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A new approach for ranking of intuitionistic fuzzy numbers

Document Type : Research Paper

Authors

Department of Mathematics, Kongu Engineering College, Erode, Tamil Nadu, India.

Abstract

The concept of an intuitionistic fuzzy number (IFN) is of importance for representing an ill-known quantity. Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an IFN is of importance for quantifying an ill-known quantity. Ranking of intuitionistic fuzzy numbers plays a vital role in decision making and linear programming problems. Also, ranking of intuitionistic fuzzy numbers is a very difficult problem. In this paper, a new method for ranking intuitionistic fuzzy number is developed by means of magnitude for different forms of intuitionistic fuzzy numbers. In Particular ranking is done for trapezoidal intuitionistic fuzzy numbers,   triangular intuitionistic fuzzy numbers, symmetric trapezoidal intuitionistic fuzzy numbers, and symmetric triangular intuitionistic fuzzy numbers.  Numerical examples are illustrated for all the defined different forms of intuitionistic fuzzy numbers.  Finally some comparative numerical examples are illustrated to express the advantage of the proposed method.

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References
[1] Atanassov K. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20, 87-96.
[2] Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers & mathematics with applications, 57(3), 413-419.
[3] Allahviranloo, T., Abbasbandy, S., & Saneifard, R. (2011). A method for ranking of fuzzy numbers using new weighted distance. Mathematical and computational applications, 16(2), 359-369.
[4] Dubey, D., & Mehra, A. (2011). Linear programming with triangular intuitionistic fuzzy number. Proceedings of the 7th conference of the european society for fuzzy logic and technology (pp. 563-569). Atlantis Press.
[5] Grzegrorzewski, P. (2003). The hamming distance between intuitionistic fuzzy sets. Proceedings of the 10th IFSA world congress, Istanbul, Turkey (Vol. 30, pp. 35-38).
[6] 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.
[7] 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.
[8] Mitchell, H. B. (2004). Ranking-intuitionistic fuzzy numbers. International journal of uncertainty, fuzziness and knowledge-based systems, 12(03), 377-386.
[9] Mahapatra, G. S., & Mahapatra, G. S. (2010). Intuitionistic fuzzy fault tree analysis using intuitionistic fuzzy numbers. International mathematical forum, 5(21), 1015-1024.
[10] Nehi, H. M. (2010). A new ranking method for intuitionistic fuzzy numbers. International journal of fuzzy systems, 12(1).
[11] Nayagam, V.L.G., Venkateshwari, G., Sivaraman, G., (2008). Ranking of intuitionistic fuzzy numbers, Proc. of international conference on fuzzy systems 2008, Fuzz-IEEE (pp. 1971-1974).
[12] Nagoorgani, A., & Ponnalagu, K. (2012). A new approach on solving intuitionistic fuzzy linear programming problem. Applied mathematical sciences, 6(70), 3467-3474.
[13] Parvathi, R., & Malathi, C. (2012). Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers. International Journal of Soft Computing and Engineering, 2, 268-273.
[14] Parvathi, R., & Malathi, C. (2012). Intuitionistic fuzzy simplex method. International journal of computer applications, 48(6), 39-48.
[15] Rezvani, S. (2013). Ranking method of trapezoidal intuitionistic fuzzy numbers. Annals of fuzzy mathematics and informatics, 5(3), 515-523.
[16] Seikh, M. R., Nayak, P. K., & Pal, M. (2012). Generalized triangular fuzzy numbers in intuitionistic fuzzy environment. International journal of engineering research and development, 5(1), 08-13.
[17] Jianqiang, W., & Zhong, Z. (2009). Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. Journal of systems engineering and electronics, 20(2), 321-326.
[18] Wang, J. (2008). Overview on fuzzy multi-criteria decision-making approach. Control and decision, 23(6), 601-606.
Journal of Fuzzy Extension and Applications
Volume 1, Issue 1
March 2020
Pages 15-26
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