Nowadays, the sustainability of human activities is a major worldwide concern. Indeed, the problem is no longer to evaluate only the efficiency of human activities, but also sustainability along many axes that can be of various kinds: economic, social, environmental, etc. Such assessments are a major challenge for today’s society. Because of the exponential development of means of data recording and storage (“big data” buzz word), and on the basis of Volume, Variety and Velocity properties of big data, scientists need to compute large amounts of data and so do not necessarily have time to clean them. In this context, they compute all available data whose types of imperfections are heterogeneous. Actors in several domains have to cope with such data, especially to assist humans in their decisions by merging them from many data sources (e.g. measurements, sensors, observations) to model behaviours of complex systems. Mathematical approaches to model imperfect data are well known and established in various scientific areas today, such as both probability based and possibility based calculus. Decisions of experts from various fields have to handle rigorous computations and aggregations of both data and their associated uncertainty. We propose a rigorous model to handle uncertainty on the attributes of objects, and a way to rigorously aggregate discrete data, whose imperfections nature are covered either by the classical probability theory (randomness), either by the possibility theory (fuzziness) thanks to the Dempster-Shafer theory.