Axiomatisation of fully probabilistic design

This text provides background of fully probabilistic design (FPD) of decision-making strategies and shows that it is a proper extension of the standard Bayesian decision making. FPD essentially minimises Kullback–Leibler divergence of closed-loop model on its ideal counterpart. The inspection of the background is important as the current motivation for FPD is mostly heuristic one, while the technical development of FPD confirms its far reaching possibilities. FPD unifies and simplifies subtasks and elements of decision making under uncertainty. For instance, (i) both system model and decision preferences are expressed in common probabilistic language; (ii) optimisation is simplified due to existence of explicit minimiser in stochastic dynamic programming; (iii) DM methodology for single and multiple aims is unified; (iv) a way is open to completion and sharing non-probabilistic and probabilistic knowledge and preferences met in knowledge and preference elicitation as well as unsupervised cooperation of decision makers.