Volume 19 • Issue 2 • PP: 66-79 • 2022
Nonagonal Neutrosophic Number and its Application in Optimization Technique
View PDF Abstract
This article discusses Nonagonal Neutrosophic number and m-valued Nonagonal Neutrosophic number. The score function, the accuracy function, hamming distance, normalized hamming distance, Euclidean distance and normalized Euclidean distance of Nonagonal and m-polar Nonagonal Neutrosophic number are derived. Some de-neutrosophication method for Nonagonal Neutrosophic number and some properties of m-valued Nonagonal Neutrosophic number are proved. In this article the optimal path of an acyclic network is estimated using Neutrosophic α-cut grade, Neutrosophic Euclidean grade technique and dynamic programming recursion method through Nonagonal Neutrosophic number. The score function and the removal area method are used to transform the Nonagonal Neutrosophic number to crisp number and the results obtained in both the methods are compared.
Keywords
References
[1] Smarandache, F. A Unifying Field in Logics Neutrosophy: Neutrosophic Probability, Set and Logic, 3rd
ed.; American Research Press: Washington, DC, USA, 2003.
[2] Wang, H.B.; Smarandache, F.; Zhang, Y.Q.; Sunderraman, R. Single Valued Neutrosophic Sets. Tech.
Sci. Appl. Math. 2010. Available online: (accessed on 31 July 2018).
[3] Deli, I.; Ali, M.; Smarandache, F. Bipolar neutrosophic sets and their application based on multi-criteria
decision making problems. arXiv, 2005; arXiv:1504.02773.
[4] Peng, J.J.; Wang, J.Q.; Wu, X.H.; Wang, J.; Chen, X.H. Multi-valuedneutrosophic sets and power
aggregation operators with their applications in multi-criteria group decision-making problems. Int. J.
Comp. Int. Syst. 2015, 8, 345–363.
[5] Wang, J.Q.; Li, X.E. The TODIM method with multi-valued neutrosophic sets. Control
Decis. 2015, 30, 1139–1142.
[6] Ye, J. Trapezoidal fuzzy neutrosophic set and its application to multiple attribute decision making. Soft
Computing. Neural Comp. Appl. 2015, 26, 1157–1166.
[7] Mohamed, M.; Abdel-Basset, M.; Hussien, A.N.; Smarandache, F. Using Neutrosophic Sets to Obtain
Pert Three-Times Estimates in Project Management, Neutrosophic Operational Research; Pons
Publishing House: Bruxelles, Belgium, 2016; Volume 1, pp. 145–156
[8] Ye, J. Exponential operations and aggregation operators of interval neutrosophic sets and their decision
making methods. SpringerPlus 2016, 5, 1488.
[9] Peng, X.; Liu, C. Algorithms for neutrosophic soft decision making based on EDAS, new similarity
measure and level soft set. J. Intell. Fuzzy Syst. 2017, 32, 955–968.
[10] Pouresmaeil, H.; Shivanian, E.; Khorram, E.; Fathabadi, H.S. An extended method using TOPSIS and
VIKOR for multiple attribute decision making with multiple decision makers and single valued
neutrosophic numbers. Adv. Appl. Stat. 2017, 50, 261–292.
[11] Bausys, R.; Zavadskas, E.K. Multicriteria decision making approach by VIKOR under interval
neutrosophic set environment. Econ. Comput. Econ. Cybern. Stud. Res. 2015, 49, 33–48
[12] Zavadskas, E.K.; Bausys, R.; Kaklauskas, A.; Ubarte, I.; Kuzminske, A.; Gudiene, N. Sustainable
market valuation of buildings by the single-valued neutrosophic MAMVA method. Appl. Soft
Comput. 2017, 57, 74–87.
[13] Abdel-Basset, M.; Mohamed, M.; Hussien, A.N.; Sangaiah, A.K. A novel group decision-making
model based on triangular neutrosophicnumbers. Soft Comput. 2017, 15, 1–15.
[14] Deli, I.; Şubaş, Y. A ranking method of single valued neutrosophic numbers and its applications to
multi-attribute decision making problems. Int. J. Mach. Learn. Cybern. 2016, 8, 1309–1322.
Cite This Article
Choose your preferred format