An automated system and a method for estimating quantities from their measured values, incorporating these estimates into decision making processes, and combining these estimates with other available knowledge (e.g. statistical, physical and logical models) are provided. Estimation is performed by utilizing finite compact representations to capture the structure of continuous or large discrete problems, allowing efficient computation of decision rules. The representations are exact, so the resulting solutions are not approximations. Decision making is accomplished by selecting decisions based on the task to be completed, results of the estimation, and any available knowledge.