What is Uncertainty and Information

In this chapter two new fuzzy assessment models are developed, the trapezoidal (TRFAM) and the Triangular (TFAM), which are proved to be equivalent to each other. These models are new original variations of the Centre of Gravity (COG) defuzzification technique, which has been properly adapted and used in earlier papers as an assessment method. The central idea of TRFAM is the replacement of the rectangles appearing in the graph of the membership function of the COG technique by isosceles trapezoids sharing common parts. In this way one treats better the ambiguous cases being at the boundaries between two successive linguistic assessment characterizations (grades). The corresponding idea of TFAM is the replacement of the rectangles by isosceles triangles. Two applications are also presented (students' and Bridge players' assessment) illustrating our results. In these applications the TRFAM and TFAM are validated through their comparison with other, already established, assessment methods.