Application of the Triangular Fuzzy Model to Assessment of Analogical Reasoning Skills

Michael Gr. Voskoglou^1, and Igor Ya. Subbotin²

¹School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Patras, Greece

²College of Letters and Sciences, National University of Los Angeles, California, USA

Cite this paper:
Michael Gr. Voskoglou and Igor Ya. Subbotin. Application of the Triangular Fuzzy Model to Assessment of Analogical Reasoning Skills. American Journal of Applied Mathematics and Statistics. 2015; 3(1):1-6. doi: 10.12691/ajams-3-1-1

Abstract

We apply the Triangular Fuzzy Assessment Model (TFAM) for analogical reasoning skills assessment. The TFAM is a new original model based on the Centre of Gravity (COG) defuzzification technique, which we have properly adapted and used in earlier papers as an assessment method of several human activities. The main idea of the TFAM is the replacement of the rectangles appearing in the graph of the COG technique by isosceles triangles sharing common parts. In this way, we can treat better the ambiguous cases of scores being at the boundaries between two successive linguistic characterizations (grades) of the level of the individuals’ performance. An application is also presented illustrating our results in practice, where the TFAM is compared with two traditional assessment methods (calculation of the means and of the GPA index) based on principles of the bivalent logic (yes-no).

Keywords:
Analogical Reasoning Fuzzy Logic Centre of Gravity (COG) defuzzification technique Triangular Fuzzy Assessment model (TFAM) GPA index

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