The paper proposes a mathematical framework that supports a formal representation of a decision aiding process in a multi-criteria and multi-actors context in an uncertain universe. For this purpose, possibility distributions representing uncertainty are characterized and indicators describing them are provided in order to simplify their quantitative interpretation. To take the interactions between criteria into account, a Choquet integral based aggregation of the possibility distributions is proposed by using a suitable decomposition in linear domains. For the summary indicator aggregation, key theoretical results on the union of the upper and lower mean values of a possibility distribution are established. The contributions of the location and imprecision criteria indicators to the indicators of the distribution associated with the global evaluation are then defined. These contribution indicators constitute the basis of the explanations aimed at aiding the decision making. In addition, a software system, called a “Feedback Based Recommendation System” (FBRS) has been developed and used to aid the marketing teams of an e-commerce company in their activities. The customers' feedback database constitutes the basis of the diagnosis functionalities of the FBRS which uses a possibility representation to model the uncertainty associated with the imprecision, the variability of the opinions of the customers.