Document Type : Research Paper


1 Mathematical Sciences, Graduate TEI of Western Greece.

2 Laboratory of Information Processing, Faculty of Science Ben M'Sik, University Hassan II, Casablanca, Morocco.


Much of a person’s cognitive activity depends on the ability to reason analogically. Analogical reasoning (AR) compares the similarities between new and past knowledge and uses them to obtain an understanding of the new knowledge. The mechanisms, however, under which the human mind works are not fully investigated and as a result AR is characterized by a degree of fuzziness and uncertainty. Probability theory has been proved sufficient for dealing with the cases of uncertainty due to randomness. During the last 50-60 years, however, various mathematical theories have been introduced for tackling effectively the other forms of uncertainty, including fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, rough sets, etc. The combination of two or more of those theories gives frequently better results for the solution of the corresponding problems. A hybrid assessment method of AR skills under fuzzy conditions is developed in this work using Grey Numbers (GN) and soft sets as tools, which is illustrated by an application on evaluating student analogical problem solving skills.


Main Subjects

  1. Polya, G. (1954). Induction and analogy in mathematics: volume I of mathematics and pausible reasoning. Princeton University Press.
  2. Voskoglou, M. G. (2008, September). Case-based reasoning: a recent theory for problem-solving and learning in computers and people. In world summit on knowledge society(pp. 314-319). Springer, Berlin, Heidelberg.
  3. Voskoglou, M. Gr. & Salem, A. B. (2014). Analogy-based and case–based reasoning: two sides of the same coin. International journal of applications of fuzzy sets and artificial intelligence, 4, 5-51.
  4. Holyoak, K. J. (1985). The pragmatics of analogical transfer. In psychology of learning and motivation(Vol. 19, pp. 59-87). Academic Press.
  5. Bugaiska, A., & Thibaut, J. P. (2015). Analogical reasoning and aging: the processing speed and inhibition hypothesis. Aging, neuropsychology, and cognition22(3), 340-356.
  6. Thibaut, J. P., & French, R. M. (2016). Analogical reasoning, control and executive functions: a developmental investigation with eye-tracking. Cognitive development38, 10-26.
  7. Voskoglou, M. G. (2019). Methods for assessing human–machine performance under fuzzy conditions. Mathematics7(3), 230.
  8. Voskoglou, M. G. (2022). Soft sets as tools for assessing human-machine performance. Egyptian computer science journal, 46(1), 1-6.
  9. Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
  10. Atanassov, K. T. (1986). Intuitionistic Fuzzy Sets. Fuzzy sets and systems, 20, 87-96
  11. Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis. American Research Press.
  12. Pawlak, Z. (1991). Rough sets: Theoretical aspects of reasoning about data(Vol. 9). Springer Science & Business Media.
  13. Voskoglou, M. G. (2019). Fuzzy systems, extensions and relative theories. WSEAS transactions on advances in engineering education16, 63-69.
  14. Ju-Long, D. (1982). Control problems of grey systems. Systems & control letters1(5), 288-294.
  15. Liu, S., & Forrest, J. Y. L. (Eds.). (2010). Advances in grey systems research. Springer.
  16. Moore, R. E., Kearfott, R. B., & Cloud, M. G. (2009). Introduction to interval analysis. Society for Industrial and Applied Mathematics.
  17. Klir, G. J. & Folger, T. A. (1988). Fuzzy sets, Uncertainty and information. Prentice-Hall.
  18. Molodtsov, D. (1999). Soft set theory—first results. Computers & mathematics with applications37(4-5), 19-31.
  19. Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers & mathematics with applications45(4-5), 555-562.
  20. Hayes, J. R. (1977). Psychological differences among problem isomorphs. Cognitive theory2, 21-41.
  21. Gentner, D., & Toupin, C. (1986). Systematicity and surface similarity in the development of analogy. Cognitive science10(3), 277-300.
  22. Holyoak, K. J., & Koh, K. (1987). Surface and structural similarity in analogical transfer. Memory & cognition15(4), 332-340.
  23. Novick, L. R. (1988). Analogical transfer, problem similarity, and expertise. Journal of experimental psychology: learning, memory, and cognition14(3), 510.
  24. Niss, M. (2003, January). Mathematical competencies and the learning of mathematics: The Danish KOM project. 3rd Mediterranean conference on mathematical education (pp. 115-124). Hellenic Mathematical Society, Athen.
  25. Shafi Salimi, P., & Edalatpanah, S. A. (2020). Supplier selection using fuzzy AHP method and D-Numbers. Journal of fuzzy extension and applications1(1), 1-14.
  26. Smarandache, F. (2020). Generalisations and alternatives of classical algebraic structures to neutroAlgebraic structures and antiAlgebraic structures. Journal of fuzzy extension and applications, 1(2), 81-83.
  27. Polymenis, A. (2021). A neutrosophic student’st–type of statistic for AR (1) random processes. Journal of fuzzy extension and applications2(4), 388-393.
  28. Kouatli, I. (2022). Modelling fuzzymetric cognition of technical analysis decisions: reducing emotional trading. Journal of fuzzy extension and applications, 3(1), 45-63.