A NEW PERSPECTIVE ON EVALUATION SYSTEM IN EDUCATION WITH INTUITIONISTIC FUZZY LOGIC AND PROMETHEE ALGORITHM

Abstract

This research attempts to seek for multi criteria decision making through the PROMETHEE method. This paper aims to propose an application of multi criteria decision making in intuitionistic fuzzy sets. The success ranking of schools was analyzed through the use of the PROMETHEE method. Besides, the most successful school was identified among these ranked schools. In this research, the intuitionistic fuzzy PROMETHEE method was employed during ranking of schools' success. The main reason for using intuitionistic fuzzy PROMETHEE is that it takes into account both intuitionistic fuzzy weights and intuitionistic fuzzy preferences at the same time. This paper applies to many fields; however, we proposed an application in the eld of education in this study. The primary purpose of this paper is expected to create an algorithm of intuitionistic fuzzy PROMETHEE and offer an application example that will shed light on many application areas. Using multi criteria decision making methods together with intuitionistic fuzzy logic will help us obtain more rational and more objective results.

Keywords

• Evaluation system in education
• fuzzy logic
• multi criteria decision making
• intuitionistic fuzzy sets
• PROMETHEE method

References

1. [1] A. Albadvi, Formulating national information technology strategies: A preference ranking model using PROMETHEE method, European Journal of Operational Research , 153, 290-296, (2004).
2. [2] A. Albadvi, S.K. Chaharsooghi, A. Esfahanipour, Decision making in stock trading: An application of promethee. European journal of operational research 177, 673-683, (2007).
3. [3] K.T. Atanassov, More on intuitionistic fuzzy sets. Fuzzy sets and systems 33, 37-45, (1989).
4. [4] K.T. Atanassov, Intuitionistic fuzzy sets, Springer, pp. 1-137, (1999).
5. [5] J.P. Brans, L'ing'eni'erie de la decision; Elaboration d'instruments d'aide a lad'ecision. Lam'ethode PROMETHEE, in: R. Nadeau, M. Landry, ed., L'aide a la d'ecision: Nature, Instruments et Perspectives d'Avenir, Qu'ebec, Canada. Presses de l'Universit'e Laval, 183-213, (1982).
6. [6] P. Vincke, J.P. Brans, A preference ranking organization method, The PROMETHEE method for Multiple Criteria Decision Making, Management Science 31, 647-656, (1985).
7. [7] M. Behzadian, R.B. Kazemzadeh, A. Albadvi, M. Aghdasi, PROMETHEE: A comprehensive literature review on methodologies and applications, European Journal of Operational Research, 200, 198-215, (2010).
8. [8] B. Mareschal, J.P. Brans, P. Vincke, et al., PROMETHEE: A new family of outranking methods in multicriteria analysis. Technical Report. ULB{Universite Libre de Bruxelles (1984).

9. [9] G. Büyüközkan, F. Göçer, Application of a new combined intuitionistic fuzzy mcdm approach based on axiomatic design methodology for the supplier selection problem. Applied Soft Computing 52, 1222-1238, (2017).
10. [10] M. Çitil, F. Tuğrul, B. Yılmaz, An Application of Multi Criteria Decision Making: Ranking of School Success, Celal Bayar University Journal of Science, 15(1), 45-50, (2019).
11. [11] N. Halouani, H. Chabchoub, J.M. Martel, Promethee-md-2t method for Project selection. European Journal of Operational Research 195, 841{849, (2009).
12. [12] R. Krishankumar, K. Ravichandran, A.B. Saeid, A new extension to promethee under intuitionistic fuzzy environment for solving supplier selection problem with linguistic preferences. Applied Soft Computing 60, 564-576, (2017).
13. [13] H. Liao, Z.S. Xu, Multi-criteria decision making with intuitionistic fuzzy PROMETHEE, Journal of Intelligent Fuzzy Systems, 27, 1703-1717, (2014a).
14. [14] H. Liao, Z. Xu, Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency. IEEE Transactions on Fuzzy Systems 22, 1669-1681, (2014b).
15. [15] H. Liao, Z. Xu, Some algorithms for group decision making with intuitionistic fuzzy preference information. International Journal of Uncertainty, Fuzziness and Knowledge- Based Systems 22, 505-529, (2014c).
16. [16] M. Majumder, Multi Criteria Decision Making. Chapter 2, Springer, (2015).
17. [17] E. Szmidt, J. Kacprzyk, Amount of information and its reliability in the ranking of Atanassov's intuitionistic fuzzy alternatives, in: E. Rakus-Andersson, R.R. Yager, N. Ichalkaranje, L. Jain, ed. Recent advances in decision making (Studies in Computational Intelligence), Berlin, Germany: Springer, (2009).
18. [18] Z. Wang, Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations, Applied Mathematical Modelling, 37, 6377-6388, (2013).
19. [19] Z.S. Xu, R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets. International journal of general systems 35, 417-433, (2006).
20. [20] Z.S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems, 15, 1179-1187, (2007a).
21. [21] Z.S. Xu, Intuitionistic preference relations and their application in group decision making, Information Sciences, 177(11), 2363-2379, (2007b).
22. [22] Z.S. Xu, H. Liao, Intuitionistic fuzzy analytic hierarchy process. IEEE transactions on fuzzy systems 22, 749-761, (2013).
23. [23] L.A. Zadeh, Fuzzy Sets, Information and Control, 8, 338-353, (1965).
24. [24] K. Zhang, C. Kluck, G. Achari, A comparative approach for ranking contaminated sites based on the risk assessment paradigm using fuzzy promethee. Environmental management 44, 952, (2009).
25. [25] F. Tuğrul, M. Çitil, B. Karasolak, M. Dağlı, Interpretation of Physical Conditions of Schools with Fuzzy Multi Criteria Decision Making, Journal of Universal Mathematics, 3(1), 46-52, (2020).
26. [26] F. Tuğrul, B. Yılmaz, M. Çitil, Application of Ranking with Similarity Measure in Multi Criteria Decision Making, Konuralp Journal of Mathematics, 7(2), 438-441, (2019a).
27. [27] F. Tuğrul, M. Çitil, S. Balcı, On The Determination Students' Aptitude Using Intuitionistic Fuzzy Logic, Journal of Universal Mathematics, 2(1), 36-41, (2019b).
28. [28] F. Tuğrul, B. Yılmaz, M. Ç itil, School Success Ranking in Multi Criteria Decision Making, Turkish Journal Mathematics and Computer Science, 10, 1-6, (2018).
29. [29] F. Tuğrul, M. Çitil, M. Gezercan, Application of Intuitionistic Fuzzy Sets in High School Determination Via Normalized Euclidean Distance Metod, Notes on Intuitionistic Fuzzy Sets, 23(1), 42-47, (2017).