Digital transformation has led to the fact that almost all organizations and companies are provided with internal private networks and manage sensitive data and applications. In this context, system administrators are superusers who can access all this sensitive material. As it is known that many frauds are caused by internal actions, we argue that it is important to be provided with strong automated logging systems even for superusers. For this purpose, blockchains are an efficient solution as they cannot be overwritten by the system administrators. However, as it is not efficient to store all the actions, we introduce in this paper a novel system based on fuzzy rules in order to efficiently manage the system logging system in a blockchain.