# Reputation and Trust Approach for Security and Safety Assurance in Intersection Management System
## 3 Trust and Reputation Approach Description
### Truth, Trust and Reputation Models
On the basis of the previously introduced definitions and assumptions, data correctness evaluation requires calculating the vectors of truth, trust and reputation values, produced by each agent to evaluate the correctness of data received from others:  
* \(\overline{Truth_{e}}= \begin{pmatrix}\ldots\\ Truth_{e_{i}}\\ \ldots\end{pmatrix} \), where \(Truth_{e_{i}}\) is the truth of data, received from agent \(e,e_{i}\in E,e_{i}\
eq e,i=1\ldots|E|\);
* \(\overline{R_{e}}= \begin{pmatrix}\ldots\\ R_{e_{i}}\\ \ldots\end{pmatrix} \), where \(R_{e_{i}}\) is the reputation of the agent \(e_{i}\), calculated by agent \(e,e_{i}\in E,e_{i}\
eq e,i=1\ldots|E|\); and
* \(\overline{Trust_{e}}= \begin{pmatrix}\ldots\\ Trust_{e_{i}}\\ \ldots\end{pmatrix} \), where \(Trust_{e_{i}}\) is the trust value to agent \(e_{i}\) of agent \(e,e_{i}\in E,e_{i}\
eq e,i=1\ldots|E|\). Below, one can find further explanation of how these indicators are calculated. 1.1 Truth assessment of the data transmitted from the agent-object to the agent-subject is based on passive knowledge \(KN_{\text{pss}}\) available to the agent-subject. \(KN_{\text{pss}}\) includes information collected using the sensor devices of the agent-subject or information transmitted from other agents. If the estimated data are represented in the form of several blocks of information, for example, the position of the group is given as the position of each individual agent, then the computation of data correctness is limited to averaging the \(Truth\) value over all the blocks. In a formalized form, we present the calculation of this indicator for the agent-object \(e_{i}\) by the agent-subject \(e\), respectively (Equation (4)). \[\overline{Truth_{e}^{s}}= \begin{pmatrix} Truth_{e_{i}}^{s_{0}}\\ \ldots\\ Truth_{e_{i}}^{s_{ll}}\end{pmatrix} , \tag{4}\]  
where \(ll\) is the number of data blocks, by which the \(Truth\) of the information is evaluated. In such a case, the vector of truth index estimates for all agents can be represented as:  
\[\overline{Truth_{e}^{s}}= \begin{pmatrix}\ldots\\ \frac{\sum_{l=1}^{ll} Truth_{e_{i}}^{s_{l}}}{bl}\\ \ldots\end{pmatrix} , \tag{5}\]where \(Truth_{e_{i}}^{s_{i}}\) is the estimated \(Truth\) value for the agent-object \(e_{i}\) by the data block \(s_{j}\). In general, each block of data is valued as correct or incorrect. The indicator is formed as:  
\[Truth_{e_{i}}^{s_{j}}= \begin{cases}1,\text{if the data is correct}\\ 0,\text{if the data is incorrect}\end{cases}  \tag{6}\]  
With such an assessment of the \(Truth\) value by data blocks, the \(Truth\) for the agent-object will be in the interval from 0 to 1. However, when the agent-subject does not have the ability to evaluate data received from the agent-object, or does not have an access to a reliable communication channel, then the \(Truth\) value is estimated based on the average values of the indicators received from other agents that conducted the agent-object data assessment:  
\[Truth_{e_{i}}=\frac{\sum Truth_{e_{i_{j_{i}}}}}{n_{truth}}, \tag{7}\]  
where \(e\in E\) and \(e_{i}\in E,n_{truth}\) is the number of agents having an estimate of the \(Truth\) of the \(e_{i}\) data. If there are no such agents, the \(Truth\) value is estimated as 0.5, i.e., the average value at which the data are not assessed as correct or incorrect.