# Reputation and Trust Approach for Security and Safety Assurance in Intersection Management System
## 3 Trust and Reputation Approach Description  
### Truth, Trust and Reputation Models  
In our research, we tried to project elements from social science to the information security field. It is supposed that device (agent) reliability can be determined by the level at which other devices assess it. Based on the assessment results, devices decide whether to trust the given agent or not. Agents can assess each other by analyzing the authenticity of the received data. Thus, in our approach, we employed three basic models: _Truth_, _Reputation_\((R)\), and _Trust_. **Definition 1**. : \(Truth\) _is an indicator characterizing the subjective assessment of data correctness, based on sensory devices, provided by the object of observation to the subject. This value can be formalized as Equation (1)._  
\[Truth_{t}=f_{tr_{t}}(data), \tag{1}\]  
_where \(Truth_{t}\) is a value of data correctness in time moment \(t\), data is the block of data being evaluated, and \(f_{tr_{t}}\) is the function of Truth evaluation in \(t\) time moment._  
**Definition 2**. : _Reputation (R) is a time-based value, appearing in assessment of the \(Truth\) value of the agent-object by the agent-subject. This value can be formalized as Equation (2)._  
\[R_{t}=f_{tr_{t}}(Truth_{t})=f_{tr_{t}}(f_{tr_{t}}(data)), \tag{2}\]  
_where \(R_{t}\) is the reputation value at \(t\) time moment and \(f_{tr_{t}}\) is the function of R evaluation in \(t\) time moment._  
Using only the above indicators does not allow unambiguously assessing the data correctness. To minimize possible inaccurate estimates of the behavior of elements and the correctness of data, we introduce a _Trust_ indicator. **Definition 3**. : _Trust is an indicator calculated on the combination of R and Truth and characterizing the subjective assessment of the agent-object behavior by the agent-subject. This value can be formalized as Equation (3)._  
\[Trust_{t}=f_{trust_{t}}(R_{t-1},Truth_{t})=f_{trust_{t}}(f_{tr_{t-1}}(f_{tr_{t-1 }}(data)),f_{tr_{t}}(data)), \tag{3}\]  
_where \(Trust_{t}\) is the value of Trust in \(t\) time moment and \(f_{trust_{t}}\) is the function of Trust evaluation in \(t\) time moment._  
Each of the presented indicators can take two opposite values, conditionally describing evaluated data as \"correct\" or \"incorrect\". \"Correct\" means that agent-subject classifies the received data from the agent-object as an actual data. \"Incorrect\", in contrast to \"correct\", indicates that the received data from the agent-object are classified as a false data. Thus, each indicator can take a value in the range \([0,1]\). However, there is a case when data received from the agent-object cannot be evaluated by the agent-subject, and the value of the indicators can be neither 0 nor 1. In this case, the agent-subject should consider valuations of these data by other group agents. In relation to these indicator values, the following assumptions are introduced:  
**Assumption 1**. : \(Truth\in[0,1]\)_;_  
**Assumption 2**. : \(R\in[0,1]\)_;_  
**Assumption 3**. : \(Trust\in[0,1]\)Suppose that \(e\in E,E\) is a set of agents. Then, all agents are considered as homogeneous in relation to their abilities to receive data from the environment using sensor devices and to transmit these data to each other. In this case, agents can accumulate collective knowledge about the environment and employ this knowledge in solving the problems of collective action optimization. The knowledge of each agent in the system can be represented in the form of the set \(KN=\{KN_{e_{0}},\ldots,KN_{e_{n}}\}\), and the knowledge of each agent can also be represented as a set \(KN_{e_{0}}=\{kn_{e_{0}},\ldots,kn_{e_{n}}\}\). Knowledge can be classified as passive and active:  
* Passive knowledge \((KN_{e_{\text{pss}}})\) represents the current knowledge about the environment that is not the result of collaborative actions. * Active knowledge \((KN_{e_{\text{act}}})\) is the knowledge gained in the process of collaborative actions.