We use relations between undirected graphs and conditional independence to introduce a new class of graphical representations, expected utility networks with hoth discrete and continuous variables and discuss some of their structural properties. We want to show that in these networks node separation with respect to the probability and utility subgraphs implies conditional utility independence, and conditional independent decisions can be effectively decentralized. An application to decision making in expected utility networks in mixed models is introduced.
The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed.