Application of Fuzzy Numbers to Assessment Processes

A fuzzy number (FN) is a special kind of FS on the set R of real numbers. The four classical arithmetic operations can be defined on FNs, which play an important role in fuzzy mathematics analogous to the role played by the ordinary numbers in crisp mathematics. The simplest form of FNs is the triangular FNs (TFNs), while the trapezoidal FNs (TpFNs) are straightforward generalizations of the TFNs. In the chapter, a combination of the COG defuzzification technique and of the TFNs (or TpFNs) is used as an assessment tool. Examples of assessing student problem-solving abilities and basketball player skills are also presented illustrating in practice the results obtained. This new fuzzy assessment method is validated by comparing its outcomes in the above examples with the corresponding outcomes of two commonly used assessment methods of the traditional logic, the calculation of the mean values, and of the grade point average (GPA) index. Finally, the perspectives of future research on the subject are discussed.