Volume 21 , Issue 4 , PP: 172-180, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
S. Gomathi 1 * , S. Krishnaprakash 2 , M. Karpagadevi 3 , Said Broumi 4
Doi: https://doi.org/10.54216/IJNS.210418
This paper introduces the concept of cubic spherical neutrosophic sets (CSNSs), a geometric representation of neutrosophic sets, as well as a specification of its operational principles. In CSNs, two aggregation operators are investigated. The shape of CSNSs represents the evaluation values of alternatives with respect to criteria in a MCDM strategy based on the two aggregation operators and cosine distance for CSNSs. The cosine distance between an alternative and the ideal alternative is used to rank them, and the best alternative(s) can be selected. A numerical example concludes by demonstrating the use of the suggested method.
neutrosophic set , cubic spherical neutrosophic set , cubic spherical neutrosophic aggregation operators , multi criteria decision making.
[1] P. Biswas, S. Pramanik and B. C. Giri, TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, Neural Comput. Appl., vol. 27, no. 3, pp. 727-737, 2016.
[2] Chatterjee, Rajashi, Pinaki Majumdar, and Syamal Kumar Samanta, On some similarity measures and entropy on quadripartitioned single valued neutrosophic sets, Journal of Intelligent & Fuzzy Systems vol. 30, no. 4, pp. 2475- 2485, 2016.
[3] Debnath, Somen, Linear Diophantine Neutrosophic Sets and Their Properties, Neutrosophic Sets and Systems vol. 53, no. 1, pp 622-641, 2023.
[4] Deli, Irfan, Mumtaz Ali, and Florentin Smarandache, Bipolar neutrosophic sets and their application based on multicriteria decision making problems, In 2015 International conference on advanced mechatronic systems (ICAMechS), pp. 249-254, 2015.
[5] Karaaslan, Faruk, and Fatih Hunu, Type-2 single-valued neutrosophic sets and their applications in multi-criteria group decision making based on TOPSIS method, J. of Ambient Int. and Humanized Computing, vol. 11, pp. 4113- 4132, 2020.
[6] Peng, Juan-juan, Jian-qiang Wang, Xiao-hui Wu, Jing Wang, and Xiao-hong Chen, Multi-valued neutrosophic sets and power aggregation operators with their applications in multi-criteria group decision-making problems, Inter. J. of Comp. Int. Sys., vol. 8, no. 2, pp. 345-363, 2015.
[7] Peng, Juan-juan, Jian-qiang Wang, Jing Wang, Hong-yu Zhang, and Xiao-hong Chen, Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems, Int. J. of sys. sci., vol 47, no. 10, pp. 2342- 2358, 2016.
[8] Rama Mallick and Surapati Pramanik, Pentapartitioned neutrosophic set and its properties, Neutrosophic Sets and Systems, vol. 36, pp.184-192, 2020.
[9] F. Smarandache, Neutrosophy, neutrosophic probability, set, and logic, Amer. Res. Press, Rehoboth, USA, 105 p., 1998; http://fs.gallup.unm.edu/eBook-neutrosophics4.pdf (4th edition)
[10] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics, third ed., Xiquan, Phoenix, 2003.
[11] F. Smarandache, Possibilistic Neutrosophic Set as a particular case of the Type-2 Neutrosophic Set.” Florentin Smarandache: 76.
[12] Y. Sun and Y. Cai, A Flexible Decision-Making Method for Green Supplier Selection Integrating TOPSIS and GRA Under the Single-Valued Neutrosophic Environment, IEEE Access, vol. 9, pp. 83025-83040, 2021.
[13] Surapati Pramanik, Interval Pentapartitioned Neutrosophic Sets, Neutrosophic Sets and Systems, Vol. 55, 2023, pp. 232-246, 2020.
[14] Tan, Rui-pu, and Wen-de Zhang, Decision-making method based on new entropy and refined single-valued neutrosophic sets and its application in typhoon disaster assessment, Applied Intelligence, vol. 51, pp. 283-307, 2021.
[15] H. Wang, F. Smarandache, Y. Zhang and R. Sunderraman, Single valued neutrosophic sets, Proc 10th Int. Conf. Fuzzy Theory Tech., pp. 10-14, 2005.
[16] H. Wang, F. Smarandache, R. Sunderraman, and Y. Q. Zhang, interval neutrosophic sets and logic: theory and applications in computing: Theory and applications in computing, vol 5, Infinite Study, 2005.
[17] J. Ye, Trapezoidal neutrosophic set and its application to multiple attribute decision-making, Neural computing and Applications, vol 26, pp. 1157-1166, 2015.
[18] J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, J. Intell. Fuzzy Syst., vol. 26, no. 5, pp. 2459-2466, 2014.
