# Three stages algorithm for finding optimal solution of balanced triangular fuzzy transportation problems

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## Abstract

In the literature, the fuzzy optimal solution of balanced triangular fuzzy transportation problem is negative fuzzy number. This is contrary to the constraints that must be non-negative. Therefore, the three stages algorithm is proposed to overcome this problem. The proposed algorithm consist of segregated method with segregating triangular fuzzy parameters into three crisp parameters. This method avoids the ranking technique. Next, total difference method is used to get initial basic feasible solution (IBFS) value based on segregating triangular fuzzy parameters. While, modified distribution algorithm is used to determine optimal solution based on IBFS velue. In order to illustrate the proposed algorithm is given the numerical example and based on the result comparison, the proposed algorithm equality to the two existing algorithms and better then the one existing algorithm. The proposed algorithm can solve in the fuzzy decision-making problems and can also be extended to an unbalanced fuzzy transportation problem.

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*JOSCEX*, vol. 2, no. 1, pp. 25-32, Mar. 2021.

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## References

L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, no. 3, pp. 338–353, 1965, doi: 10.1016/S0019-9958(65)90241-X.

A. Kumar, J. Kaur, and P. Singh, “A new method for solving fully fuzzy linear programming problems,” Appl. Math. Model., vol. 35, no. 2, pp. 817–823, 2011, doi: 10.1016/j.apm.2010.07.037.

S. Chandran and G. Kandaswamy, “A fuzzy approach to transport optimization problem,” Optim. Eng., vol. 17, no. 4, pp. 965–980, 2016, doi: 10.1007/s11081-012-9202-6.

G. De França Aguiar, B. De Cássia Xavier Cassins Aguiar, and V. E. Wilhelm, “New methodology to find initial solution for transportation problems: A case study with fuzzy parameters,” Appl. Math. Sci., vol. 9, no. 17–20, pp. 915–927, 2015, doi: 10.12988/ams.2015.4121018.

A. Kumar and P. Singh, “A new method for solving fully fuzzy linear programming problems,” Ann. Fuzzy Math. Inf., vol. 3, pp. 103–118, 2012.

A. Ebrahimnejad, “A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers,” Appl. Soft Comput. J., vol. 19, pp. 171–176, 2014, doi: 10.1016/j.asoc.2014.01.041.

N. Mathur, P. K. Srivastava, and A. Paul, “Trapezoidal fuzzy model to optimize transportation problem,” Int. J. Model. Simulation, Sci. Comput., vol. 7, no. 3, 2016, doi: 10.1142/S1793962316500288.

D. Hunwisai and P. Kumam, “A method for solving a fuzzy transportation problem via Robust ranking technique and ATM,” Cogent Math., vol. 4, no. 1, 2017, doi: 10.1080/23311835.2017.1283730.

K. Balasubramanian and S. Subramanian, “Optimal solution of fuzzy transportation problems using ranking function,” Int. J. Mech. Prod. Eng. Res. Dev., vol. 8, no. 4, pp. 551–558, 2018, doi: 10.24247/ijmperdaug201856.

D. Chakraborty, D. K. Jana, and T. K. Roy, “A new approach to solve fully fuzzy transportation problem using triangular fuzzy number,” Int. J. Oper. Res., vol. 26, no. 2, pp. 153–179, 2016, doi: 10.1504/IJOR.2016.076299.

R. K. Saini, A. Sangal, and O. Prakash, “Fuzzy transportation problem with generalized triangular-trapezoidal fuzzy number,” in Advances in Intelligent Systems and Computing, 2018, vol. 583, pp. 723–734, doi: 10.1007/978-981-10-5687-1_64.

D. Rani and T. R. Gulati, “A new approach to solve unbalanced transportation problems in imprecise environment,” J. Transp. Secur., vol. 7, no. 3, pp. 277–287, 2014, doi: 10.1007/s12198-014-0143-5.

A. Kumar and A. Kaur, “Application of Classical Transportation Methods to Find the Fuzzy Optimal Solution of Fuzzy Transportation Problems,” Fuzzy Inf. Eng., vol. 3, no. 1, pp. 81–99, 2011, doi: 10.1007/s12543-011-0068-7.

A. Kaur and A. Kumar, “A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers,” Appl. Soft Comput. J., vol. 12, no. 3, pp. 1201–1213, 2012, doi: 10.1016/j.asoc.2011.10.014.

R. Kumar, S. A. Edalatpanah, S. Jha, and R. Singh, “A Pythagorean fuzzy approach to the transportation problem,” Complex Intell. Syst., vol. 5, no. 2, pp. 255–263, 2019, doi: 10.1007/s40747-019-0108-1.

P. K. Srivastava and D. C. S. Bisht, “A Segregated Advancement in the Solution of Triangular Fuzzy Transportation Problems,” Am. J. Math. Manag. Sci., pp. 1–11, 2020, doi: 10.1080/01966324.2020.1854137.

P. Pandian and G. Natarajan, “A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems,” Appl. Math. Sci., vol. 4, no. 1–4, pp. 79–90, 2010, doi: 10.1504/IJMMNO.2021.111715.

A. Edward Samuel and M. Venkatachalapathy, “IZPM for unbalanced fuzzy transportation problems,” Int. J. Pure Appl. Math., 2013, doi: 10.12732/ijpam.v86i4.8.

K. Selvakumari and S. Sathya Geetha, “A new approach for solving intuitionistic fuzzy transportation problem,” J. Adv. Res. Dyn. Control Syst., vol. 12, no. 5 Special Issue, pp. 956–963, 2020, doi: 10.5373/JARDCS/V12SP5/20201841.

A. Edward Samuel and M. Venkatachalapathy, “Improved zero point method for solving fuzzy transportation problems using ranking function,” Far East J. Math. Sci., vol. 75, no. 1, pp. 85–100, 2013.

A. Edward Samuel, “Improved zero point method (IZPM) for the transportation problems,” Appl. Math. Sci., vol. 6, no. 109–112, pp. 5421–5426, 2012.

T. Karthy and K. Ganesan, “Improved zero point method for the fuzzy optimal solution to fuzzy transportation problems,” Glob. J. Pure Appl. Math., vol. 12, no. 1, pp. 255–260, 2016.

A. Akilbasha, G. Natarajan, and P. Pandian, “A new approach for solving transportation problems in fuzzy nature,” Int. J. Appl. Eng. Res., vol. 11, no. 1, pp. 498–502, 2016.

A. Baykasoğlu and K. Subulan, “A direct solution approach based on constrained fuzzy arithmetic and metaheuristic for fuzzy transportation problems,” Soft Comput., vol. 23, no. 5, pp. 1667–1698, 2019, doi: 10.1007/s00500-017-2890-2.

M. A. Imron and B. Prasetyo, “Improving algorithm accuracy K-Nearest Neighbor using Z-Score Normalization and Particle Swarm Optimization to predict customer churn,” J. Soft Comput. Explor., vol. 1, no.1, pp. 56–62, 2020.

R. H. Saputra and B. Prasetyo, “Improve the accuracy of c4.5 algorithm using particle swarm optimization (pso) feature selection and bagging technique in breast cancer diagnosis,” J. Soft Comput. Explor., vol. 1, no.1, pp. 47–55, 2020.

D. Aprilianto, “SVM optimization with correlation feature selection based binary particle swarm

optimization for diagnosis of chronic kidney disease,” J. Soft Comput. Explor., vol. 1, no.1, pp. 24–31, 2020.

A. Ebrahimnejad, “An improved approach for solving fuzzy transportation problem with triangular fuzzy numbers,” J. Intell. Fuzzy Syst., vol. 29, no. 2, pp. 963–974, 2015, doi: 10.3233/IFS-151625.