Fuzzy Measures for Students’ Mathematical Modelling Skills

MM is one of the central ideas in the nowadays mathematics education. In an earlier paper applying ideas from fuzzy logic we have developed a model formalizing the MM process and we have used the total possibilistic uncertainty as a measure of students’ MM capacities. In the present paper we develop two alternative fuzzy measures for MM. The first of them concerns an adaptation for use in a fuzzy environment of the well known Shannon’s formula for measuring a system’s probabilistic uncertainty. The second one is based on the idea of the center of mass of the represented a fuzzy set figure, that is commonly used in fuzzy logic approach to measure performance. The above (three in total) fuzzy measures for MM are compared to each other and a classroom experiment presented in our earlier paper is reconsidered here illustrating our results in practice.