## 4 Iterative Trust and Reputation Computation Model
### Model of Total Trust and Reputation  
Trust in service-oriented network environments such as B2C e-commerce include direct and indirect factors. However, when a new service client or buyer evaluates the trust status of the service provider before making a transaction decision, direct trust and indirect trust factors are not separated. Trust evaluation is as an integral psychological conception. Indirect trust is focused on the reputation of the service providers based on recommendations of the total online service clients, and the computation formulate of reputation is denoted by Equation (11). The reputation system based on the trust reviews is illustrated by Figure 1. There are in total \(N\) service clients and one service provider. In order to describe the total trust computation model clearly, we give a discrete difference formulate of total trust, direct trust, and reputation. In the following equations, time variable \(t\) is with the unit step such as \(t_{i+1}-t_{i}=1,i\in Z\). At the time \(t_{i}\), total trust value and direct trust regarding the service provider from a new service client (denoted \(j\) th service client) are denoted as \(T^{(j)}(t_{i})\) and \(f_{dw}^{(j)}(t_{i})\), and \(r(t_{i})\) denotes reputation value at that time. The integrated quantitative total trust value can be calculated as  
\[T^{(j)}(t_{i})=\beta f_{dw}^{(j)}(t_{i})+(1-\beta)r(t_{i}) \tag{13}\]  
where the weight factor \(\beta\in[0,1]\) balances the values of direct trust and reputation values. If \(\beta=1\), the total trust value from the new service client will be equal to his direct trust. If \(\beta=0\), the total trust value come from the reputation. Equation (10), Equations (11) and (13) give the relation of total trust, direct trust, and reputation value such as  
\[T^{(j)}(t_{i})=\beta C^{(j)}*T^{(j)}{}_{c}(t_{i})\frac{e^{a^{(j)}t_{i}}-e^{-a ^{(j)}t_{i}}}{e^{a^{(j)}t_{i}}+e^{-a^{(j)}t_{i}}}+(1-\beta)\frac{1}{N}\sum_{l =1}^{N}C^{(l)}*T^{(l)}_{c}*\lambda_{(l)}{}^{(t_{i}-t_{0})}\frac{e^{a^{(l)}t_{i }}-e^{-a^{(l)}t_{i}}}{e^{a^{(l)}t_{i}}+e^{-a^{(l)}t_{i}}} \tag{14}\]  
If Equation (12) is used to simulate the decrement processes of the total trust, the integrated total trust value can be calculated as  
\[T^{(j)}(t_{i})=\beta C^{(j)}*T^{(j)}{}_{c}(t_{i})\frac{e^{-a^{(j)}t_{i}}-e^{a ^{(j)}t_{i}}}{e^{-a^{(j)}t_{i}}+e^{a^{(j)}t_{i}}}+(1-\beta)\frac{1}{N}\sum_{l =1}^{N}C^{(l)}*T^{(l)}_{c}*\lambda_{(l)}{}^{(t_{i}-t_{0})}\frac{e^{-a^{(l)}t_ {i}}-e^{a^{(l)}t_{i}}}{e^{-a^{(l)}t_{i}}+e^{a^{(l)}t_{i}}} \tag{15}\]  
The iterative total trust and reputation model will be further proposed. Total trust values of \(j\)th service client at time \(t_{i}\) and \(t_{i+1}\) are \(T^{(j)}(t_{i})\) and \(T^{(j)}(t_{i+1})\), and the reputation values of the service provider at time \(t_{i}\) and \(t_{i+1}\) are \(r(t_{i})\) and \(r(t_{i+1})\), and the \(j\)th service client is in the total \(N\) service clients. As we see, reputation is the collecting, processing, and aggregating of trustworthy information about the service provider. The role in trust of each service client is to change and sustain the reputation of the service provider. In addition, the service provider earns and retains this trust via his reputation. The reputation of the service provider with the whole range conception is interactive with psychological status of trust. If we assume that the total trust value of the service client has the same derivative with direct trust, the difference form of Equation (3) can be used to calculate the total trust values \(T^{(j)}(t_{i+1})\) of \(j\)th service client by \(T^{(j)}(t_{i})\) at time\(t_{i}\) as \[T^{(j)}(t_{i+1})=T^{(j)}(t_{i})+C^{(j)}*T^{(j)}_{\ \ c}(t_{i})*(\alpha^{(j)}-( \frac{e^{a^{(j)}t_{i}}-e^{-a^{(j)}t_{i}}}{e^{a^{(j)}t_{i}}+e^{-a^{(j)}t_{i}}})^{2 })(t_{i+1}-t_{i}) \tag{16}\]  
The total trust \(T^{(j)}(t_{i+1})\) at time \(t_{i+1}\) is determined by the total trust value \(T^{(j)}(t_{i})\) at time \(t_{i}\) and reputation value \(r(t_{i})\) at time \(t_{i}.\) The time variable \(t\) has a unit step.