belief functions into simple support functions is much simpler and general than the original one by Shafer.

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