uncertainty. The foundation of the trust representation is that an opinion (an evidence or a confidence) about trust can be represented as a four-tuple (trust, distrust, uncertainty, base rate), where trust, distrust and uncertainty must add up to one, and hence are dependent through additivity. Subjective logic is an example of computational trust where uncertainty is inherently embedded in the calculation process and is visible at the output. It is not the only one, it is e.g. possible to use a similar quadruplet (trust, distrust, unknown, ignorance) to express the value of confidence, as long as the appropriate operations are defined. Despite the sophistication of the subjective opinion representation, the particular value of a four-tuple related to trust can be easily derived from a series of binary opinions about a particular actor or event, thus providing a strong link between this formal metric and empirically observable behaviour. Finally, there are CertainTrust and CertainLogic. Both share a common representation, which is equivalent to subjective opinions, but based on three independent parameters named 'average rating', 'certainty', and 'initial expectation'. Hence, there is a bijective mapping between the CertainTrust-triplet and the four-tuple of subjective opinions. Fuzzy logic Fuzzy systems, as trust metrics can link natural language expressions with a meaningful numerical analysis. Application of fuzzy logic to trust has been studied in the context of peer-to-peer networks to improve peer rating. Also for grid computing it has been demonstrated that fuzzy logic allows to solve security issues in reliable and efficient manner. Properties of trust metrics The set of properties that should be satisfied by a trust metric vary, depending on the application area. Following is a list of typical properties. Transitivity Transitivity is a highly desired property of a trust metric. In situations where A trusts B and B trusts C, transitivity concerns the extent to which A trusts C. Without transitivity, trust metrics are unlikely to be used to reason about trust in more complex relationships. The intuition behind transitivity follows everyday experience of 'friends of a friend' (FOAF), the foundation of social networks. However, the attempt to attribute exact formal semantics to transitivity reveals problems, related to the notion of a trust scope or context. For example, defines conditions for the limited transitivity of trust, distinguishing between direct trust and referral trust. Similarly, shows that simple trust transitivity does not always hold, based on information on the Advogato model and,