Skip Navigation Links.
Collapse <span class="m110 colortj mt20 fontw700">Volume 12 (2024)</span>Volume 12 (2024)
Collapse <span class="m110 colortj mt20 fontw700">Volume 11 (2023)</span>Volume 11 (2023)
Collapse <span class="m110 colortj mt20 fontw700">Volume 10 (2022)</span>Volume 10 (2022)
Collapse <span class="m110 colortj mt20 fontw700">Volume 9 (2021)</span>Volume 9 (2021)
Collapse <span class="m110 colortj mt20 fontw700">Volume 8 (2020)</span>Volume 8 (2020)
Collapse <span class="m110 colortj mt20 fontw700">Volume 7 (2019)</span>Volume 7 (2019)
Collapse <span class="m110 colortj mt20 fontw700">Volume 6 (2018)</span>Volume 6 (2018)
Collapse <span class="m110 colortj mt20 fontw700">Volume 5 (2017)</span>Volume 5 (2017)
Collapse <span class="m110 colortj mt20 fontw700">Volume 4 (2016)</span>Volume 4 (2016)
Collapse <span class="m110 colortj mt20 fontw700">Volume 3 (2015)</span>Volume 3 (2015)
Collapse <span class="m110 colortj mt20 fontw700">Volume 2 (2014)</span>Volume 2 (2014)
Collapse <span class="m110 colortj mt20 fontw700">Volume 1 (2013)</span>Volume 1 (2013)
American Journal of Applied Mathematics and Statistics. 2018, 6(2), 67-71
DOI: 10.12691/AJAMS-6-2-5
Original Research

Application of Fuzzy Relation Equations to Student Assessment

Michael Gr. Voskoglou1,

1Department of Mathematical Sciences, Graduate Technological Educational Institute of Western Greece, Patras, Greece

Pub. Date: May 02, 2018

Cite this paper

Michael Gr. Voskoglou. Application of Fuzzy Relation Equations to Student Assessment. American Journal of Applied Mathematics and Statistics. 2018; 6(2):67-71. doi: 10.12691/AJAMS-6-2-5

Abstract

Mathematical modelling appears today as a dynamic tool for teaching/learning mathematics, because it connects mathematics with real world applications and therefore increases the student interest on the subject. Fuzzy relation equations, which are obtained by the composition of binary fuzzy relations, are used in this work as a tool for evaluating student mathematical modelling skills. A classroom application and other suitable examples are also presented illustrating our results.

Keywords

Fuzzy Sets (FS), Fuzzy Binary Relations (FBR), Fuzzy Relation Equations (FRE), Mathematical Modelling (MM), student assessment

Copyright

Creative CommonsThis 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]  Czogala, E., Drewniak, J. & Pedryz, W., Fuzzy relation equations on a finite set, Fuzzy Sets and Systems, 7, 89-101, 1982.
 
[2]  Higashi, M. & Klir, G.J., Resolution of finite fuzzy relation equations, Fuzzy Sets and Systems, 13, 65-82, 1984.
 
[3]  Ghosh, D. & Pal, A., Analysis of Faculty Teaching Based on Student Feedback Using Fuzzy Relation Equations, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 5, 94-109, 2015.
 
[4]  Kaufmann, A., Introduction to the Theory of Fuzzy Subsets, New York: Academic Press, 1975.
 
[5]  Klir, G. J. & Folger, T. A., Fuzzy Sets, Uncertainty and Information, New Jersey: Prentice-Hall, 1988.
 
[6]  Paul, L. C., Wang, Fuzzy relation equation (II): the branch- point solutions and the categorized minimal solutions, Springer, 2006.
 
[7]  Perfilieva, I., Fuzzy function as an approximate solution to a system of fuzzy relation equations, Fuzzy Sets and Systems, 147 (3), 363-383, 2004
 
[8]  Perfilieva, I. Noskova, L., System of fuzzy relation equation with inf- composition: Complete set of solutions, Fuzzy Sets and Systems, 159 (17), 2256-2271, 2008.
 
[9]  Prevot, M., Algorithm for the solution of fuzzy relations, Fuzzy Sets and Systems, 5, 319-322, 1981.
 
[10]  Sanchez, E., Resolution of Composite Fuzzy Relation Equations, Information and Control, 30, 38-43, 1976.
 
[11]  Subbotin, I., Badkoobehi, H. & Bilotskii, N.N., Application of Fuzzy Logic to Learning Assessment, Didactics of Mathematics: Problems and Investigations, 22, 38-41, 2004.
 
[12]  Voskoglou, M.Gr., The Process of Learning Mathematics: A Fuzzy Set Approach, Didactics of Mathematics: Problems and Investigations, 10, 9-13, 1999.
 
[13]  Voskoglou, M.Gr., Mathematical Modelling as a Teaching Method of Mathematics, Journal for Research in Innovative Teaching (National University, CA, USA), 8(1), 35-50, 2015.
 
[14]  Voskoglou, M.Gr., Finite Markov Chain and Fuzzy Logic Assessment Models: Emerging Research and Opportunities, Columbia, SC: Createspace.com. – Amazon, 2017.
 
[15]  L.A. Zadeh, Similarity relations and fuzzy orderings, Information Sciences, 3, 177-200, 1971.