Reproducing scoring function(RSF) is one of the several methods proposed to induce a decision-maker to reveal his true opinion in terms of probability. Reproducing scoring function can induce a decision maker or probability assessor (PA) to report his true belief by rewarding honest PAs and punishing dishonest PAs. Thus, a consistent and repeated use of the reproducing scoring function will improve the accuracy of the assessor``s report. In addition to engendering honesty, RSF can also be employed to evaluate the validity of probability assessments. So far, discussions on the reproducing scoring function have been based on the point probability estimation scheme for the likelihood of an unknown event. In this thesis, the reproducing scoring function is extended to the interval representation scheme which can express the PA``s confidence on his report in a natural way and, therefore, is more reasonable. Assuming the beliefs are distributed over the interval with a given probability density function, reward sum is defined as the expected sore. The reward sum does not satisfy all the requirements of the reproducing scoring function for general probability density functions. However, it does satisfy the requirements for almost all useful probability density functions such as the uniform density functions, the triangle-type density functions such as the uniform density functions, the triangle-type density functions, and the symmetric density functions.