Volume 27 , Issue 2 , PP: 275-286, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Melita Vinoliah E. 1 , Krishnaveni G. 2 , Balaganesan M. 3 , Sudha G. 4 , Chiranjibe Jana 5 * , Nikola Ivković 6
Doi: https://doi.org/10.54216/IJNS.270223
The transportation problem is a linear programming challenge focused on allocating resources efficiently across multiple locations while minimizing costs. Widely used in operations research, the transportation problem has numerous practical applications. Traditional approaches often struggle with imprecise data, which membership grades and fuzzy set theory can be used to address. Fuzzy sets concept provides a valuable framework for analysing transportation models under uncertainty. Neutrosophic sets have gained significant attention as a powerful tool for handling incomplete, ambiguous, and inconsistent data. Their ability to manage indeterminacy has made them increasingly popular in decision-making research, leading to extensive studies on their applications. This paper explores the use of imprecise parameters to improve transportation problem solution methods, emphasizing the versatility and advancements of neutrosophic sets. While various techniques exist for interpreting neutrosophic sets, certain limitations and field-specific requirements persist. In this study, trapezoidal fuzzy neutrosophic numbers make up fundamental components with respect to transportation problem. The proposed mathematical operations, algorithmic process, and framework achieve a 95% confidence level in clarifying uncertainties compared to the results with other methods. The effectiveness has been demonstrated with a numerical example for this approach, with comparisons to existing methods highlighting its advantages.
Neutrosophic Fuzzy number , Neutrosophic fuzzy transportation problem (NFTP) , Operations on NFTP , Score function
[1] K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets Syst., vol. 20, no. 1, pp. 1–6, 1986.
[2] Kaur and A. Kumar, "A new method for solving fuzzy transportation problems using ranking function," Appl. Math. Model, vol. 35, no. 2, pp. 5652–5666, 2011.
[3] Arockiasironmani and S. Santhi, "A New Technique for Solving Fuzzy Transportation Problem Using Trapezoidal Fuzzy Numbers," J. Algebraic Stat., vol. 13, pp. 2216–2222, 2022.
[4] S. Broumi et al., "A New Distance Measure for Trapezoidal Fuzzy Neutrosophic Number Based on the Centroids," Neutrosophic Sets Syst., vol. 35, no. 2, pp. 478–502, 2020.
[5] S. Chandrasekaran, G. Kokila, and J. Saju, "A New Approach to Solve Fuzzy Travelling Salesman Problems by using Ranking Functions," Int. J. Sci. Res. (IJSR), vol. 4, no. 5, pp. 2258–2260, 2015.
[6] S. K. Das, A. Goswami, and S. S. Alam, "Multiobjective transportation problem with interval cost, source and destination parameters," Eur. J. Oper. Res., vol. 117, no. 1, pp. 100–112, 1999.
[7] S. Dhouib, "Optimization of travelling salesman problem on single valued triangular neutrosophic number using dhouib-matrix-TSP1 heuristic," Int. J. Eng., vol. 34, no. 12, pp. 1–6, 2021.
[8] G. Sharma, S. H. Abbas, and V. K. Gupta, "A New Approach to Solve Fuzzy Transportation Problem for Trapezoidal Number," J. Prog. Res. Math., vol. 4, no. 3, pp. 386–392, 2015.
[9] K. B. Haley, "New methods in mathematical programming - the solid transportation problem," Oper. Res., vol. 10, no. 4, pp. 448–463, 1962.
[10] J. Ye, "Trapezoidal Neutrosophic set and its Application to Multiple Attribute Decision-Making," Neural Comput. Appl., vol. 26, no. 1, pp. 1157–1166, 2015.
[11] K. Kalaivani and P. Kaliyaperumal, "A neutrosophic approach to the transportation problem using single-valued trapezoidal neutrosophic numbers," Proyecciones J. Math., vol. 42, no. 2, pp. 533–547, 2023.
[12] M. M. Uddin et al., "Zero Next to Zero (ZnZ) Method: A New Approach for Solving Transportation Problem," J. Phys. Sci., vol. 26, pp. 13–23, 2021.
[13] S. Muruganandam and R. Srinivasan, "A New Algorithm for Solving Fuzzy Transportation Problems with Trapezoidal Fuzzy Numbers," Int. J. Recent Trends Eng. Res. (IJRTER), vol. 2, no. 3, pp. 428–437, 2016.
[14] M. K. Purushothkumar and Ananthanarayanan, "Fuzzy Transportation problem of Trapezoidal Fuzzy numbers with New Ranking Technique," IOSR J. Math. (IOSR-JM), vol. 13, no. 1, pp. 6–12, 2017.
[15] M. R. Kumar and S. Subranmanian, "Solution of Fuzzy Transportation Problems with Trapezoidal Fuzzy Numbers using Robust Ranking Methodology," Int. J. Pure Appl. Math., vol. 119, no. 16, pp. 3763–3775, 2018.
[16] R. K. Saini, A. Sangal, and M. Manisha, "Application of Single Valued Trapezoidal Neutrosophic Numbers in Transportation Problem," Neutrosophic Sets Syst., vol. 35, no. 2, pp. 563–583, 2020.
[17] R. K. Saini, A. Sangal, and A. Ahirwar, "A Novel Approach by using Interval-Valued Trapezoidal Neutrosophic Numbers in Transportation Problem," Neutrosophic Sets Syst., vol. 51, no. 1, pp. 234–253, 2022.
[18] F. Smarandache, "A concept of neutrosophic intuitionistic fuzzy set," 1995, p. 386.
[19] K. Sangeetha, T. Priyadharshini, and S. Mayuriya, "Solving Fuzzy Transportation Problem using Trapezoidal Fuzzy Numbers," Eng. Technol., vol. 4, no. 4, pp. 244–249, 2018.
[20] S. Dhouib, "Solving the Single –Valued Trapezoidal Neutrosophic Transportation Problem Through the Novel Dhouib-Matrix-TP1 Heuristic," Math. Problems Eng., vol. 2021, p. 11, 2021.
[21] E. Shell, "Distribution of a product by several properties, directorate of management analysis," in Proc. Second Symp. Linear Program, vol. 2, 1955, pp. 615–642.
[22] Thamaraiselvi and R. Santhi, "A New Approach for Optimization of Real Life Transportation Problems in Neutrosophic Environment," Math. Problems Eng., vol. 2016, p. 9, 2016.
[23] R. M. Umanmageswari and G. Uthra, "Generalized Single Valued Neutrosophic Trapezoidal Numbers and their Application to Solve Transportation Problem," J. Study Res., vol. 12, no. 1, pp. 164–170, 2020.
[24] L. A. Zadeh, "Fuzzy sets," Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
