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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 20 • Issue 1 • PP: 68-76 • 2023

Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system

S. Ghousia Begum 1*
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,
N. Jose Parvin Praveena 2
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,
A. Rajkumar 3
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,
D. Nagarajan 4
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,
broumi said 5
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1Research Scholar, Department of Mathematics, Hindustan Institute of Technology and science, Padur, Chennai, India
2Department of Mathematics, St.Joseph’s College of Engineering, Chennai, India
3Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India
4Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India
5Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.200106
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© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: August 16, 2022 Accepted: December 15, 2022
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Abstract

The following paper introduces a methodology to calculate the least cost for a directed network through Travelling salesman problem. Dynamic programming method is used to find the minimum Cost. The recursion formula is used. The edge weights of the networks are being taken in terms of Triangular, Trapezoidal and Pentagonal Neutrosophic set. Score function for the Triangular, Trapezoidal and Pentagonal Neutrosophic sets are being defined for deneutrosophication. The least cost is estimated using all the above said Neutrosophic sets and the result is compared

Keywords

Triangular Neutrosophic Number (TNN) Trapezoidal Neutrosophic Number (TRNN) Pentagonal Neutrosophic number (PNN) Least Cost Travelling salesman Deneutrosophication Recursion formula Dynamic Programming

References

[1] Avishek Chakraborty, Said Broumi and Prem Kumar Singh (2019). Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment. Neutrosophic Sets and Systems, Vol.28.

[2] Jose Parvin Praveena, N., Sahayanatha Stalin,N and Rajkumar, A (2020). Estimation of shortest path using dynamic programming through Neutrosophic environment. Advances in Mathematics: Scientific journal, no.10, 7803-7809.

[3] Kacprzyk,J., Fuzzy dynamic programming – basic issues, in: M. Delgado et al. (Eds.), Fuzzy Optimization: Recent Advances, Physica, Heidelberg, 1994, pp. 321 – 331.

[4] Kacprzyk,J., Fuzzy dynamic programming – basic issues, in: M. Delgado et al. (Eds.), Fuzzy Optimization: Recent Advances, Physica, Heidelberg, 1994, pp. 321 – 331.

[5] Kacprzyk,J., A.O. Esogbue, Fuzzy dynamic programming: Main developments and applications, Fuzzy Sets and Systems 81 (1996) 31 – 45.

[6] Nancy Garg H (2016) an improved score function for ranking Neutrosophic sets and its application to decision making process. Int J Uncertain Quantif 6(5): 377-385.

[7] Rajkumar, A., Richard, A.S (2020).De- Neutrosophication technique of single valued linear heptagonal neutrosophic number. Advances in Mathematics: Scientific journal

[8] Smarandache,F., A unifyeing field in logics. Neutrosophy: Neutrosophic probability, set and logic. Rehoboth American Research press ,1998.

[9] Wang H, Smarandache F, Zhang Y, Sunderrraman R (2005) interval Neutrosophic sets and logic: theory and applications in computing: theory and applications in computing. Infinite

study, Hexis, p 97.

[10] Wang,H., F. Smarandache, Y.Q. Zhang and R. Suunderraman. Single valued Neutrosophic sets, Multispace and Multistructure, 4(2010),410-413.

[11] Wang H., Smarandache F, Zhang Y, Sunderrraman R (2005) interval Neutrosophic sets and logic: theory and applications in computing: theory and applications in computing. Infinite

study, Hexis, p 97.

Cite This Article

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format_quote
Begum, S. Ghousia, Praveena, N. Jose Parvin, Rajkumar, A., Nagarajan, D., said, broumi. "Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system." International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 1, 2023, pp. 68-76. DOI: https://doi.org/10.54216/IJNS.200106
Begum, S., Praveena, N., Rajkumar, A., Nagarajan, D., said, b. (2023). Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system. International Journal of Neutrosophic Science, Volume 20(Issue 1), 68-76. DOI: https://doi.org/10.54216/IJNS.200106
Begum, S. Ghousia, Praveena, N. Jose Parvin, Rajkumar, A., Nagarajan, D., said, broumi. "Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system." International Journal of Neutrosophic Science Volume 20, no. Issue 1 (2023): 68-76. DOI: https://doi.org/10.54216/IJNS.200106
Begum, S., Praveena, N., Rajkumar, A., Nagarajan, D., said, b. (2023) 'Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system', International Journal of Neutrosophic Science, Volume 20(Issue 1), pp. 68-76. DOI: https://doi.org/10.54216/IJNS.200106
Begum S, Praveena N, Rajkumar A, Nagarajan D, said b. Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system. International Journal of Neutrosophic Science. 2023;Volume 20(Issue 1):68-76. DOI: https://doi.org/10.54216/IJNS.200106
S. Begum, N. Praveena, A. Rajkumar, D. Nagarajan, b. said, "Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system," International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 1, pp. 68-76, 2023. DOI: https://doi.org/10.54216/IJNS.200106
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