Trust management model is fundamental for information security in open networks. The fuzzy nature of subjective trust is considered, and the fuzzy set theory has been used to model the issues of trust management. The formalized valuation of subjective trust is given, the definition of trust class and the evaluation of trust are discussed, derivation rules of trust relationships are presented and a subjective trust management model is provided. The formal model proposed in this paper provides a new valuable way for studying trust management in open networks.