Multi-criteria decision analysis can be a useful tool in routing out and ranking different alternatives. However, many such analyses involve imprecise information, including estimates of utilities, outcome probabilities and criteria weights. This paper presents a general multi-criteria approach, allowing the modelling of multi-criteria and probabilistic problems in the same tree form, which includes a decision tree evaluation method integrated with a framework for analyzing decision situations under risk with a criteria hierarchy. The general method of probabilistic multi-criteria analysis extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise and uncertain facts. Thus, it relaxes the requirement for precise numerical estimates of utilities, probabilities, and weights. The evaluation is done relative to a set of decision rules, generalizing the concept of admissibility and computationally handled through the optimization of aggregated utility functions. The approach required design and development of computationally intensive algorithms for which there was no template