A Hybrid Model for Assessing Student Mathematical Skills

Transactions on Fuzzy Sets and Systems

مقاله 5، دوره 2، شماره 1، مرداد 2023، صفحه 61-71   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2022.1971496.1052

نویسنده

Michael Gr. Voskoglou^*

Department of Mathematical Sciences, Graduate Technological Educational Institute of Western Greece, Meg. Alexandrou 1, 263 34 Patras, Greece.

چکیده

‎Student assessment is a very important process in education‎, ‎because it helps the instructor to determine student mistakes and to improve their performance by reforming his/her teaching plans‎. ‎A hybrid assessment method using qualitative grades for evaluating student mathematical skills is presented in this work‎. ‎The paper starts with the mathematical background which is necessary for the understanding of its contents‎. ‎This includes basic information about fuzzy‎, ‎neutrosophic and soft sets‎, ‎and about grey numbers‎. ‎It also includes a description of the use of the center of gravity ($COG$) defuzzification technique for assessing a student group's quality performance‎. ‎The $COG$ technique is compared with the classical method of calculating the $GPA$ index‎. ‎The hybrid assessment method‎, ‎which is based on all the previous concepts and processes‎, ‎is developed next and the article closes with the final conclusion and some recommendations for future research‎.

کلیدواژه‌ها

Fuzzy set (FS)‎؛ ‎Fuzzy logic (FL)‎؛ ‎Neutrosophic set (NS)‎؛ ‎Soft set (SS)‎؛ ‎Grey number (GN)‎؛ ‎COG defuzzification technique‎؛ ‎Rectangular fuzzy assessment model (RFAM)‎؛ ‎GPA index‎

مراجع

[1] K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
[2] J. Deng, Control Problems of Grey Systems, Systems and Control Letters, (1982), 288-294.
[3] J. Deng, Introduction to Grey System Theory, The Journal of Grey System, 1 (1989), 1-24.
[4] D. Dubois and H. Prade, Interval-Valued Fuzzy Sets, Possibility Theory and Imprecise Probability, Proceedings EUSFLAT-LFA, (2005), 314-319.

[5] D. Dubois and H. Prade, Possibility theory, probability theory and multiple-valued logics: A clarification, Ann. Math. Artif. Intell., 32 (2001), 35-66.
[6] D. Dubois and H. Prade, Possibility Theory and its Applications: a Retrospective and Prospective view. In: Della Riccia, G. Dubois, D. Kruse, R. Lenz, H. J. (eds) Decision Theory and Multi-Agent Planning. CISM International Centre for Mechanical Sciences, Springer, Vienna, 482 (2006), 89-109.
[7] J. Garcia and S. E. Rodabaugh, Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued intuitionistic sets, intuitionistic fuzzy sets and topologies, Fuzzy Sets and Systems, 156 (2005), 445-484.
[8] G. J. Klir and T. A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, (1988).
[9] P. K. Maji, R. Biswas and A. R. Roy, Soft Set Theory, Computers and Mathematics with Applications, 45 (2003), 555-562.
[10] D. Molodtsov, Soft Set Theory first results, Computers and Mathematics with Applications, 37(4-5) (1999), 19-31.
[11] R. A. Moore, R. B. Kearfort and M. G. Clood, Introduction to Interval Analysis, 2nded., SIAM, Philadelphia, PA, USA, (1995).
[12] Z. Pawlak, Rough Sets: Aspects of Reasoning about Data, Kluer Academic Publishers, Dordrecht, (1991).
[13] F. G. Shi and C. Z. Fan, Fuzzy soft sets as L-fuzzy sets, Journal of Intelligent & Fuzzy Systems, 37 (2019).
[14] F. Smarandache, Neutrosophy / Neutrosophic Probability, Set, and Logic, Proquest, Michigan, USA, (1998).
[15] F. Smarandache, Subtraction and Division of Neutrosophic Numbers, Critical Review, 13 (2016), 103-110.
[16] I. Ya. Subbotin, H. Badkoobehi and N.N. Bilotckii, Application of fuzzy logic to learning assessment, Didactics of Mathematics: Problems and Investigations, 22 (2004), 38-41.
[17] M. Gr. Voskoglou, The process of learning mathematics : A Fuzzy Sets approach, Millenium- Revista do I.S.P.V., 17 (2000), 272-279.
[18] M. Gr. Voskoglou, Fuzziness or probability in the process of learning: A general question illustrated by examples from teaching mathematics, The Journal of Fuzzy Mathematics, 17(3) (2009), 679-686.
[19] M. Gr. Voskoglou, Finite Markov Chain and Fuzzy Logic Assessment Models: Emerging Research and Opportunities, Createspace independent publishing platform (Amazon), Columbia, SC, (2017).
[20] M. Gr. Voskoglou, Methods for Assessing Human-Machine Performance under Fuzzy Conditions, Mathematics, 7(230) (2019).
[21] M. Gr. Voskoglou, Generalizations of Fuzzy Sets and Relative Theories, in M. Voskoglou (Ed.), An Essential Guide to Fuzzy Systems, Nova Science Publishers, NY, (2019), 345-353.
[22] M. Gr. Voskoglou, Application of soft sets to assessment processes, American Journal of Applied Mathematics and Statistics, 10(1) (2022), 1-3.

[23] M. Gr. Voskoglou, A Hybrid Model for Decision Making Utilizing TFNs and Soft Sets as Tools, Equations, 2 (2022), 65-69.
[24] M. Gr. Voskoglou, A Combined Use of Soft Sets and Grey Numbers in Decision Making, Journal of Computational and Cognitive Engineering, (2022), 1-4.
[25] M. Gr. Voskoglou and S. Broumi, A Hybrid Method for the Assessment of Analogical Reasoning Skills, Journal of Fuzzy Extension and Applications, 3(2) (2022), 152-157.
[26] M. Gr. Voskoglou, S. Broumi and F. Smarandache, A combined use of soft and neutrosophic sets for student  assessment with qualitative grades, Journal of Neutrosophic and Fuzzy Systems, 4(1) (2022), 15-20.
[27] H. Wang, F. Smarandanche, Y. Zhang, and R. Sunderraman, Single Valued Neutrosophic Sets, Review of the Air Force Academy (Brasov), 1(16) (2010), 10-14.
[28] L. A. Zadeh, Fuzzy Sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1 (1978), 3-28.
[29] L. A. Zadeh, Fuzzy Sets, Inf. Control, 8 (1965), 338-353.
[30] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern., 3 (1973), 28-44.