Perceptual Computer for Grading Mathematics Tests within Bilingual Education Program

  • Dan Tavrov
  • Liudmyla Kovalchuk-Khymiuk
  • Olena Temnikova
  • Nazar-Mykola Kaminskyi
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 754)


In this paper, we propose an outline of a perceptual computer for grading mathematical tests written by students studying within the bilingual education program. A generic approach to implementing such a computer is proposed. Concrete implementation is described for the case of teaching mathematics in French. The perceptual computer constructed for this case is tested with real tests written by students of one of Kyiv bilingual schools. Results show that the grades obtained using words are compatible with the grades assigned using conventional numbers, which validates the use of the perceptual computer to reduce subjectivity and uncertainty for a teacher.


Perceptual computing Bilingual education Type-2 fuzzy set 


  1. 1.
    Skutnabb-Kangas, T., McCarty, T.L.: Key concepts in bilingual education: Ideological, historical, epistemological, and empirical foundations. In: Hornberger, N. (ed.) Encyclopedia of Language and Education, pp. 1466–1482. Springer, New York (2008)Google Scholar
  2. 2.
    Moschkovich, J.N.: Bilingual/multilingual issues in learning mathematics. In: Lerman, S. (ed.) Encyclopedia of Mathematics Education, pp. 57–61. Springer, Dordrecht (2014)Google Scholar
  3. 3.
    Xingle, F., Zhaoyun, S., Yan, C., Yupu, B.: The exploration and research on bilingual education of computer discipline. Int. J. Educ. Manage. Eng. (IJEME) 2(10), 52–58 (2012). Scholar
  4. 4.
    Phyue, S.L.: Development of Myanmar-English Bilingual WordNet like Lexicon. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 6(10), 28–35 (2014). Scholar
  5. 5.
    Kovalchuk-Khymiuk, L.O., Tavrov, D.Y.: The fuzzy inference system for assessing of students’ performance during the bilingual teaching of mathematics. In: System Analysis and Information Technologies: Materials of the 17th International Scientific and Technical Conference, SAIT 2015, pp. 245–247 (2015). (in Ukrainian)Google Scholar
  6. 6.
    Mitra, M., Das, A.: A fuzzy logic approach to assess web learner’s joint skills. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 7(9), 14–21 (2015). Scholar
  7. 7.
    Liu, S., Chen, P.: Research on fuzzy comprehensive evaluation in practice teaching assessment of computer majors. Int. J. Modern Educ. Comput. Sci. (IJMECS) 7(11), 12–19 (2015). Scholar
  8. 8.
    Zadeh, L.A.: From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 46(1), 105–119 (1999)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mendel, J.M.: The perceptual computer: an architecture for computing with words. In: Proceedings of Modeling with Words Workshop in the Proceedings of FUZZ-IEEE 2001, pp. 35–38 (2001)Google Scholar
  10. 10.
    Mendel, J.M., Wu, D.: Perceptual Computing. Aiding People in Making Subjective Judgments. Wiley, Hoboken (2010)CrossRefGoogle Scholar
  11. 11.
    Mendel, J.M.: Fuzzy sets for words: a new beginning. In: Proceedings of FUZZ-IEEE 2003, St. Louis, MO, pp. 37–42 (2003)Google Scholar
  12. 12.
    Wu, D., Mendel, J.M.: Enhanced Karnik-Mendel algorithms. IEEE Trans. Fuzzy Syst. 17(4), 923–934 (2009)CrossRefGoogle Scholar
  13. 13.
    Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic, Theory and Applications. Prentice Hall, Upper Saddle River (1995)zbMATHGoogle Scholar
  14. 14.
    Wu, D., Mendel, J.M.: Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Trans. Fuzzy Syst. 15(6), 1145–1161 (2007)CrossRefGoogle Scholar
  15. 15.
    Vlachos, I., Sergiadis, G.: Subsethood, entropy, and cardinality for interval-valued fuzzy sets—an algebraic derivation. Fuzzy Sets Syst. 158, 1384–1396 (2007)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Liu, F., Mendel, J.M.: Encoding words into interval type-2 fuzzy sets using an interval approach. IEEE Trans. Fuzzy Syst. 16, 1503–1521 (2008)CrossRefGoogle Scholar
  17. 17.
    Type-2 Fuzzy Logic Software. Accessed 29 Nov 2017

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”KyivUkraine

Personalised recommendations