Working with a non-stationary stream of data requires for the analysis system to evolve its model (the parameters as well as the structure) over time. In particular, concept drifts can occur, which makes it necessary to forget knowledge that has become obsolete. However, the forgetting is subjected to the plasticity stability dilemma. It says that increase forgetting improve reactivity of the adaptation to the new data while reducing the robustness of the system. Based on a set of inference rules, Evolving Fuzzy Systems - EFS - have proven to be effective in addressing the data stream learning problem. However tackling the stability plasticity dilemma is still an open question. This paper proposes a coherent method to integrate forgetting in Evolving Fuzzy System, based on the recently introduced notion of concept drift anticipation. The forgetting is applied with two methods: an exponential forgetting of the premise part and a differed directional forgetting of the conclusion part of EFS to preserve the coherence between both parts. The originality of the approach consists in applying the forgetting only in the anticipation module and in keeping the EFS (called principal system) learned without any forgetting. Then, when a drift is detected in the stream, a selection mechanism is proposed to replace the obsolete parameters of the principal system with more suitable parameters of the anticipation module. An evaluation of the proposed methods is carried out on benchmark online datasets, with a comparison with state-of-the-art online classifiers (Learn++.NSE, PENsemble, pclass) as well as with the original system using different forgetting strategies.