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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 20 , Issue 1 , PP: 68-76, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

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

S. Ghousia Begum 1 * , N. Jose Parvin Praveena 2 , A. Rajkumar 3 , D. Nagarajan 4 , Broumi Said 5

  • 1 Research Scholar, Department of Mathematics, Hindustan Institute of Technology and science, Padur, Chennai, India - (ghousiabs@hindustanuniv.ac.in)
  • 2 Department of Mathematics, St.Joseph’s College of Engineering, Chennai, India - ( jose30102003@gmail.com)
  • 3 Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India - (arajkumar@hindustanuniv.ac.in)
  • 4 Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India - (dnrmsu2002@yahoo.com)
  • 5 Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco - ( broumisaid78@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.200106

    Received: August 16, 2022 Accepted: December 15, 2022
    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 As :
    Ghousia, S.. , Jose, N.. , Rajkumar, A.. , Nagarajan, D.. , Said, Broumi. Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system. International Journal of Neutrosophic Science, vol. , no. , 2023, pp. 68-76. DOI: https://doi.org/10.54216/IJNS.200106
    Ghousia, S. Jose, 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, (), 68-76. DOI: https://doi.org/10.54216/IJNS.200106
    Ghousia, S.. Jose, N.. Rajkumar, A.. Nagarajan, D.. Said, Broumi. Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system. International Journal of Neutrosophic Science , no. (2023): 68-76. DOI: https://doi.org/10.54216/IJNS.200106
    Ghousia, S. , Jose, 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 , () , 68-76 . DOI: https://doi.org/10.54216/IJNS.200106
    Ghousia S. , Jose 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. (): 68-76. DOI: https://doi.org/10.54216/IJNS.200106
    Ghousia, S. Jose, N. Rajkumar, A. Nagarajan, D. Said, B. "Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system," International Journal of Neutrosophic Science, vol. , no. , pp. 68-76, 2023. DOI: https://doi.org/10.54216/IJNS.200106

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