Abstract: Trust management model is fundamental for information security in open networks. In this paper, the fuzzy nature of subjective trust is considered, and the conceptions of linguistic variable and fuzzy logic are introduced into subjective trust management. A formal trust metric is given, fuzzy IF-THEN rules are applied in mapping the knowledge and experiences of trust reasoning that humanity use in everyday life into the formal model of trust management, the reasoning mechanisms of trust vectors are given, and a subjective trust management model is provided. The formal model proposed provides a new valuable way for studying subjective trust management in open networks.