An Interval Arithmetic Approach in solving Interval-Valued Trapezoidal Neutrosophic Fuzzy Multi-Objective Multi-Item Solid Transportation Problem
Abstract
Unpredictability and uncertainty occur worldwide in various aspects of real life. We cannot predict some specific outcomes or events precisely due to multiple factors, randomness, complexity and limited information. These situations can be handled efficiently in a systematic way by using neutrosophic sets. In real-world applications, transportation is essential in all sorts of movement of goods, services and people to meet various needs and demands efficiently. This study concentrated on the multiple objectives, multiple choice transportation problem in interval-valued trapezoidal neutrosophic contexts. The conversion procedure employs a de-neutrosophication process that relies on interval numbers rather than crisp numbers. By using an interval-valued trapezoidal neutrosophic fuzzy programming method based on interval number, the identified uncertain transportation problem is then solved. Additionally, an illustrative instance is presented to showcase the successful implementation of the proposed methodology.
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S. M. Lee and L. J. Moore, “Optimizing transportation problems with multiple objectives,” AIIE transactions, vol. 5, no. 4, pp. 333–338, 1973.
L. A. Zadeh, “Fuzzy sets,” Information and Control, 1965.
F. Jim´enez and J. L. Verdegay, “Uncertain solid transportation problems,” Fuzzy sets and systems, vol. 100, no. 1-3, pp. 45–57, 1998.
S. Pramanik and T. K. Roy, “Multiobjective transportation model with fuzzy parameters: priority based fuzzy goal programming approach,” Journal of Transportation Systems Engineering and Information Technology, vol. 8, no. 3, pp. 40–48, 2008.
P. Kundu, S. Kar, and M. Maiti, “Multi-objective multi-item solid transportation problem in fuzzy environment,” Applied mathematical modelling, vol. 37, no. 4, pp. 2028–2038, 2013.
D. Chakraborty, D. K. Jana, and T. K. Roy, “Multi-objective multi-item solid transportation problem with fuzzy inequality constraints,” Journal of Inequalities and Applications, vol. 2014, pp. 1–21, 2014.
D. Rani, T. Gulati, and A. Kumar, “On fuzzy multiobjective multi-item solid transportation problem,” Journal of Optimization, vol. 2015, no. 1, p. 787050, 2015.
P. K.Giri, M. K. Maiti, and M. Maiti, “Fully fuzzy fixed charge multi-item solid transportation problem,” Applied Soft Computing, vol. 27, pp. 77–91, 2015.
M. B. Kar, P. Kundu, S. Kar, and T. Pal, “A multi-objective multi-item solid transportation problem with vehicle cost, volume and weight capacity under fuzzy environment,” Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 1991–1999, 2018.
M. Kamal, A. Alarjani, A. Haq, F. N. K. Yusufi, and I. Ali, “Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of f it,” Transport, vol. 36, no. 4, pp. 317–338, 2021.
H. Khalifa, M. Elhenawy, M. Masoud, H. Bhuiyan, and N. R. Sabar, “On multi-objective multi-item solid transportation problem in fuzzy environment,” International journal of applied and computational mathematics, vol. 7, no. 1, p. 24, 2021.
D. Mardanya and S. K. Roy, “New approach to solve fuzzy multi-objective multi-item solid transportation problem,” RAIRO-Operations Research, vol. 57, no. 1, pp. 99–120, 2023.
S. Rekabi, F. Goodarzian, H. S. Garjan, F. Zare, J. Mu˜nuzuri, and I. Ali, “A data-driven mathematical model to design a responsive-sustainable pharmaceutical supply chain network: a benders decomposition approach,” Annals of Operations Research, pp. 1–42, 2023.
K. T. Atanassov, On intuitionistic fuzzy sets theory. Springer, 2012, vol. 283.
S. Pramanik, T. K. Roy, and P. Garden, “An intuitionistic fuzzy goal programming approach to vector optimization problem,” NIFS11, vol. 5, 2005.
D. Chakraborty, D. K. Jana, and T. K. Roy, “A new approach to solve multi-objective multichoice multi-item atanassov’s intuitionistic fuzzy transportation problem using chance operator,” Journal of intelligent & fuzzy systems, vol. 28, no. 2, pp. 843–865, 2015.
S. K. Roy, A. Ebrahimnejad, J. L. Verdegay, and S. Das, “New approach for solving intuitionistic fuzzy multi-objective transportation problem,” S¯adhan¯a, vol. 43, pp. 1–12, 2018.
S. Samanta, D. K. Jana, G. Panigrahi, and M. Maiti, “Novel multi-objective, multi-item and four-dimensional transportation problem with vehicle speed in lr-type intuitionistic fuzzy environment,” Neural computing and Applications, vol. 32, pp. 11937–11955, 2020.
S. Midya, S. K. Roy, and V. F. Yu, “Intuitionistic fuzzy multi-stage multi-objective fixedcharge solid transportation problem in a green supply chain,” International Journal of Machine Learning and Cybernetics, vol. 12, pp. 699–717, 2021.
Shivani and D. Rani, “Multi-objective multi-item four dimensional green transportation problem in interval-valued intuitionistic fuzzy environment,” International Journal of System Assurance Engineering and Management, vol. 15, no. 2, pp. 727–744, 2024.
F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability. Infinite Study, 2005.
P. Biswas, S. Pramanik, and B. C. Giri, “Distance measure based madm strategy with interval trapezoidal neutrosophic numbers,” Neutrosophic Sets and Systems, vol. 19, pp. 40–46, 2018.
R. M.Rizk-Allah, A. E. Hassanien, and M. Elhoseny, “A multi-objective transportation model under neutrosophic environment,” Computers & Electrical Engineering, vol. 69, pp. 705–719, 2018.
S. K. Das and S. K. Roy, “Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment,” Computers & Industrial Engineering, vol. 132, pp. 311–324, 2019.
B. K. Giri and S. K. Roy, “Neutrosophic multi-objective green four-dimensional fixed-charge transportation problem,” International Journal of Machine Learning and Cybernetics, vol. 13, no. 10, pp. 3089–3112, 2022.
S. Khalil, S. Kousar, G. Freen, and M. Imran, “Multi-objective interval-valued neutrosophic optimization with application,” International Journal of Fuzzy Systems, pp. 1–13, 2022.
A. Revathi, S. Mohanaselvi, and B. Said, “An efficient neutrosophic technique for uncertain multi objective transportation problem,” Neutrosophic Sets and Systems, vol. 53, no. 1, p. 27, 2023.
E. Hosseinzadeh and J. Tayyebi, “A compromise solution for the neutrosophic multi-objective linear programming problem and its application in transportation problem,” Journal of applied research on industrial engineering, vol. 10, no. 1, pp. 1–10, 2023.
A. Kumar, P. Singh, and Y. Kacher, “Neutrosophic hyperbolic programming strategy for uncertain multi-objective transportation problem,” Applied Soft Computing, vol. 149, p. 110949, 2023.
G. Gupta, Shivani, and D. Rani, “Neutrosophic goal programming approach for multiobjective fixed-charge transportation problem with neutrosophic parameters,” OPSEARCH, pp. 1–27, 2024.
A. Nagarajan, K. Jeyaraman, and S. K. Prabha, “Multiobjective solid transportation problem with interval cost in source and demand parameters,” International Journal of Computer & Organization Trends, vol. 8, no. 1, pp. 33–41, 2014.
H. Dalman, N. G¨ uzel, and M. Sivri, “A fuzzy set-based approach to multi-objective multiitem solid transportation problem under uncertainty,” International Journal of Fuzzy Systems, vol. 18, pp. 716–729, 2016.
T. Sifaoui and M. A¨ ıder, “Uncertain interval programming model for multi-objective multiitem fixed charge solid transportation problem with budget constraint and safety measure,” Soft Computing, vol. 24, no. 13, pp. 10123–10147, 2020.
M. Ma, M. Friedman, and A. Kandel, “A new fuzzy arithmetic,” Fuzzy sets and systems, vol. 108, no. 1, pp. 83–90, 1999.
S. Sinika and G. Ramesh, “To enhance new interval arithmetic operations in solving linear programming problem using interval-valued trapezoidal neutrosophic numbers,” Mathematics and Statistics, vol. 11, no. 4, pp. 710–725, 2023.
Published
2025-07-23
How to Cite
SINIKA, S.; RAMESH, G..
An Interval Arithmetic Approach in solving Interval-Valued Trapezoidal Neutrosophic Fuzzy Multi-Objective Multi-Item Solid Transportation Problem.
Yugoslav Journal of Operations Research, [S.l.], july 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1354>. Date accessed: 31 aug. 2025.
doi: https://doi.org/10.2298/YJOR240818018S.
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Research Articles
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