Application of Mathematical Modeling in Multi Criteria Decision Making Process: Intuitionistic Fuzzy PROMETHEE
Abstract
In this paper, the intuitionistic fuzzy PROMETHEE method is explained in detail and an original application has been made. The aim of the paper is to bring innovation to the evaluation system in the field of education by using the intuitionistic fuzzy PROMETHEE method. The advantages of using the PROMETHEE method, which is one of the many methods used in multi-criteria decision-making problems, in the intuitionistic fuzzy sense are explained in detail. Intuitionistic fuzzy PROMETHEE is a method that attracts our attention thanks to its benefits such as allowing the researcher to observe the positive and negative rankings simultaneously, expressing the degree of hesitation, changing the significance weights of the criteria, and using different methods when identifying the significance levels for each criterion, putting the degree of hesitation of significance weights into action, and enabling decision-makers, who are given the opportunity to use different criteria types and different criteria types for alternatives and criteria, to establish a unique system; moreover, the method also provides us numerous advantages while using it in our application area. It is of great importance for decision-makers to determine the specific importance level for each criterion. In this paper, controlled sets are used to express the importance of the criteria in the form of intuitionistic fuzzy values. The intuitionistic fuzzy-based PROMETHEE algorithm, aiming to contribute to the education system by examining the factors affecting the students' achievement, is a unique algorithm, and it is the first to shed light on various researchers.
Keywords
Intuitionistic fuzzy PROMETHEE Intuitionistic fuzzy theory Multi criteria decision making Selection and evaluation in education
References
- L. A. Zadeh, Fuzzy sets Information and Control, 8 (1965) 338-353.
- K. Atanassov, Intuitionistic fuzzy sets Fuzzy Sets Syst., 20(1) (1986), 87-96.
- K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets Syst., 33(1) (1989), 37-45.
- M. Majumder, Multi Criteria Decision Making, Chapter 2, Springer, (2015), 35-47.
- J. P. Brans, Lingenierie de la decision; Elaboration dinstruments daidealadecision, Lamethode PROMETHEE, in: R. Nadeau, M. Landry, ed., Laidea la Decision: Nature, Instruments et Perspectives d Avenir, Quebec, Canada, Presses de lUniversite Laval, (1982), 183-213.
- G. Büyüközkan, F. Göçer, Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem, Appl. Soft Comput., 52 (2017), 1222-1238.
- A. Albadvi, Formulating national information technology strategies: A preference ranking model using PROMETHEE method, Eur. J. Oper. Res., 153 (2004), 290-296.
- A. Albadvi, S. K. Chaharsooghi, A. Esfahanipour, Decision making in stock trading: An application of PROMETHEE, Eur. J. Oper. Res., 177 (2007) 673-683.
- M. Behzadian, R. B. Kazemzadeh, A. Albadvi, M. Aghdasi, PROMETHEE: A comprehensive literature reviewon methodologies and applications, Eur. J. Oper. Res., 200 (2010), 198-215.
- J. P. Brans, B. Mareschal, P. Vincke, PROMETHEE: a new family of outranking methods in multicriteria analysis, Oper. Res., IFORS 84 (1984), 477-490.
- N. Halouani, H. Chabchoub, J. M. Martel, PROMETHEEMD-2T method for project selection, Eur. J. Oper. Res., 195 (2009), 841-849.
- R. Krishankumar, K. S. Ravichandran, A. B. Saeid, A new extension to PROMETHEE under intuitionistic fuzzy environment for solving supplier selection problem with linguistic preferences, Appl. Soft Comput., 60 (2017), 564-576.
- K. J. Zhang, C. Kluck, G. Achari, A comparative approach for ranking contaminated sites based on the risk assessment paradigm using fuzzy PROMETHEE, Environ Manage., 44 (2009), 952-967.
- F. Tuğrul, M. Çitil, Evaluating the factors affecting success of students with the intuitionistic fuzzy PROMETHEE method, 3rd International Conference on Pure and Applied Mathematics, Van, Turkey, 2020.
- F. Tuğrul, M. C¸ itil, A new perspective on evaluation system in education with intuitionistic fuzzy logic and PROMETHEE algorithm, Journal of Universal Mathematics, 4(1) (2021), 13-24.
- F. Tuğrul, Application of intuitionistic fuzzy logic with a new method in multi criteria decision making process, Ph.D. Thesis. Kahramanmaras¸ S¨utc¸ ¨u ˙Imam University, 2021.
- Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Trans. Fuzzy Syst., 15 (2007), 1179-1187.
- Z. S. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy set, Int. J. Gen. Syst., 35 (2006), 417-433.
- 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), 7-19.
- H. C. Liao, Z. S. Xu, Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency, IEEE Trans. Fuzzy Syst., 22(6) (2014), 1669-1681.
- G. Çuvalcıoğlu, Some properties of controlled set theory, Notes on Intuitionistic Fuzzy Set, 20(2) (2014) 37-42.
- G. Çuvalcıoğlu, Controlled set theory, Bogolyubov Readings, DIF-2013, Ukraine, 342 (2013).
- H. C. Liao, Z. S. Xu, Some algorithms for group decision making with intuitionistic fuzzy preference information, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 22(4) (2014), 505-529.
- Z. J. Wang, Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations, Appl. Math. Model., 37 (2013), 6377-6388.
- Z. S. Xu, H. C. Liao, Intuitionistic fuzzy analytic hierarchy process, IEEE Trans. Fuzzy Syst., 22(4) (2014), 749-761.
- P. H. Vincke, J. P. Brans, A preference ranking organization method: (The PROMETHEE Method for Multiple Criteria Decision-Making), Manag. Sci., 31(6) (1985), 647-656.
- Z. S. Xu, Intuitionistic preference relations and their application in group decision making, Information Sciences, 177(11) (2007), 2363-2379.
- H. Liao, Z. S. Xu, Multi-criteria decision making with intuitionistic fuzzy PROMETHEE, J. Intell. Fuzzy Syst., 27 (2014), 1703-1717.
Abstract
References
- L. A. Zadeh, Fuzzy sets Information and Control, 8 (1965) 338-353.
- K. Atanassov, Intuitionistic fuzzy sets Fuzzy Sets Syst., 20(1) (1986), 87-96.
- K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets Syst., 33(1) (1989), 37-45.
- M. Majumder, Multi Criteria Decision Making, Chapter 2, Springer, (2015), 35-47.
- J. P. Brans, Lingenierie de la decision; Elaboration dinstruments daidealadecision, Lamethode PROMETHEE, in: R. Nadeau, M. Landry, ed., Laidea la Decision: Nature, Instruments et Perspectives d Avenir, Quebec, Canada, Presses de lUniversite Laval, (1982), 183-213.
- G. Büyüközkan, F. Göçer, Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem, Appl. Soft Comput., 52 (2017), 1222-1238.
- A. Albadvi, Formulating national information technology strategies: A preference ranking model using PROMETHEE method, Eur. J. Oper. Res., 153 (2004), 290-296.
- A. Albadvi, S. K. Chaharsooghi, A. Esfahanipour, Decision making in stock trading: An application of PROMETHEE, Eur. J. Oper. Res., 177 (2007) 673-683.
- M. Behzadian, R. B. Kazemzadeh, A. Albadvi, M. Aghdasi, PROMETHEE: A comprehensive literature reviewon methodologies and applications, Eur. J. Oper. Res., 200 (2010), 198-215.
- J. P. Brans, B. Mareschal, P. Vincke, PROMETHEE: a new family of outranking methods in multicriteria analysis, Oper. Res., IFORS 84 (1984), 477-490.
- N. Halouani, H. Chabchoub, J. M. Martel, PROMETHEEMD-2T method for project selection, Eur. J. Oper. Res., 195 (2009), 841-849.
- R. Krishankumar, K. S. Ravichandran, A. B. Saeid, A new extension to PROMETHEE under intuitionistic fuzzy environment for solving supplier selection problem with linguistic preferences, Appl. Soft Comput., 60 (2017), 564-576.
- K. J. Zhang, C. Kluck, G. Achari, A comparative approach for ranking contaminated sites based on the risk assessment paradigm using fuzzy PROMETHEE, Environ Manage., 44 (2009), 952-967.
- F. Tuğrul, M. Çitil, Evaluating the factors affecting success of students with the intuitionistic fuzzy PROMETHEE method, 3rd International Conference on Pure and Applied Mathematics, Van, Turkey, 2020.
- F. Tuğrul, M. C¸ itil, A new perspective on evaluation system in education with intuitionistic fuzzy logic and PROMETHEE algorithm, Journal of Universal Mathematics, 4(1) (2021), 13-24.
- F. Tuğrul, Application of intuitionistic fuzzy logic with a new method in multi criteria decision making process, Ph.D. Thesis. Kahramanmaras¸ S¨utc¸ ¨u ˙Imam University, 2021.
- Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Trans. Fuzzy Syst., 15 (2007), 1179-1187.
- Z. S. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy set, Int. J. Gen. Syst., 35 (2006), 417-433.
- 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), 7-19.
- H. C. Liao, Z. S. Xu, Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency, IEEE Trans. Fuzzy Syst., 22(6) (2014), 1669-1681.
- G. Çuvalcıoğlu, Some properties of controlled set theory, Notes on Intuitionistic Fuzzy Set, 20(2) (2014) 37-42.
- G. Çuvalcıoğlu, Controlled set theory, Bogolyubov Readings, DIF-2013, Ukraine, 342 (2013).
- H. C. Liao, Z. S. Xu, Some algorithms for group decision making with intuitionistic fuzzy preference information, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 22(4) (2014), 505-529.
- Z. J. Wang, Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations, Appl. Math. Model., 37 (2013), 6377-6388.
- Z. S. Xu, H. C. Liao, Intuitionistic fuzzy analytic hierarchy process, IEEE Trans. Fuzzy Syst., 22(4) (2014), 749-761.
- P. H. Vincke, J. P. Brans, A preference ranking organization method: (The PROMETHEE Method for Multiple Criteria Decision-Making), Manag. Sci., 31(6) (1985), 647-656.
- Z. S. Xu, Intuitionistic preference relations and their application in group decision making, Information Sciences, 177(11) (2007), 2363-2379.
- H. Liao, Z. S. Xu, Multi-criteria decision making with intuitionistic fuzzy PROMETHEE, J. Intell. Fuzzy Syst., 27 (2014), 1703-1717.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | August 31, 2022 |
| Submission Date | February 14, 2022 |
| Acceptance Date | May 10, 2022 |
| Published in Issue | Year 2022 Volume: 5 Issue: 2 |
Cite
Journal of Mathematical Sciences and Modelling
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