Volume 18 , Issue 4 , PP: 385-394, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Amala S. Richard 1 , A.Rajkumar 2 , D.Nagarajan 3 * , Broumi Said 4
Doi: https://doi.org/10.54216/IJNS.180432
Neutrosophic set (NS) is generalization of Intuitionistic Fuzzy Set(IFS) and Fuzzy Set (FS) where Neutrosophic Set(NS) is the collection of Membership, Non-Membership, Indeterminacy Membership of the constituent element. This paper includes the modified circle breaking techinque which is used to evaluate the Shortest Path Problem in which edge weight are protrayed in Single Valued Linear Heptagonal Neutrosophic Number (SVLHNN) and an numerical illustration is given for the efficiency of the given algorithm.
Shortest Path Problem , Modified Circle Breaking Algorithm , Single Valued Linear Heptagonal Neutrosophic Number  ,
[1] L.A Zadeh, Fuzzy sets, Information and Control, 8(5): 338- 353; 1965.
[2] K.Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20: 87-96, 1986.
[3] F. Smarandache, A unifying field in logics neutrosophy: neutrosophic probability, set and logic, American
Research Press, Rehoboth 1998.
[4] A. Chakraborty, S. Mondal and S. Broumi, De-Neutrosophication technique of pentagonal neutrosophic
number and application in minimal spanning tree, Neutrosophic Sets and Systems; vol. 29, pp. 1-18, doi:
10.5281/zenodo.3514383, 2019.
[5] Amala S Richard and A. Rajkumar De-Neutrosophication Technique of Single Valued Linear Heptagonal
Neutrosophic Number, Advances in Mathematics: Scientific Journal 9 (2020), no.10, 7811–7818 ISSN:
1857-8365 (printed); 1857-8438 doi.org/10.37418/amsj.9.10.13
[6] Avishek Chakraborty, Application of Pentagonal Neutrosophic Number in Shortest Path Problem
International Journal of Neutrosophic Science (IJNS)Vol. 3, No. 1, PP. 21-28, 2020
[7] S.Broumi, A.Dey, M.Talea, A.Bakali, F.Smarandache, D.Nagarajan, M.Lathamaheswari and R. Kumar
Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment, Complex and Intelligent
Systems ,pp-1-8, 2019.
[8] Lehua Yang, Dongmei Li and Ruipu Tan, Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph
Based on Circle-Breaking Algorithm, Symmetry 2020, 12, 1360; doi:10.3390/sym12081360
www.mdpi.com/journal/symmetry
[9] Broumi, S.Bakali, A. Bahnasse, A. Neutrosophic sets: On overview. New Trends Neutrosophic Theor. Appl.
2018, 2, 403434.
[10] R. Kumar, S. A. Edalatpanah, S. Jha, S. Broumi and A. Dey, Neutrosophic shortest path problems,
Neutrosophic Sets and Systems, vol. 23, pp. 5-15, 2018.
[11] S. Broumi, M. Talea, A. Bakali, F. Smarandache and P. K. Kishore Kumar, "Shortest path problem on single
valued neutrosophic graphs," 2017 International Symposium on Networks, Computers and Communications
(ISNCC), 2017, pp. 1-6, doi: 10.1109/ISNCC.2017.8071993.
[12] Broumi, S., Nagarajan, D., Bakali, A. et al. The shortest path problem in interval valued trapezoidal and
triangular neutrosophic environment. Complex Intell. Syst. 5, 391–402 (2019).
https://doi.org/10.1007/s40747-019-0092-5
[13] Koca, G., Demir, E., İcan, Ö., Karamaşa, Ç. (2021). Analyzing Shortest Path Problem via Single-Valued
Triangular Neutrosophic Numbers: A Case Study. In: Smarandache, F., Abdel-Basset, M. (eds) Neutrosophic
Operational Research. Springer, Cham. https://doi.org/10.1007/978-3-030-57197-9_2
[14] M. Mullai, S. Broumi, A. Stephen "Shortest Path Problem by Minimal Spanning Tree Algorithm using
Bipolar Neutrosophic Numbers", International Journal of Mathematics Trends and Technology
(IJMTT). V46(2):79-87 June 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense
Research Group.
[15] Ruxiang Liu Study on single-valued neutrosophic graph with application in shortest path problem CAAI
transcation on intelligence technology. https://doi.org/10.1049/trit.2020.0111