A neutrosophic approach to the transportation problem using single-valued trapezoidal neutrosophic numbers


  • Palanivel Kaliyaperumal Vellore Institute of Technology.
  • Kalaivani K. Vellore Institute of Technology.




fuzzy set, single-valued neutrosophic set, ranking function, neutrosophic transportation problem


In general, a fuzzy set can’t handle situations of inconsistencies and inexact data, however, the Neutrosophic Set (NS) has been used to address such types of issues in all real world problems. The neutrosophic set is an extension of the fuzzy set and the intuitionistic fuzzy set, that can deal with imperfect, inconsistent, and indeterminate data in all the related problems. This article proposed a conventional neutrosophic approach using a ranking function for the transportation problem. This approach has considered a single-valued neutrosophic set for the entire transportation problem with the numerical illustration.

Single valued trapezoidal neutrosophic numbers are well-known and used in solving the transportation problem and its extension. Besides, a novel ranking function is proposed with the help of membership functions, which gives the best optimal solution. Moreover, the obtained optimal solution has been compared with recent new approaches. This research will help to get the best optimal solution for the transportation problem under uncertainty.

Author Biographies

Palanivel Kaliyaperumal, Vellore Institute of Technology.

Department of Mathematics, School of Advanced Sciences.

Kalaivani K., Vellore Institute of Technology.

Department of Mathematics, School of Advanced Sciences.


M. Abdel-Basset, M. Mohamed and A. K. Sangaiah, “Neutrosophic ahp-delphi group decision making model based on trapezoidal neutrosophic numbers”, Journal of Ambient Intelligence and Humanized Computing, vol. 9, no. 5, pp. 1427-1443, 2018. [On line]. Available: https://bit.ly/3FK2SM7

K. T. Atanassov, Intuitionistic fuzzy sets. Springer, 1999.

P. Biswas, S. Pramanik and C. Giri Binod, “Topsis method for multi-attribute group decision-making under single-valued neutrosophic environment”. Neural computing and Applications, vol. 27, 3, pp. 727-737, 2016. [On line]. Available: https://bit.ly/400LtXE

S. Broumi, A. Bakali, M. Talea, F. Smarandache and L. Vladareanu, “Computation of shortest path problem in a network with svtrapezoidal neutrosophic numbers”, In International Conference on Advanced Mechatronic Systems (ICAMechS), pp. 417-422, 2016. [On line]. Available: https://bit.ly/406hb5N

S. Das, R. Das and S. Pramanik, “Single valued bipolar penta partitioned neutrosophic set and its application in MADM strategy”, Neutrosophic Sets and Systems, vol. 49, pp. 9, 2022. [On line]. Available: https://bit.ly/3lt8CmF

S. Das, B. Shil and B.C. Tripathy, “Tangent similarity measure based madm-strategy under svpns-environment”, Neutrosophic Sets and Systems, vol. 43, pp. 93-104, 2021. [On line]. Available: https://bit.ly/3LFZohn

I. Deli and Y. Subas, “Single valued neutrosophic numbers and their applications to multicriteria decision making problem”, Neutrosophic Sets and Systems, vol. 2, 1, pp. 1-13, 2014. [On line]. Available: https://bit.ly/3yYHtet

I. Deli and Y. Subas, “A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems”, International Journal of Machine Learning and Cybernetics, vol. 8, pp. 1309-1322, 2017. https://doi.org/10.1007/s13042-016-0505-3

S. Dhouib, “Solving the single-valued trapezoidal neutrosophic transportation problems through the novel dhouib-matrix-tp1 heuristic”, Mathematical Problems in Engineering, vol. 2021, pp. 1-11, 2021. https://doi.org/10.1155/2021/3945808

D. S. Dinagar and K. Palanivel, “The transportation problem in fuzzy environment”, International journal of algorithms, computing and mathematics, vol. 2, no. 3, pp. 65-71, 2009.

A. N. Hussian, M. Mohamed, M. Abdel-Baset and F. Smarandache, “Neutrosophic linear programming problems”, Neutrosophic Linear Programming, pp. 15-27. [On line]. Available: https://bit.ly/3lu16Yz

P. Kaliyaperumal and A. Das, “A mathematical model for nonlinear optimization which attempts membership functions to address the uncertainties”, Mathematics, vol. 10, no. 10, pp. 1743, 2022. https://doi.org/10.3390/math10101743

K. Karagul and Y. Sahin, “A novel approximation method to obtain initial basic feasible solution of transportation problema”, Journal of King Saud University- Engineering Sciences, vol. 32, 3, pp. 211-218, 2020. https://doi.org/10.1016/j.jksues.2019.03.003

A. Kumar, P. Singh, P. Kaur and A. Kaur, “A new approach for ranking generalized trapezoidal fuzzy numbers”, World Academy of Science, Engineering and Technology, vol. 68, pp. 229-302, 2010. https://doi.org/10.5281/zenodo.1082927

X. Li and X. Zhang, “Single-valued neutrosophic hesitant fuzzy choquet aggregation operators for multi-attribute decision making”, Symmetry, vol. 10, no. 2, pp. 50, 2018. https://doi.org/10.3390/sym10020050

L. Lu and X. Luo, “Emergency transportation problem based on single-valued neutrosophic set”, Discrete Dynamics in Nature and Society, vol. 2020, no. 2, pp. 1-8, 2020. https://doi.org/10.1155/2020/4813497

I. Maiti,, Mandalt. and S. Pramanik, “Neutrosophic goal programming strategy for multi-level multi-objective linear programming problema”, Journal of ambient intelligence and humanized computing, vol 11, pp. 3175-3186, 2020. https://doi.org/10.1007/s12652-019-01482-0

K. Palanivel, “Fuzzy commercial traveler problem of trapezoidal membership functions within the sort of α optimum solution using ranking technique”, Afrika Matematika, vol. 27, no. 1, pp. 263-277, 2016. https://doi.org/10.1007/s13370-015-0331-x

S. Pramanik and D. Banerjee, “Neutrosophic number goal programming for multi-objective linear programming problem in neutrosophic number environment”, MOJ Current Research & Review, vol 1, no. 3, 2018. https://doi.org/10.15406/mojcrr.2018.01.00021

F. Smarandache, “Neutrosophic set-a generalization of the intuitionistic fuzzy set”, Infinite Study, 2010.

A. Thamaraiselvi and R. Santhi, “A new approach for optimization of real life transportation problem in neutrosophic environment”, Mathematical Problems in Engineering, vol. 2016, no. 2, pp. 1-13, 2016. https://doi.org/10.1155/2016/5950747

R. Umamageswari and G. Uthra, “Generalized single valued neutrosophic trapezoidal numbers and their application to solve transportation problema”, Studia Rosenthaliana, vol. 11, no. 1, pp. 164-170, 2020. [On line]. Available: https://bit.ly/3TxVeKq

H. Wang, F. Smarandache, Y. Zhang and R. Sunderraman, Single valued neutrosophic sets, infinite study. [On line]. Available: https://bit.ly/42HOZbf

J. Ye, “Trapezoidal neutrosophic set and its application to multiple attribute decision-making”, Neural Computing and Applications, vol. 26, no. 5, pp. 1157-1166, 2015.https://doi.org/10.1007/s00521-014-1787-6

L.A. Zadeh, Fuzzy set information and control, vol. 8, pp. 338-353, 1965.



How to Cite

P. Kaliyaperumal and K. K., “A neutrosophic approach to the transportation problem using single-valued trapezoidal neutrosophic numbers”, Proyecciones (Antofagasta, On line), vol. 42, no. 2, pp. 533-547, Mar. 2023.