A novel approach that uses ranking functions to solve fuzzy transportation problems
DOI:
https://doi.org/10.31272/jae.i152.1564Keywords:
fuzzy number, fuzzy set, magnitude ranking function, trapezoidal fuzzy numberAbstract
Transportation costs are defined as trapezoidal fuzzy values, and we provide a novel way to deal with this issue in an uncertain setting. Supply, demand, and transportation unit costs could all start to seem odd for various real-world reasons. We can display these erroneous values as fuzzy numbers. Fuzzy numbers and values have found widespread application in many domains, including AI and experimental sciences. We used the magnitude ranking function to convert trapezoidal fuzzy numbers into crisp values, and then we developed the first fundamental solution to the fuzzy transportation problem. Next, the max-min method was implemented. In this numerical example, we show how fuzzy algorithms can be used in a new way to solve transportation problems.
Downloads
References
[1] R. E. Bellman and L. A. Zadeh,( 1970), “Decision-making in a fuzzy environment,” Manage. Sci., vol. 17, no. 4, p. B-141, doi: https://doi.org/10.1287/mnsc.17.4.B141. DOI: https://doi.org/10.1287/mnsc.17.4.B141
[2] S. Chanas, W. Kołodziejczyk, and A. Machaj,( 1984), “A fuzzy approach to the transportation problem,” Fuzzy sets Syst., vol. 13, no. 3, pp. 211–221, doi: https://10.1016/0165-0114(84)90057-5 . DOI: https://doi.org/10.1016/0165-0114(84)90057-5
[3] G. B. Dantzig,( 1951), “Application of the Simplex Method to a Transportation Problem - Ch XXIII,” Act. Anal. Prod. Alloc., pp. 359–373, doi: https://10.12691/ajams-5-2-3.
[4] S.-T. Liu and C. Kao,( 2004), “Solving fuzzy transportation problems based on extension principle,” Eur. J. Oper. Res., vol. 153, no. 3, pp. 661–674, https://doi.org/10.17654/2277141722005. DOI: https://doi.org/10.1016/S0377-2217(02)00731-2
[5] A. Arockiasironmani and S. Santhi,( 2022), “A New Technique for Solving Fuzzy Transportation Problem Using Trapezoidal Fuzzy Numbers,” J. Algebr. Stat., vol. 13, no. 2, pp. 2216–2222, doi: https://publishoa.com/.
[6] A. N. Gani and K. A. Razak, (2006), “Two stage fuzzy transportation problem,” KHAZAYIN Econ. Adm. SCIEN, vol. 35, no. 12, p. Pages 5652-5661, doi: https://doi.org/10.1016/j.apm.2011.05.012.
[7] A. Kumar, A. Bansal, and N. Neetu,( 2011), “A method for solving fully fuzzy linear system with trapezoidal fuzzy numbers,” IJO, vol. 2, no. 2, doi: http://doi:10.5899/2011/jfsva-00102. DOI: https://doi.org/10.1155/2011/943161
[8] A. Kaur and A. Kumar,( 2011), “A new method for solving fuzzy transportation problems using ranking function,” Appl. Math. Model., vol. 35, no. 12, pp. 5652–5661, http:/10.1016/j.apm.2011.05.012. DOI: https://doi.org/10.1016/j.apm.2011.05.012
[9] N. M. Sharma and A. P. Bhadane,( 2016), “An alternative method to north-west corner method for solving transportation problem,” Int. J. Res. Eng. Appl. Manag., vol. 1, no. 12, pp. 1–3, [Online]. Available: http://www.ijream.org/
[10] S. Poonam, S. H. Abbas, and V. K. Gupta,( 2012), “Fuzzy transportation problem of trapezoidal numbers with α-cut and ranking technique,” Int. J. Fuzzy Math. Syst., vol. 2, no. 3, pp. 263–267, doi: http://www.ripublication.com
[11] M. G. Voskoglou,( 2024), “Parametric decision-making in a fuzzy environment,” Data-Driven Model. with Fuzzy Sets Embrac. Uncertain., no. May, pp. 30–45, http:/10.1016/j.apm.2011.05.012. DOI: https://doi.org/10.1201/9781003487029-3
[12] R. Sharma and S. L. Tyagi,( 2025), “A New Efficient Method to Solve Bi-Objective Transportation Problems Under Fuzzy Parameters A New Efficient Method to Solve Bi-Objective Transportation Problems Under Fuzzy Parameters,” BAGHDAD Sci. J., vol. 22, no. 8, doi: https://doi.org/10.21123/2411-7986.5036 . DOI: https://doi.org/10.21123/2411-7986.5036
[13] S. S. H. 1 Arian Latif Jasim Muhammad1,( 2025), “A New Method For Finding Optimal Solution For Fully Fuzzy Transportation Problems,” Univ. Kirkuk J. Adm. Econ. Sci., vol. 15, no. 1, p. 215, https://doi.org/10.32894/1913-015-001-016. DOI: https://doi.org/10.32894/1913-015-001-016
[14] A. Kaur and A. Kumar, (2012 ),“A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers,” Appl. Soft Comput., vol. 12, no. 3, pp. 1201–1213, Mar. 2012, doi: 10.1016/J.ASOC.2011.10.014. DOI: https://doi.org/10.1016/j.asoc.2011.10.014
[15] K Nathiya, KR Balasubramanian,(2024), “Solution of fuzzy transportation problems with trapezoidal fuzzy numbers” AIP Conference Proceedings, Volume 3193, Issue 1, no.1-20, 11 November 2024, https://doi.org/10.1063/5.0232728. DOI: https://doi.org/10.1063/5.0232728
[16] Laxminarayan Sahoo,(2023), “transportation problem in fermatean fuzzy environmen” RAIRO-Oper. Res. 57 ,145–156, https://doi.org/10.1051/ro/2022210. DOI: https://doi.org/10.1051/ro/2022210
[17] Ali, W., Javaid, S. (2025), “A solution of mathematical multi-objective transportation problems using the fermatean fuzzy programming approach”. Int J Syst Assur Eng Manag. https://doi.org/10.1007/s13198-025-02716-5. DOI: https://doi.org/10.1007/s13198-025-02716-5
[18] Veena Yadahalli , M. Saradha(2024), “A Robust Ranking Technique to Solve Fuzzy Transportation Problem of Triangular Fuzzy Number” , Journal of Informatics and Mathematical Sciences, Vol. 16, No. 1, pp. 77–84, http://doi.org/10.26713/jims.v16i1.2746. DOI: https://doi.org/10.26713/jims.v16i1.2746
[19] V. Vidhya,K. Ganesan.(2022), “A New Ranking Approach for Solving Fuzzy Transportation Problem with Pentagonal Fuzzy Number” Mathematics and Statistics Vol. 10(4), pp. 816 – 824.
https://doi.org/10.13189/ms.2022.100412. DOI: https://doi.org/10.13189/ms.2022.100412
[20] J.Ch.Yadav,M.Rizwanullah.(2026), “Optimisation of fuzzy transportation problem using new ranking approach with fuzzy numbers”. International Journal of Mathematics in Operational ResearchVol. 32, No.4. https://doi.org/10.1504/IJMOR.2025.150942. DOI: https://doi.org/10.1504/IJMOR.2025.10074631
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Alaa Shnaishel Cheetar, Fathala Ali Chachan
This work is licensed under a Creative Commons Attribution 4.0 International License.
The journal of Administration & Economics is an open- access journal that all contents are free of charge. Articles of this journal are licensed under the terms of the Creative Commons Attribution International Public License CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/legalcode) that licensees are unrestrictly allowedto search, download, share, distribute, print, or link to the full text of the articles, crawl them for indexing and reproduce any medium of the articles provided that they give the author(s) proper credits (citation). The journal allows the author(s) to retain the copyright of their published article.
Creative Commons-Attribution (BY) 
