Application of the Grey System Theory to Assessment with Approximate Data

The Grey System theory introduced by Deng in 1982 has been nowadays proved to be an effective tool for studying systems with “poor” information data (uncertain, incomplete, etc.) In the present research Grey Numbers are used as tools for evaluating a system's mean performance when utilizing qualitative grades and not numerical scores for this purpose. Although this new assessment method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers as tools developed in an earlier work, it reduces the required computational burden, since it requires the calculation of two components only (instead of three in the case of the Triangular Fuzzy Numbers) for obtaining the mean value of the Grey Numbers involved. Examples are also presented on student and athlete assessment illustrating the new method and showing that a system's quality performance, calculated by the traditional GPA index, may lead to different assessment conclusions.