# A Model for Deriving Trust and Reputation on Blockchain-Based e-Payment System +
## 2 Related Work
### Trust  
In essence, trust can be thought of as a directional reputation of one by the other among two entities, where the relationship between the two can be either direct or indirect through another entity [20]. Only the entities (two for direct, three for indirect) involved in these relationship(s) will contribute to the calculation of trust. Other than that, the calculation will similarly be based on the \(NE\) and \(TDW\). However, our model adds one extra concept to trust calculation: losing confidence is much easier than maintaining confidence. Generally in human life, we put a great deal of effort and time to get someone's trust. Same for businesses, and we apply this rule to the model.  
Specifically, trust between user A and B are derived as follows. First, the model checks if there are any transactions between user A and B. If so, direct trust will be calculated. Otherwise, it calculates indirect trust between them via C who has done transactions with both [PERSON] and B, if any (See Figure 1b). For every update of transactions, it checks again the existence of transactions between the two. If true, indirect trust is replaced by newly calculated direct trust.  
**Direct Trust (DTR):** To derive \(DTR\), the system first determines whether the evaluatee maintains the evaluator's trust or not as shown in Equation (7). \(\beta_{A\to B}(t)\) represents the psychological factor of trust from A to B. If the normalized evaluation given by A is same or above the previous \(DTR\), the weight \(\beta\) is set to 0.05 as it means the trust of A to B remains as before or improves. On the other hand, if lower, \(\beta\) is set to 0.25 as it could mean [PERSON] loses confidence in [PERSON]. If there is no transaction between [PERSON] and B, \(DTR\) cannot be calculated (NULL) and \(ITR\) substitutes for its role. If there were transactions but [PERSON] has never evaluated [PERSON], \(DTR\) is set to the neutral value 0.5. If the current evaluation is the first time that A grades B, \(DTR\) is initialized to \(NE\). Otherwise, \(DTR\) is derived from the incoming \(NE\) values weighted by \(\beta_{A\to B}(t)\).  
**Indirect Trust (ITR):** When it comes to a situation where a customer has no \(DTR\) information (prior transaction) with a seller, the customer faces the following problem; \"I do not know her. How can I trust her?\" Although the customer can check the seller's reputation, it may not be enough for her to make a decision if the reputation is below her expectation. In this case, \(ITR\) shows off its ability. To calculate the \(ITR\) from A to B, our model determines a broker X who has the highest \(DTR\) product (\(max(DTR_{A\to X}*DTR_{X\to B})\)) among others who have done transactions with both A and B. Once the broker is determined, \(ITR\) is derived according to Equation (9). Figure 3 illustrates an example of \(ITR\) calculation between the \"user\" and the \"target\", given that there is no direct trust (past transaction) between the two. In this example, user A will be selected as the broker to calculate the \(ITR\). If new \(DTR\) becomes available between the two entities, previously derived \(ITR\) is replaced by the newly generated \(DTR\).