•The general membership functions of four types thresholds for the grades on attribute eigenvalue are proposed.•The trust information uncertainty degree in social network is researched.•A new method to generate the incomplete social network based on the trust information uncertainty degree and variable weight function is proposed.•A novel multi-objective decision optimization model for network security situation grade assessment under multi-source information is proposed. Grade assessment of network security situation is summarized as a typical multi-index grade assessment problem. However, the existed methods for grade assessment of network security situation do not consider multi-source information such as the trust information among experts, the preference information among companies and heterogeneous information of companies. The above problems are unable to be solved through traditional assessment methods. The aim of this paper is to establish a novel multi-objective decision model for the grade assessment of network security situation under multi-source information. On the basis of describing the grade assessment problem of network security situation, the membership functions of four-type thresholds for the grades on attribute eigenvalue are put forward. Two trust information uncertainty degrees in social network are defined, and the trust transfer operator based on trust information uncertainty degree and multi-path trust integration method based on the variable weight function is proposed. Afterwards, a new method to generate the incomplete social network is used to identify the weights of experts. Then, a multi-objective decision grade assessment optimization model is further established to obtain the network security situation grades and grade discrimination based on the two-tuple linguistic operator. The proposed method provides a theoretical basis for constructing and testing the grade assessment of network security situation. Meanwhile, it develops the grade assessment system of advanced network security situation and improves the ability to protect network security.