Title: Application of triangular fuzzy numbers to analogical reasoning

Authors: Michael Gr. Voskoglou

Addresses: School of Technological Applications, Graduate Technological Educational Institute of Western Greece, Patras, 26334, Greece

Abstract: In this work a combination is applied of triangular fuzzy numbers (TFNs) and of the centre of gravity (COG) defuzzification technique as means for assessing student skills in solving mathematical problems by analogy. A classroom experiment is also presented performed with students of the Graduate Technological Educational Institute (T. E. I.) of Western Greece, which illustrates our results in practice. In order to check the validity of the fuzzy assessment method, its outcomes in this experiment are compared to the corresponding outcomes of two traditional assessment methods of the bi-valued logic, the calculation of the mean value of student scores and the grade point average (GPA) index. The usefulness of the fuzzy approach becomes evident when linguistic grades only and not numerical scores are used for student assessment.

Keywords: AR; analogical reasoning; APS; analogical problem solving; student assessment; grade point average (GPA) index; fuzzy assessment methods; FSs; fuzzy sets; FNs; fuzzy numbers; TFNs; triangular fuzzy numbers.

DOI: 10.1504/IJQRE.2018.092302

International Journal of Quantitative Research in Education, 2018 Vol.4 No.3, pp.240 - 254

Available online: 30 May 2018 *

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