P2P applications are rapidly gaining acceptance among users of Internet-based services, especially because of their capability of exchanging resources while preserving the anonymity of both requestors and providers. However, concerns have been raised about the possibility that malicious users can exploit the network to spread tampered-with resources (e.g., malicious programs and viruses). A considerable amount of research has then focused on the development of trust and reputation models in P2P networks. In this paper, we propose to use fuzzy techniques in the design of reputation systems based on collecting and aggregating peers' opinions. Fuzzy techniques are used in the evaluation and synthesis of all the opinions expressed by peers. The behavior of the proposed system is described by comparison with probabilistic approaches.