counterpart in the relationship. A low ability value should result from the existence of conflicting data and this should make the observer unable to fill in the uncertainty gap. When there are not enough observations to distinguish rating trends data might ppear to be highly conflicting. We propose the following formula to model uncertainty from prediction error where k is the number of common experiences(ratings)of the two entities that form a relationship, Pr is the predicted rating of item x calculated using some prediction calculation formula and Ix is the real rate that the entity has given to item x. m represents the maximum value that a rating can take and it is used here as a measure of rating. As can be seen, uncertainty is inversely proportional to the number of ex periences. This agrees with the definition of uncertainty we presented in the pre- vious section The logical reasoning for deriving formula(4.1) for Uncertainty is the following. Incertainty is proportional to the prediction error for every user's single experience, therefore the numerator represents the absolute error between the predicted value (using a rating prediction formula) and the real (rated) value. The denominator m has been used for normalizing the error to the range 0-1. The summing symbol has been used to include all the experiences(k in number) of a particular user. Finally, the division by the total number of experiences(k)is done to get the average norma lized error. In the sum we take every pair of common ratings and try to predict what the rate p would be. Therefore it is assumed that on every prediction calculation all but the real rating of the value that is to be predicted exist Unlike Beta mapping [14 where u tends to 0 as the number of experiences grows, in our model the trend remains quite uncertain because u is also dependent on the average prediction error. In the extreme case where there is high controversy in the data, u will reach a value close to 1, leaving a small space for belief and dis- belief. Another interesting characteristic of our model is the asymmetry in the trust relationships produced, which adheres to the natural form of relationships since the levels of trust that two entities place on each other may not be necessarily the same As regards the other two properties b(belief) and d(disbelief), we set them up in such a way that they are dependent on the value of the Correlation Coefficient CC We made the following two assumptions The belief (disbelief) property reaches its maximum value(1-u) when CC=l(or The belief (disbelief) property reaches its minimum value(1-u) when CC=-1(or CC=l respectively) which are expressed by the two formulae b=(1-)a+CC) (4.3)counterpart in the relationship. A low ability value should result from the existence of conflicting data and this should make the observer unable to fill in the uncertainty gap. When there are not enough observations to distinguish rating trends data might appear to be highly conflicting. We propose the following formula to model uncertainty from prediction error: ¦  k x xx m rp k u 1 1 (4.1) where k is the number of common experiences (ratings) of the two entities that form a relationship, px is the predicted rating of item x calculated using some prediction calculation formula and rx is the real rate that the entity has given to item x. m represents the maximum value that a rating can take and it is used here as a measure of rating. As can be seen, uncertainty is inversely proportional to the number of ex￾periences. This agrees with the definition of uncertainty we presented in the pre￾vious section. The logical reasoning for deriving formula (4.1) for Uncertainty is the following: Uncertainty is proportional to the prediction error for every user’s single experience; therefore the numerator represents the absolute error between the predicted value (using a rating prediction formula) and the real (rated) value. The denominator m has been used for normalizing the error to the range 0-1. The summing symbol has been used to include all the experiences (k in number) of a particular user. Finally, the division by the total number of experiences (k) is done to get the average norma￾lized error. In the sum we take every pair of common ratings and try to predict what the rate p would be. Therefore it is assumed that on every prediction calculation all but the real rating of the value that is to be predicted exist. Unlike Beta mapping [14] where u tends to 0 as the number of experiences grows, in our model the trend remains quite uncertain because u is also dependent on the average prediction error. In the extreme case where there is high controversy in the data, u will reach a value close to 1, leaving a small space for belief and dis￾belief. Another interesting characteristic of our model is the asymmetry in the trust relationships produced, which adheres to the natural form of relationships since the levels of trust that two entities place on each other may not be necessarily the same. As regards the other two properties b (belief) and d (disbelief), we set them up in such a way that they are dependent on the value of the Correlation Coefficient CC. We made the following two assumptions: x The belief (disbelief) property reaches its maximum value (1-u) when CC=1 (or CC=-1 respectively) x The belief (disbelief) property reaches its minimum value (1-u) when CC= -1 (or CC=1 respectively) which are expressed by the two formulae: )1( 2 )1( CC u b   (4.2) )1( 2 )1( CC u d   (4.3) 108 G. Pitsilis et al