A Comparative Analysis of the Ranking Functions for the IVIFVs and A New Score Function

Year 2022, Volume: 35 Issue: 4, 1484 - 1502, 01.12.2022

Melda Kokoç Süleyman Ersöz

https://doi.org/10.35378/gujs.841069

Abstract

The ranking of interval-valued intuitionistic fuzzy values (IVIFVs) has an important role in real-life decision-making problems. Even though there are many approaches related to the ranking methods of the IVIFVs, some of them have some shortcomings. In this study, the disadvantages of the existing ranking functions of the IVIFVs are discussed. It is revealed that both the most popular ranking functions and their recently improved versions may lead to unacceptable results. Furthermore, in this article, a new score function is offered to cope with the shortcomings of the ranking functions. The importance and performance of this new score function are proven with the help of many examples. Also, the decision-making algorithm adapted by integrating the new function is presented to illustrate the applicability of the new score function in the decision-making problems.

Keywords

Accuracy function, Interval-valued intuitionistic fuzzy set, Ranking, Score function

References

• [1] Wei, A. P., Li, D. F., Lin, P. P., and Jiang, B. Q., "An information-based score function of interval-valued intuitionistic fuzzy sets and its application in multiattribute decision making", Soft Computing, 1-11, (2020).
• [2] Zadeh, L. A., "Fuzzy sets", Information Control, 8(3): 338-353, (1965).
• [3] Atanassov, K., "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1): 87-96, (1986).
• [4] Niu, L. L., Li, J., Li, F. L. and Wang, Z. X., "Multi-criteria decision-making method with double risk parameters in interval-valued intuitionistic fuzzy environments", Complex & Intelligent Systems, 6(3): 669-679, (2020).
• [5] Ye, J., "Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment", Expert Systems with Applications, 36(3): 6899-6902, (2009).
• [6] Tu, C. C. and Chen, L. H., "Novel score functions for interval-valued intuitionistic fuzzy values", Proceedings of SICE Annual Conference (SICE), (2012).
• [7] Joshi, B. P. and Kharayat, P. S., "An accuracy function for interval-valued intuitionistic fuzzy number", International Journal of Mathematical Archive, 6(1): 51-55, (2015).
• [8] Atanassov, K. and Gargov, G., "Interval valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31: 343-349, (1989).
• [9] Garg, H., "A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems", Applied Soft Computing, 38: 988-999, (2016).
• [10] Nayagam, V. L. G., Jeevaraj, S. and Dhanasekaran, P., "An intuitionistic fuzzy multi-criteria decision-making method based on non-hesitance score for interval-valued intuitionistic fuzzy sets", Soft Computing, 21(23): 7077-7082, (2017).
• [11] Talukdar, P. and Dutta, P., "A new ranking approach for interval valued intuitionistic fuzzy sets and its application in decision making", International Journal of Fuzzy System Applications, 8(2): 89-104, (2019).
• [12] Xu, Z. S., "Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making", Control and Decision, 22(2): 215-219, (2007).
• [13] Lee, W., "A novel method for ranking interval-valued intuitionistic fuzzy numbers and its application to decision making", International Conference on Intelligent Human-Machine Systems and Cybernetics, (2009).
• [14] Bai, Z. Y., "An interval-valued intuitionistic fuzzy TOPSIS method based on an improved score function", Scientific World Journal, 879089, (2013).
• [15] Wang, Z. X. and Niu, L. L., "A new scoring function of intervai-valued intuitionistic fuzzy number and its application in multi-attribute decision making", Fuzzy Systems and Mathematics, 27(4): 167–172, (2013).
• [16] Wang, C. Y. and Chen, S. M., "An improved multiattribute decision making method based on new score function of interval-valued intuitionistic fuzzy values and linear programming methodology", Information Sciences, 411: 176-184, (2017).
• [17] Wang, C. Y. and Chen, S. M., "A new multiple attribute decision making method based on linear programming methodology and novel score function and novel accuracy function of interval-valued intuitionistic fuzzy values", Information Sciences, 438: 145-155, (2018).
• [18] Gong, R. and Ma, L., "A new score function and accuracy function of interval-valued intuitionistic fuzzy number and its application", Systems Engineering -Theory & Practice, 30(2): 463- 475, (2019).
• [19] Jia, Q., Hu, J. and Zhang, W., "A novel fault detection model based on Atanassov’s interval-valued intuitionistic fuzzy sets", Belief Rule Base and Evidential Reasoning, IEEE Access, 8: 4551-4567, (2019).
• [20] Nayagam, V. L. G., Muralikrishnan, S. and Sivaraman, G., "Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets", Expert Systems with Applications, 38(3), 1464-1467, (2011).
• [21] Nayagam, V. L. G. and Sivaraman, G., "Ranking of interval-valued intuitionistic fuzzy sets", Applied Soft Computing, 11(4): 3368-3372, (2011).
• [22] Kang, J., Lan, R. and Wang, S. S., "A new accuracy function of interval-valued intuitionnistic fuzzy numbers and its application in decision making", Journal of Xi’an Uniandrsity of Post and Telecommunications, 20(3): 86-91, (2015).
• [23] Sahin, R., "Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets", Soft Computing, 20(7): 2557-2563, (2016).
• [24] Zhang, F. Xu, S., "Remarks to "Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets", Soft Computing, 21(9): 2263-2268, (2017).
• [25] Joshi, D. and Kumar, S., "Improved accuracy function for interval-valued intuitionistic fuzzy sets and its application to multi–attributes group decision making", Cybernetics and Systems, 49(1): 64-76, (2018).
• [26] Huang, W. W., Zhang, F. W. and Xu, S. H., "A complete ranking method for interval-valued intuitionistic fuzzy numbers and its applications to multicriteria decision making", Soft Computing, 1-8, (2020).
• [27] Nguyen, H., "A generalized p-norm knowledge-based score function for an interval-valued intuitionistic fuzzy set in decision making", IEEE Transactions on Fuzzy Systems, 28(3): 409-423, (2019).
• [28] Hao, Y. and Chen, X., "Study on the ranking problems in multiple attribute decision making based on interval‐valued intuitionistic fuzzy numbers", International Journal of Intelligent Systems, 33(3): 560-572, (2018).
• [29] Liu, B. and Luo, M. X., "Multicriteria decision making based on interval-valued intuitionistic fuzzy sets with a new kind of accuracy function", Quantitative Logic and Soft Computing 2016: Springer, 477-486, (2017).