Peer-to-peer (P2P) systems are based upon the cooperative interactions of member peers. Typically, peers are both autonomous and self-interested, meaning that there is no hierarchy of control or power, and that individuals seek to maximise their own goal achievement, rather than acting in a benevolent or socially-oriented manner. Consequently, interaction outcomes are uncertain, since peers can break their commitments or provide sub-standard contributions or services. Thus, when a peer cooperates it is entering into an uncertain interaction, that has an associated risk of failure or reduced performance. For peers to be effective they need some mechanism for managing this risk of failure. In this paper we show how peers can use trust to manage this risk. Our model of trust uses fuzzy logic to allow peers to represent and reason with uncertain and imprecise information regarding others’ trustworthiness.