1
Department of Mathematics, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India
(palanimaths86@gmail.com)
2
Fuzzy Algebras and Decision-Making Problems Research Unit, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand
(aiyared.ia@up.ac.th)
3
Laboratory of Information Processing, Faculty of Science Ben MSik, University of Hassan II, Casablanca, Morocco
(broumisaid78@gmail.com)
4
Department of Mathematics, Little Flower College-680103, Guruvayoor, India
(lejojmanavalan@gmail.com)
5
Department of Mathematics, Al- Ameen Engineering College, Erode
(sundarimaths@gmail.com)
Abstract :
In contrast to the Pythagorean interval valued fuzzy soft set and the neutrosophic interval valued fuzzy soft set, the Pythagorean neutrosophic interval valued fuzzy soft set is a generalization of these sets. We discuss aggregating PyNIVFS decision matrixes by using aggregated operations. The VIKOR method, which is an extension of neutrosophic fuzzy soft sets, is a powerful method for evaluating multi-criteria group decision making. The score function in this approach is based on the aggregation of the VIKOR method to a PyNIVFSpositive and negative solution. Optimal alternatives are introduced under closeness. An investment company plans to purchase some shares of the top five companies in the stock exchange to invest some money on. In order to minimize this factor, they decided to invest some of their cash in percentages of 30 dollars, 25 dollars, 20 dollars, 15 dollars and
Keywords :
PyNIVFS set; MCGDM; VIKOR; aggregation operator.
References :
[1] C.L. Hwang, K. Yoon, Multiple Attributes Decision Making Methods and Applications, Springer, Berlin Heidelberg, 1981.
[2] Z. Xiao, W.J. Chen, and L.L. Li, A method based on interval-valued fuzzy soft set for multi attribute group decision making problems under uncertain environment, Knowledge and Information Systems, 34, (2013), 653-669.
[3] L. A. Zadeh, Fuzzy sets, Information and control, 8(3), (1965), 338-353.
[4] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, 20(1), (1986), 87-96.
[5] M. Gorzalczany, A method of inference in approximate reasoning based on interval valued fuzzy sets, Fuzzy Sets and Systems, 21, (1987) 1-17.
[6] Ranjit Biswas, Vague Groups, International journal of Computational Cognition, 4(2),(2006), 20-23.
[7] R. R. Yager, Pythagorean membership grades in multi criteria decision-making, IEEE Trans. Fuzzy Systems, 22, (2014), 958-965.
[8] X. Peng, and Y. Yang, Fundamental properties of interval valued pythagorean fuzzy aggregation operators, International Journal of Intelligent Systems, (2015), 1-44.
[9] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani and T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, Journal of Intelligent and Fuzzy Systems, 36, (2019), 2829-284.
[10] B.C. Cuong and V. Kreinovich, Picture fuzzy sets a new concept for computational intelligence problems, in Proceedings of 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE, (2013), 1-6.
[11] M. Akram, W. A. Dudek, Farwa Ilyas, Group decision making based on Pythagorean fuzzy TOPSIS method, Int. J. Intelligent System, 34, (2019), 1455-1475.
[12] M. Akram, W. A. Dudek, J. M. Dar, Pythagorean Dombi Fuzzy Aggregation Operators with Application in Multi-criteria Decision-making, Int. J. Intelligent Systems, 34, (2019), 3000-3019.
[13] M. Akram, X. Peng, A. N. Al-Kenani, A. Sattar, Prioritized weighted aggregation operators under complex Pythagorean fuzzy information, Journal of Intelligent and Fuzzy Systems, 39(3), (2020), 4763-4783.
[14] T.M. Athira, S.J. John and H. Garg, Entropy and distance measures of Pythagorean fuzzy soft sets and their applications, Journal of Intelligent and Fuzzy Systems, (2019), 1-14.
[15] H. Garg, Some picture fuzzy aggregation operators and their applications to multi criteria decisionmaking, Arabian Journal for Science and Engineering, 42(12) (2017), 5275-5290.
[16] H. Garg, New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications, International Journal of Intelligent Systems, 34(1), (2019), 82-106.
[17] Z. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems, 15, (2007), 1179-1187.
[18] W.F. Liu, J. Chang, X. He, Generalized Pythagorean fuzzy aggregation operators and applications in decision making, Control Decis. 31, (2016), 2280-2286.
[19] K. Rahman, S. Abdullah,, M. Shakeel, MSA. Khan and M. Ullah, Interval valued Pythagorean fuzzy geometric aggregation operators and their application to group decision-making problem, Cogent Mathematics, 4, (2017), 1-19.
[20] K. Rahman, A. Ali, S. Abdullah and F. Amin, Approaches to multi attribute group decision-making based on induced interval valued Pythagorean fuzzy Einstein aggregation operator, New Mathematics and Natural Computation, 14(3), (2018), 343-361.
[21] Z. Yang, J. Chang, Interval-valued Pythagorean normal fuzzy information aggregation operators for multiple attribute decision making approach, IEEE Access, 8, (2020), 51295-51314.
[22] X.D. Peng, Y. Yang, J.P. Song, Pythagorean fuzzy soft set and its application, Computer Engineering, 41(7), (2015), 224-229.
[23] K. Ullah, T. Mahmood, Z. Ali and N. Jan, On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition, Complex and Intelligent Systems, 1-13, (2019).
[24] C. Jana and M. Pal, Application of bipolar intuitionistic fuzzy soft sets in decision making problem, International Journal of Fuzzy System Applications, 7(3),(2018), 32-55.
[25] C. Jana and M. Pal, A Robust single valued neutrosophic soft aggregation operators in multi criteria decision making, Symmetry, 11(110), (2019), 1-19.
[26] C. Jana, M. Pal, and J. Wang, A robust aggregation operator for multi criteria decision making method with bipolar fuzzy soft environment, Iranian Journal of Fuzzy Systems, 16(6), (2019), 1-16.
| Style | # |
|---|---|
| MLA | M. Palanikumar, Aiyared Iampan, Said Broumi, Lejo J Manavalan, K. Sundareswari. "Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach." International Journal of Neutrosophic Science, Vol. 22, No. 1, 2023 ,PP. 104-113 (Doi : https://doi.org/10.54216/IJNS.220108) |
| APA | M. Palanikumar, Aiyared Iampan, Said Broumi, Lejo J Manavalan, K. Sundareswari. (2023). Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach. Journal of International Journal of Neutrosophic Science, 22 ( 1 ), 104-113 (Doi : https://doi.org/10.54216/IJNS.220108) |
| Chicago | M. Palanikumar, Aiyared Iampan, Said Broumi, Lejo J Manavalan, K. Sundareswari. "Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach." Journal of International Journal of Neutrosophic Science, 22 no. 1 (2023): 104-113 (Doi : https://doi.org/10.54216/IJNS.220108) |
| Harvard | M. Palanikumar, Aiyared Iampan, Said Broumi, Lejo J Manavalan, K. Sundareswari. (2023). Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach. Journal of International Journal of Neutrosophic Science, 22 ( 1 ), 104-113 (Doi : https://doi.org/10.54216/IJNS.220108) |
| Vancouver | M. Palanikumar, Aiyared Iampan, Said Broumi, Lejo J Manavalan, K. Sundareswari. Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 1 ): 104-113 (Doi : https://doi.org/10.54216/IJNS.220108) |
| IEEE | M. Palanikumar, Aiyared Iampan, Said Broumi, Lejo J Manavalan, K. Sundareswari, Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 1 , (2023) : 104-113 (Doi : https://doi.org/10.54216/IJNS.220108) |