Fuzzy Logic as a Tool for Assessing Students’ Knowledge and Skills

Abstract

Fuzzy logic, which is based on fuzzy sets theory introduced by Zadeh in 1965, provides a rich and meaningful addition to standard logic. The applications which may be generated from or adapted to fuzzy logic are wide-ranging and provide the opportunity for modeling under conditions which are imprecisely defined. In this article we develop a fuzzy model for assessing student groups’ knowledge and skills. In this model the students’ characteristics under assessment (knowledge of the subject matter, problem solving skills and analogical reasoning abilities) are represented as fuzzy subsets of a set of linguistic labels characterizing their performance, and the possibilities of all student profiles are calculated. In this way, a detailed quantitative/qualitative study of the students’ group performance is obtained. The centroid method and the group’s total possibilistic uncertainty are used as defuzzification methods in converting our fuzzy outputs to a crisp number. According to the centroid method, the coordinates of the center of gravity of the graph of the membership function involved provide a measure of the students’ performance. Techniques of assessing the individual students’ abilities are also studied and examples are presented to illustrate the use of our results in practice.

Keywords

• fuzzy sets
• fuzzy logic
• defuzzification
• students’ assessment