Ranking triangular intuitionistic fuzzy numbers: A Nagel point approach and applications in multi-criteria decision making

Authors

  • K. Arun Prakash Department of Mathematics, Kongu Engineering College, Erode, Tamil Nadu, India.
  • M. Suresh * Department of Mathematics, Kongu Engineering College, Erode, Tamil Nadu, India.

https://doi.org/10.48313/uda.v3i2.95

Abstract

Ordinary fuzzy sets have been expanded into several varieties, including type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy, and others, to assist us model uncertainty. For every element in an Intuitionistic Fuzzy Set (IFS), there are membership and non-membership functions. Intuitionistic Fuzzy Numbers (IFNs) plays a vital role in many applications. In this paper, a new ranking approach of IFNs were done based on nagel points. The proposed new ranking was validated by certain results and numerical examples. In last section, we put the suggested ranking principle into practice for the installation of an aeronautical research organization center through a case study.    

Keywords:

Intuitionistic fuzzy sets, Intuitionistic fuzzy number, Triangular intuitionistic fuzzy number, Nagel Point, Multi-criteria decision making problem

References

  1. [1] Shakouri, B., Abbasi Shureshjani, R., Daneshian, B., & Hosseinzadeh Lotfi, F. (2020). A parametric method for ranking intuitionistic fuzzy numbers and its application to solve intuitionistic fuzzy network data envelopment analysis models. Complexity. https://doi.org/10.1155/2020/6408613
  2. [2] Lakshmana Gomathi Nayagam, V., Jeevaraj, S., & Sivaraman, G. (2016). Complete ranking of intuitionistic fuzzy numbers. Fuzzy information and engineering, 8(2), 237–254. https://doi.org/10.1016/J.FIAE.2016.06.007
  3. [3] Bharati, S. K. (2017). Ranking method of intuitionistic fuzzy numbers. Global journal of pure and applied mathematics, 13(9), 4595–4608. https://www.ripublication.com/gjpam17/gjpamv13n9_16.pdf
  4. [4] Atalik, G., & Senturk, S. (2020). A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers. Journal of intelligent and fuzzy systems, 39(5), 6271–6278. https://doi.org/10.3233/JIFS-189095
  5. [5] Rezvani, S., & Wang, X. (2018). A new type-2 intuitionistic exponential triangular fuzzy number and its ranking method with centroid concept and Euclidean distance. IEEE international conference on fuzzy systems. IEEE. https://doi.org/10.1109/FUZZ-IEEE.2018.8491685
  6. [6] Elaiyaperumal, R. Gajivaradhan, P. & Suguna, M. (2019). Defuzzification by area of region (AOR) in an intuitionistic fuzzy environment. The international journal of analytical and experimental modal analysis. 11(9), 3282-3288.
  7. [7] Christi, D. M. S. A., & Kasthuri, B. (2015). Transportation problem with triangular intuitionistic fuzzy numbers solved using ranking technique and russell’s method. Fuzzy systems, 7(6), 173–176. https://www.ciitresearch.org/dl/index.php/fs/article/view/FS082015004.
  8. [8] Salahshour, S. (2012). A novel approach for ranking triangular intuitionistic fuzzy numbers. AWERProcedia information technology and computer science, 1(12), 442-446. https://www.academia.edu/2685596
  9. [9] Kumar, T., Bajaj, R. K., & Kaushik, R. (2017). Expected value based ranking of intuitionistic fuzzy variables. AIP conference proceedings, 1860(1), 020030. https://doi.org/10.1063/1.4990329
  10. [10] Li, D. F. (2010). A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Computers & mathematics with applications, 60(6), 1557–1570. https://doi.org/10.1016/J.CAMWA.2010.06.039
  11. [11] Ummusalma, B., & Selvakumari, K. (2017). TOPSIS method for decision making problem by accuracy function of triangular intuitionistic fuzzy number. International journal of pure and applied mathematics, 114(6), 161–168.
  12. [12] Liang, C., Zhao, S., & Zhang, J. (2014). Aggregation operators on triangular intuitionistic fuzzy numbers and its application to multi-criteria decision making problems. Foundations of computing and decision sciences, 39(3), 189–208. https://doi.org/10.2478/FCDS-2014-0011
  13. [13] Stanujkic, D., Zavadskas, E. K., Karabasevic, D., Urosevic, S., & Maksimovic, M. (2017). An approach for evaluating website quality in hotel industry based on triangular intuitionistic fuzzy numbers. Informatica, 28(4), 725–748. https://doi.org/10.15388/INFORMATICA.2017.153
  14. [14] Edalatpanah, S. A. (2019). A data envelopment analysis model with triangular intuitionistic fuzzy numbers. International journal of data envelopment analysis, 7(4), 47–58. https://www.researchgate.net/publication/339617696
  15. [15] Wang, F. (2021). Preference degree of triangular fuzzy numbers and its application to multi-attribute group decision making. Expert systems with applications, 178, 114982. https://doi.org/10.1016/J.ESWA.2021.114982
  16. [16] Saini, N., Bajaj, R. K., Gandotra, N., & Dwivedi, R. P. (2018). Multi-criteria decision making with triangular intuitionistic fuzzy number based on distance measure & parametric entropy approach. Procedia computer science, 125, 34–41. https://doi.org/10.1016/J.PROCS.2017.12.007
  17. [17] Gautam, S. S., & Singh, S. R. (2016). TOPSIS for multi criteria decision making in intuitionistic fuzzy environment. International journal of computer applications, 156(8), 975–8887. https://doi.org/10.5120/ijca2016912514
  18. [18] Selvaraj, J., & Majumdar, A. (2021). A new ranking method for interval-valued intuitionistic fuzzy numbers and its application in multi-criteria decision-making. Mathematics 2021, 9(21), 2647. https://doi.org/10.3390/MATH9212647
  19. [19] Xu, J., Dong, J. Y., Wan, S. P., & Gao, J. (2019). Multiple attribute decision making with triangular intuitionistic fuzzy numbers based on zero-sum game approach. Iranian journal of fuzzy systems, 16(3), 97–112. https://doi.org/10.22111/IJFS.2019.4648
  20. [20] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
  21. [21] Nehi, H. M. (2010). A new ranking method for intuitionistic fuzzy numbers. International journal of fuzzy systems, 12(1), 80. https://openurl.ebsco.com/EPDB%3Agcd%3A13%3A16172957
  22. [22] Nagoorgani, A., & Ponnalagu, K. (2012). A new approach on solving intuitionistic fuzzy linear programming problem. Applied mathematical sciences, 6(70), 3467–3474. https://www.researchgate.net/publication/264419657
  23. [23] Arun Prakash, K., Suresh, M. & Vengataasalam, S. (2016). A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept. Mathematical sciences, 10, 177-184. https://doi.org/10.1007/s40096-016-0192-y
  24. [24] Mohan, S., Kannusamy, A. P., & Samiappan, V. (2020). A new approach for ranking of intuitionistic fuzzy numbers. Journal of fuzzy extension & applications, 1(1), 15-26. https://doi.org/10.22105/jfea.2020.247301.1003

Downloads

Published

2026-06-19

Issue

Vol. 3 No. 2 (2026): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Prakash, K. A. (2026). Ranking triangular intuitionistic fuzzy numbers: A Nagel point approach and applications in multi-criteria decision making. Uncertainty Discourse and Applications, 3(2), 168-181. https://doi.org/10.48313/uda.v3i2.95

Similar Articles

1-10 of 53

You may also start an advanced similarity search for this article.