# Reliability Model Based Dynamic Multi-Level Trust Analysis
## 1 Introduction  
Trust is an important reference data for both parties to interact in online social networks (OSNs). Objective and accurate trust can reduce the risk of interaction, such as the behavior of malicious users. It is quite difficult for the OSN users to estimate the risk of interacting with others in the networks before determining to perform interactions [1]. Therefore, an objective and reliable trust evaluation mechanism becomes particularly important for OSNs. But trust is a complex concept, which contains both sociological and psychological factors. Thus, it is often complex and difficult to model and quantify trust in OSNs [2]. Trust representation models usually include two types: discrete [3; 4; 5; 6; 7; 8; 9; 10; 11] and continuous [12; 13; 14; 15]. Refs. [3; 5; 7] use multiple discrete trust degrees to describe the trust relationships, and edge sign is used in [6]. In particular, Refs. [8; 10; 11] express trust from multiple perspectives. Ref. [4] uses the matrix of trusts and the matrix of distrusts to complete the expression of trust between users. Refs. [13; 15] generate the final trust value by integrating trust from multiple perspectives. Furthermore, Refs. [12; 14] respectively introduce measurement and error propagation theory and network flow. The discrete multi-level trust model refers to a trust modeling method, which divides the trust relationship between users into multiple levels or perspectives to map the different degrees of description in the real-world [13]. The discrete multi-level trust model refers to a trust modeling method which divides the trust relationship between users into multiple levels to map the different degrees of description in the real-world [8]. After an interaction ends, the user can choose a trust level for the other party based on their feelings. Multi-level models based on this modeling approach [9; 10; 11] are convenient for users to give intuitive evaluations that fit their feelings. However, there are two problems with this approach: Firstly, this model can only rank trust and cannot obtain accurate trust. It is not accurateenough to describe trust. Secondly, it is not easy to find a sound computational principle based on this model. The continuous trust model is just the opposite. The continuous model can more accurately describe the trust and is easier to calculate. However, the continuous model is not easy for users to accurately express their feelings as a real value. Therefore in [16], a multi-level trust representation model with probability values was proposed. A trust calculation method based on multi-valued decision diagram (MDD) was designed. Combining the characteristics of discrete and continuous models, this method not only can facilitate the rating by users, but also can express trust more accurately. However, the model of [16] treats distrust simply as a level of trust without considering characteristics of distrust. Thus, the propagation and computation rules for the distrust are assumed to be the same as those for trust. In the actual interaction process, the information regarding not only who to trust but also who cannot be trusted is critical to minimize and even avoid risks [17]. Actually, it is often more important to predict distrust for a trust or to trustee [18; 19]. Studies in [20; 21] show that trust and distrust coexist in the human brain. Sometimes we have no or little contact with the predicted party, so simply classifying the party as being trustful or distrustful is biased. In Ref. [19], the authors talk about the concepts of trust and distrust. There are two perspectives of trust and distrust. One of the opinions is that distrust is the opposite of trust and the other one is distrust is not only the opposite to trust. The early approaches model the trust by a single real number, completely ignoring the difference between distrust and neutrality [22; 23]. It is clear that the indiscriminate definition of distrust and neutrality as lack of trust is unreasonable [24].