Defuzzification of Fuzzy Numbers for Student Assessment

Michael Gr. Voskoglou^1,

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

Cite this paper

Michael Gr. Voskoglou. Defuzzification of Fuzzy Numbers for Student Assessment. American Journal of Applied Mathematics and Statistics. 2015; 3(5):206-210. doi: 10.12691/AJAMS-3-5-5

Abstract

In an earlier work, recently published in this journal, we have used the Triangular Fuzzy Numbers (TFNs) as an assessment tool of student skills. This approach led to an approximate linguistic characterization of the students’ overall performance, but it was not proved to be sufficient in all cases for comparing the performance of two different student groups, since two TFNs are not always comparable. In the present paper we complete the above fuzzy assessment approach by presenting a defuzzification method of TFNS based on the Center of Gravity (COG) technique, which enables the required comparison. In addition we extend our results by using the Trapezoidal Fuzzy Numbers (TpFNs) too, which are a generalization of the TFNs, for student assessment and we present suitable examples illustrating our new results in practice.

Keywords

Human Assessment, Fuzzy Logic, Fuzzy Numbers (FNs), Triangular (TFNs) and Trapezoidal (TpFNs) FNs, Center of Gravity (COG) defuzzification technique

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Jones, A., Kaufmman, A. & Zimmerman, H. J. (Eds.), Fuzzy Sets: Theory and Applications, NATO ASI Series, Series C: Mathematical and Physical Sciences, Vol. 177, Reidel Publishing Company, Dordrecht, Holland.
[2]	Hanss, M., Applied Fuzzy Arithmetic, An Introduction with Engineering Applications, Springer-Verlag, Berlin-Heidelberg, 2005.
[3]	Kaufmann, A. & Gupta, M., Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold Company, New York, 1991.
[4]	Klir, G. J., Folger, T. A., Fuzzy Sets, Uncertainty and Information, London, Prentice-Hall, London, 1988.
[5]	Subbotin, I. Ya., Badkoobehi, H., Bilotskii, N. N., Application of fuzzy logic to learning assessment. Didactics of Mathematics: Problems and Investigations, 22, 38-41, 2004.
[6]	Subbotin, I. Ya, & Voskoglou, M. Gr., A Triangular Fuzzy Model for Assessing Critical Thinking Skills, International Journal of Applications of Fuzzy Sets and Artificial intelligence, 4, 173-186, 2014.
[7]	Theodorou, J., Introduction to Fuzzy Logic, Tzolas Publications, Thessaloniki, Greece, 2010 (in Greek language).
[8]	Voskoglou, M. Gr., Stochastic and fuzzy models in Mathematics Education, Artificial Intelligence and Management, Saarbrucken - Germany, Lambert Academic Publishing, 2011.
[9]	Voskoglou, M. Gr., Assessing Students Individual Problem Solving Skills, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 3, 39-49, 2013.
[10]	Voskoglou, M. Gr., Measuring the Uncertainty of Human Reasoning, American Journal of Applied Mathematics and Statistics, 2(1), 1-6, 2014.
[11]	Voskoglou, M. Gr. & Subbotin, I. Ya., Fuzzy Methods for Student Assessment, International Journal of Education and Information Technology, 1(1), 20-28, 2015.
[12]	Voskoglou, M. Gr., Use of the Triangular Fuzzy Numbers for Student Assessment, American Journal of Applied Mathematics and Statistics, 3(4), 146-150, 2015.