A new ranking method for trapezoidal intuitionistic fuzzy numbers and its application to multi-criteria decision making
DOI:
https://doi.org/10.15837/ijccc.2023.2.5118Keywords:
ranking method; trapezoidal intuitionistic fuzzy number; multi-criteria decision making.Abstract
The ranking of intuitionistic fuzzy numbers is paramount in the decision making process in a fuzzy and uncertain environment. In this paper, a new ranking function is defined, which is based on Robust’s ranking index of the membership function and the non-membership function of trapezoidal intuitionistic fuzzy numbers. The mentioned function also incorporates a parameter for the attitude of the decision factors. The given method is illustrated through several numerical examples and is studied in comparison to other already-existent methods. Starting from the new classification method, an algorithm for solving fuzzy multi-criteria decision-making (MCDM) problems is proposed. The application of said algorithm implies accepting the subjectivity of the deciding factors, and offers a clear perspective on the way in which the subjective attitude influences the decision-making process. Finally, a MCDM problem is solved to outline the advantages of the algorithm proposed in this paper.
References
Atalik, G.; Senturk, S. (2019). A new ranking method for triangular intuitionistic fuzzy number based on Gergonne point, Journal of Quantitative Sciences, 1(1), 59-73, 2019.
Atanassov, K.T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-97, 1986.
https://doi.org/10.1016/S0165-0114(86)80034-3
Bharati, S. K. (2017). Ranking Method of Intuitionistic Fuzzy Numbers, Global Journal of Pure and Applied Mathematics, 13(9), 4595-4608, 2017.
De P. K.; Das, D. (2012). Ranking of trapezoidal intuitionistic fuzzy numbers, 12th International Conference on Intelligent Systems Design and Applications (ISDA), 184-188, 2012.
https://doi.org/10.1109/ISDA.2012.6416534
Dhankhar, C.; Kumar, K. (2022). Multi-attribute decision-making based on the advanced possibility degree measure of intuitionistic fuzzy numbers, Granular Computing, 7 217-227, 2022.
https://doi.org/10.1007/s41066-021-00261-7
Dutta, P.; Borah, G. (2022). Multicriteria group decision making via generalized trapezoidal intuitionistic fuzzy number-based novel similarity measure and its application to diverse COVID- 19 scenarios, Artifcial Intelligence Review, https://doi.org/10.1007/s10462-022-10251-z, 2022.
https://doi.org/10.1007/s10462-022-10251-z
Grzegrorzewski P. (2003). The hamming distance between intuitionistic fuzzy sets, In Proceedings of the 10th IFSA world congress, Istanbul, Turkey, 35-38, 2003.
Ye, J. (2011). Expected value method for intuitionistic trapezoidal fuzzy multicriteria decisionmaking problems, Expert Systems with Applications, 38, 11730-11734, 2011.
https://doi.org/10.1016/j.eswa.2011.03.059
Jafarian, E.; Rezvani, M. A. (2013). A valuation-based method for ranking the intuitionistic fuzzy numbers, Journal of Intelligent and Fuzzy Systems, 24, 133-144, 2013.
https://doi.org/10.3233/IFS-2012-0537
Li, D. F. (2010). A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers and Mathematics with Applications, 60, 155-1570, 2010.
https://doi.org/10.1016/j.camwa.2010.06.039
Li, D. F.; Nan, J. X.; Zhang, M. J. (2010). A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making, International Journal of Computational Intelligence Systems, 3(5), 522-530, 2010.
https://doi.org/10.1080/18756891.2010.9727719
Mitchell, H. B (2004). Ranking intuitionistic fuzzy numbers, International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 12(3), 377-386, 2004.
https://doi.org/10.1142/S0218488504002886
Mohan, S.; Kannusamy, A. P.; Samiappan, V. A. (2020). New Approach for Ranking of Intuitionistic Fuzzy Numbers, Journal of Fuzzy Extension and Applications, 1(1), 15-26, 2020.
Nagarajan, R.; Solairaju, A. (2010). Computing Improved Fuzzy Optimal Hungarian Assignment Problems with Fuzzy Costs under Robust Ranking Techniques, International Journal of Computer Applications, 6(4), 6-13, 2010.
https://doi.org/10.5120/1070-1398
Nayagam, V. L. G.; Venkateshwari, G.; Sivaraman, G. (2006). Ranking of intuitionistic fuzzy numbers, IEEE International Conference on Fuzzy Systems, 1971-1974, 2006.
Nayagam, V.L.G.; Jeevaraj, S.; Sivaraman, G. (2016). Complete Ranking of Intuitionistic Fuzzy Numbers, Fuzzy Information and Engineering, 8(2), 237-254, 2016.
https://doi.org/10.1016/j.fiae.2016.06.007
Nadaban, S.; Dzitac, S.; Dzitac, I. (2016). Fuzzy TOPSIS: A General View, Procedia Computer Science, 91 (2016) 823-831.
https://doi.org/10.1016/j.procs.2016.07.088
Nehi, H. M.; Maleki, H. R. (2005). Intuitionistic fuzzy numbers and it's applications in fuzzy optimization problem, In Proceedings of the 9th WSEAS international conference on systems, Athens, Greeces, 1-5, 2005.
Prakash, K. A.; Suresh, M.; Vengataasalam, S. (2016). A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept, Mathematical Sciences, 10(4) 177-184, 2016.
https://doi.org/10.1007/s40096-016-0192-y
Rajarajeswari, P.; Sahaya Sudha, P. (2014). Solving a Fully Fuzzy Linear Programming Problem by Ranking, International Journal of Mathematics Trends and Technology, 9(2), 159-164, 2014.
https://doi.org/10.14445/22315373/IJMTT-V9P519
Ren, H.P.; Liu, M.F.; Zhou, H. (2019). Extended TODIM Method for MADM Problem under Trapezoidal Intuitionistic Fuzzy Environment, International Journal of Computers Communications & Control, 14(2), 220-232, 2019.
https://doi.org/10.15837/ijccc.2019.2.3428
Rezvani, S. (2013). Ranking method of trapezoidal intuitionistic fuzzy numbers, Annals of Fuzzy Mathematics and Informatics, 5(3), 515-523, 2013.
https://doi.org/10.5899/2013/jfsva-00139
Roseline, S.S.; Amirtharaj, E. C. H. (2013). A new method for ranking of intuitionistic fuzzy numbers, Indian Journal of Applied Research, 3(6) 1-2, 2013.
https://doi.org/10.15373/2249555X/JUNE2013/183
Uthra, G. ; Thangavelu, K.; Shunmugapriya, S. (2018). Ranking Generalized Intuitionistic Fuzzy Numbers, International Journal of Mathematics Trends and Technology, 56(7), 530-538, 2018.
https://doi.org/10.14445/22315373/IJMTT-V56P569
Wang, J.; Zhang, Z. (2009). Aggregation operators on intuitionistic trapezoidal fuzzy numbers and its application to multi-criteria decision making problems, Journals of System Engineering and Electronics, 20(2), 321-326, 2009.
Xing, Z.; Xiong, W.; Liu, H. (2018). A Euclidian Approach for Ranking Intuitionistic Fuzzy Values, IEEE Transactions on Fuzzy Systems, 26(1), 353-365, 2018.
https://doi.org/10.1109/TFUZZ.2017.2666219
Xu, J.; Yu, L.; Gupta, R. (2020). Evaluating the Performance of the Government Venture Capital Guiding Fund Using the Intuitionistic Fuzzy Analytic Hierarchy Process, Sustainability, 12(7), 6908, 2020.
https://doi.org/10.3390/su12176908
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8(3), 338-356, 1965.
Additional Files
Published
Issue
Section
License
Copyright (c) 2023 Lorena Popa
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.
