A novel parametric ranking method for intuitionistic fuzzy numbers

Document Type : Original Manuscript

Author

Khatam Al-Anbia university of Behbahan

Abstract

Since the inception of intuitionistic fuzzy sets in 1986, many authors have proposed different methods for ranking intuitionistic fuzzy numbers (IFNs). How ever, due to the complexity of the problem, a method which gives a satisfactory result to all situations is a challenging task. Most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination and some produce different rankings for the same situation and some methods cannot rank crisp numbers. For overcoming the above problems, in this paper, a new parametric ranking method for IFNs is proposed. It is developed based on the concept α-cuts and β-cuts and area on left side of IFNs. The proposed ranking method is applied to solve partner selection problem in which the rating of partner on attributes are expressed by using triangular IFNs. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method. 

Keywords

References

[1] S. Aggarwal, C. Gupta, Solving intuitionistic fuzzy solid transportation problem via new ranking method based on signed distance, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 24(04) (2016), 483–501.
[2] Z. Ai, Z. Xu, Q. Lei, Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers, Fuzzy Optimization and Decision Making, 161 (2017), 71–87.
[3] K. T. Atanassov, Intuitionistic fuzzy sets. Fuzzy sets and Systems, 20(1) (1986), 87-96.
[4] P. Burillo, H. Bustince, V. Mohedano, Some Definitions of Intuitionistic Fuzzy Number. First Properties, In Proceedings of the 1st Workshop on Fuzzy Based Expert Systems, (1994), 53–55.
[5] S. M. Chen, J. M. Tan, Handling multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy sets and systems, 67(2) (1994), 163–172.
[6] R. Chutia, B. Chutia, A new method of ranking parametric form of fuzzy numbers using value and ambiguityApplied Soft Computing, 52 (2017), 1154–1168.
[7] S. Das, D. Guha, Ranking of intuitionistic fuzzy number by centroid point, Journal of Industrial and Intelligent Information, 1(2) (2013), 107–110.
[8] S. Das, D. Guha, A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to MCDM problems, Fuzzy Information and Engineering, 8(1) (2016), 41–74.
[9] R. Ezzati, S. Khezerloo, S. Ziari, Application of parametric form for ranking of fuzzy numbers, Iranian Journal of Fuzzy Systems, 12(1) (2015), 59–74.
[10] P. Grzegorzewski, Distances and Orderings in a Family of Intuitionistic Fuzzy Numbers, In EUSFLAT Conf., (2003), 223–227.
[11] D. H. Hong, C.‘H. Choi, Multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy sets and systems, 114(1) (2000), 103–113.
[12] S. Jeevaraj, P. Dhanasekaran, A linear ordering on the class of Trapezoidal intuitionistic fuzzy numbers, Expert Systems with Applications, 60 (2016), 269–279.
[13] W. Jianqiang, Z. Zhong, Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems, Journal of Systems Engineering and Electronics, 20(2) (2009), 321–326.
[14] V. Lakshmana Gomathi Nayagam, S. Jeevaraj, S. Geetha, Total ordering for intuitionistic fuzzy numbers, Complexity, 21S2 (2016), 54–66.
[15] H.W.Liu,G.J.Wang,Multi-criteria decision-making methods based on intuitionistic fuzzy sets,European Journal of Operational Research, 179(1) (2007), 220–233.
[16] D. F. Li, A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers and Mathematics with Applications, 60(6) (2010), 1557–1570.
[17] D. F. Li, J. X. Nan, M. J. Zhang, A ranking method of triangular intuitionistic fuzzy numbers and application to decision making, International Journal of Computational Intelligence Systems, 3(5) (2010), 522–530.
[18] M. Ma, M. Friedman, A. Kandel, A new fuzzy arithmetic, Fuzzy sets and systems, 108(1) (1999), 83–90.
[19] H. B. Mitchell, Ranking-intuitionistic fuzzy numbers, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(03) (2004), 377–386.
[20] G. Nayagam, V. Lakshmana, G. Venkateshwari, G. Sivaraman, Ranking of Intuitionistic Fuzzy Numbers, In Fuzzy Systems, IEEE International Conference, (2008), 1971–1974.
[21] H. M Nehi, A new ranking method for intuitionistic fuzzy numbers, International Journal of Fuzzy Systems, 12(1) (2010), 80–86.
[22] K. A. Prakash, M. Suresh, S. Vengataasalam, A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept, Mathematical Sciences, 10(4) (2016), 177–184.
[23] S. Rezvani, Ranking method of trapezoidal intuitionistic fuzzy numbers, Annals of Fuzzy Mathematics and Informatics, 5(3) (2013), 515–523.
[24] R. A. Shureshjani, M. Darehmiraki, A new parametric method for ranking fuzzy numbers, Indagationes Mathematicae, 24(3) (2013), 518–529.
[25] J. S. Su, Fuzzy programming based on interval-valued fuzzy numbers and ranking, International Journal Contemporary Mathematical Sciences,2 (2007), 393–410.
[26] S. P. Wan, J. Y. Dong, Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi attribute group decision making, Applied Soft Computing, 29 (2015), 153–168.
[27] X. Wang, E. E. Kerre, Reasonable properties for the ordering of fuzzy quantities(I), Fuzzy sets and systems, 118(3) (2001), 375–385.
[28] G. Wei, Some arithmetic aggregation operators with intuitionistic trapezoidal fuzzy numbers and their application to group decision making, Journal of Computers, 5(3) (2010), 345–351.
[29] J. Wu, Q. W. Cao, Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers, Applied Mathematical Modelling, 37(1) (2013), 318–327.
[30] Z. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, International journal of general systems, 35(4) (2006), 417-433.
[31] J. Ye, Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment, Expert Systems with Applications, 36(3) (2009), 6899–6902.
[32] Z. Yue, An intuitionistic fuzzy projection-based approach for partner selection, Applied Mathematical Modelling, 37(23) (2013), 9538–9551.
[33] X. T. Zeng, D. F. Li, G. F. Yu, A value and ambiguity-based ranking method of trapezoidal intuitionistic fuzzy numbers and application to decision making, Sci World Journal, 2014 (2014), 1–8.
[34] M. Zhang, J. Nan, A Compromise Ratio Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Its Application to MADM Problems, Iranian Journal of Fuzzy Systems, 10(6) (2013), 21–37.
Iranian Journal of Fuzzy Systems
Volume 16, Issue 1
January and February 2019
Pages 129-143

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