The discounting operation is a well known operation on belief functions, which has proved to be useful in many applications. However, the discounting operation only allows one to weaken a source, whereas it is sometimes useful to strengthen it when it is deemed to be too cautious. For that purpose, the de-discounting operation was introduced as the inverse operation of the discounting operation by Denoeux and Smets. From another point of view, Zhu and Basir introduced an extension of the classical discounting operation by allowing the discount rate to be out of the range [0,1]. This operation performs a discounting or a de-discounting of a belief function. A new interpretation of this scheme is presented in this paper. A more general form of reinforcement process, as well as a parameterized family of transformations encompassing all previous schemes, are also introduced