Within the framework of evidence theory, data fusion consists in obtaining a single belief function by the combination of several belief functions resulting from distinct information sources. The most popular rule of combination, called Dempster’s rule of combination (or the orthogonal sum), has several interesting mathematical properties such as commutativity or associativity. However, combining belief functions with this operator implies normalizing the results by scaling them proportionally to the conflicting mass in order to keep some basic properties. Although this normalization seems logical, several authors have criticized it and some have proposed other solutions. In particular, Dempster’s combination operator is a poor solution for the management of the conflict between the various information sources at the normalization step. Conflict management is a major problem especially during the fusion of many information sources. Indeed, the conflict increases with the number of information sources. That is why a strategy for re-assigning the conflicting mass is essential. In this paper, we define a formalism to describe a family of combination operators. So, we propose to develop a generic framework in order to unify several classical rules of combination.