Fonctions de croyance : décompositions canoniques et règles de combinaison. (Belief functions: canonical decompositions and combination rules)

In comparison to possibility theory, the Transferable Belief Model (TBM) – a nonproba-bilistic interpretation of Dempster-Shafer theory – enjoys little choice in terms of aggre-gation operators for the fusion of information. In this thesis, the problem of introducingsome flexibility for the combination of belief functions – the mathematical tool allowingthe representation of information in the TBM – is tackled. Our first contribution is to intro-duce infinite families of conjunctive and disjunctive combination rules for belief functions,mimicking thus the situation in possibility theory for what concerns conjunctive and dis-junctive operators. Our second contribution is a set of results making an infinite family ofcombination rules, introduced initially in a pure formal manner and called the α-junctions,of practical interest. First, we show that these rules correspond to a particular form ofknowledge about the truthfulness of the sources of information. Second, we provideseveral new simple means for the computation of the combination by an α-junction.