Application of Grey Numbers and Neutrosophic Sets to Assessment Processes
Subject Areas : Fuzzy Optimization and Modeling Journal
1 - Mathematical Sciences - School of Engineering - University of Peloponnese - 26334 Patras -Greece
Keywords: fuzzy set, Grey Number, Grey system, Neutrosophic set, Assessment under Fuzzy Conditions,
Abstract :
Zadeh extended in 1965 crisp sets to the concept of fuzzy set (FS) on the purpose of tackling mathematically the partial truths and the definitions with no clear boundaries. In a later stage FSs were extensively used for tackling the existing in the real world uncertainty. Neutrosophic sets (NSs) are extensions of FSs in which each element of the universal set is characterized, apart from Zadeh’s membership degree, by the degrees of non-membership and indeterminacy. Grey numbers (GNs) are real numbers with known range, represented by a closed real interval, but with unknown exact value. GNs and NSs are used in this paper as tools for assessment processes under fuzzy conditions. The use of GNs enables the evaluation of the mean performance of a group of objects when qualitative grades (linguistic expressions) are used for the individual assessment of its members. The use of NSs, on the other hand, is useful for assessing the overall performance of a group, when one, due to incomplete assessment data, is not sure about the exactness of the grades assigned to its members. It is concluded that the suitable combination of two or more theories related to FSs give better assessment outcomes in general. Examples are also presented on student assessment illustrating our results.
1. Antony Crispin Sweety, C.. Jansi, R..(2021), Fermatean Neutrosophic Sets, International Journal of Advanced Research in Computer and Communication Engineering, 10(6), 24-27.
2. Atanassov, K.T. (1986), Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20(1), 87-96.
3. Broumi, S., et al. (2023), Faculty Performance Evaluation Through Multicriteria Decision Analysis Using Interval -Valued Fermatean Neutrosophic Sets, Mathematics, 11, 3817.
4. Deng, J. (1982), Control Problems of Grey Systems, Systems and Control Letters, 288.
5. Jeevaraj S. (2021), Ordering of interval valued Fermatean fuzzy sets and its applications, Expert Systems with Applications, 185,115613.
6. Liu, S. F. & Lin, Y. (Eds.) (2010), Advances in Grey System Research, Springer, Berlin – Heidelberg, Germany.
7. Moore, R.A., Kearfort, R. B. & Clood, M.J. (1995), Introduction to Interval Analysis, 2nd Printing, SIAM, Philadelphia, USA.
8. Smarandache, F. (1998), Neutrosophy/ Neutrosophic probability, set, and logic, Proquest, Michigan, USA.
9. Voskoglou, M.Gr. (2019), Assessing Human-Machine Performance under Fuzzy Conditions, Mathematics, 7, article 230.
10. Voskoglou, M.Gr. (2022), Soft sets as tools for assessing human-machine performance, Egyptian Computer Science Journal, 46(1), 1-6.
11. Voskoglou, M.Gr. (2022), Use of Grey Numbers and Soft Sets as Assessment Tools, Asian Journal of Pure and Applied Mathematics, 4(3), 171-177.
12. Voskoglou, M.Gr. (2022), Use of Soft Sets and the Bloom’s Taxonomy for Assessing Learning skills, Transactions on Fuzzy Sets and Systems, 1(1), 106-113.
13. Voskoglou, M.Gr., Broumi, S. (2022), A Hybrid Method for the Assessment of Analogical Reasoning skills, Journal of Fuzzy Extension and Applications, 3(2), 152-157.
14. Voskoglou, M.Gr., Broumi, S., Smarandache, F. (2022), A Combined Use of Soft and Neutrosophic Sets for Student Assessment with Qualitative Grades, Journal of Neutrosophic and Fuzzy Systems, 4(1), 15-20.
15. Voskoglou, M.Gr. (2022), A Hybrid Method for Assessment with Linguistic Grades, Oriental Journal of Physical Sciences, 7(1), 26-29.
16. Voskoglou, M.Gr. (2023), Assessing the Effectiveness of Flipped Learning for Teaching Mathematics to Management Students, American Journal of Applie Mathematics and Statistics, 11(1), 30-34.
17. Voskoglou, M.Gr. (2023), Neutrosophic Assessment of Student Mathematical Skills, Physical and Mathematical Education, 38(2), 22-26.
18. Voskoglou, M.Gr. (2023), An Application of Neutrosophic Sets to Decision Making, Neutrosophic Sets and Systems, 53, 1-9.
19. Wang, H., Smarandanche, F., Zhang, Y. and Sunderraman, R. (2010), Single Valued Neutrosophic Sets, Review of the Air Force Academy (Brasov), 1(16), 2010, 10-14.
20. Zadeh, L.A. (1965), Fuzzy Sets, Information and Control, 8, 338-353.
21. Zadeh, L.A. (1978), Fuzzy Sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28.