The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fully fuzzy transportation problem with minimum uncertainty. In this paper, the fully fuzzy transportation problem is transformed into equivalent transportation problem involving interval numbers. The solutions to these transportation problems involving interval numbers are then obtained with the help of transportation problem technique. A set of five random numerical examples has been solved using the proposed approach.

interval numbers, fuzzy numbers, interval transportation problem, fully fuzzy transportation problems.

Received: November 10, 2021; Accepted: December 20, 2021; Published: January 14, 2022

How to cite this article: Ladji Kané, Moctar Diakité, Hawa Bado and Moussa Konaté, Solving fully fuzzy transportation problems, Universal Journal of Mathematics and Mathematical Sciences 15 (2022), 63-96. DOI: 10.17654/2277141722005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] Jagdeep Kaur and Amit Kumar, An introduction to fuzzy linear programming problems: theory, methods and applications, Studies in Fuzziness and Soft Computing, Springer International Publishing, Switzerland, Vol. 340, 2016.
[2] Seyed Hadi Nasseri, Ali Ebrahimnejad and Bing-Yuan Cao, Fuzzy linear programming: solution techniques and applications, Studies in Fuzziness and Soft Computing, Springer International Publishing Switzerland AG, Vol. 379, 2019.
[3] Amarpreet Kaur, Janusz Kacprzyk and Amit Kumar, Fuzzy transportation and transshipment problems, Studies in Fuzziness and Soft Computing 379, Springer Nature Switzerland AG, 2020.
[4] M. Ahlatcioglu, M. Sivri and N. Güzel, Transportation of the fuzzy amounts using the fuzzy cost, Journal of Marmara for Pure and Applied Sciences 8 (2004), 139 155.
[5] S. D. Chanas and D. Kuchta, A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems 82 (1996), 299-305.
[6] S. Chanas, W. Kolodziejckzy and A. A. Machaj, A fuzzy approach to the transportation problem, Fuzzy Sets and Systems 13 (1984), 211-221.
[7] D. S. Dinagar and K. Palanivel, The transportation problem in fuzzy environment, International Journal of Algorithms, Computing and Mathematics 2 (2009), 65 71.
[8] A. Edward Samuel and P. Raja, Algorithmic approach to unbalanced fuzzy transportation problem, International Journal of Pure and Applied Mathematics (IJPAM) 5 (2017), 553-561.
[9] M. Gen, K. Ida and Y. Li, Solving bicriteria solid transportation problem, humans information and technology, IEEE International Conference 2 (1994), 1200-1207.
[10] A. Nagoor Gani and K. A. Razak, Two stage fuzzy transportation problem, Journal of Physical Sciences 10 (2006), 63-69.
[11] Y. J. Lai and C. L. Hwang, Fuzzy Mathematical Programming Methods and Application, Springer, Berlin, 1992.
[12] F. T. Lin, Solving the transportation problem with fuzzy coefficients using genetic algorithms, Proceedings IEEE International Conference on Fuzzy Systems, 2009, pp. 20-24.
[13] T. S. Liou and M. J. Wang, Ranking fuzzy number with integral values, Fuzzy Sets and Systems 50(3) (1992), 247-255.
[14] S. T. Liu and C. Kao, Solving fuzzy transportation problems based on extension principle, European J. Oper. Res. 153 (2004), 661-674.
[15] M. A. Parra, A. B. Terol and M. V. R. Uria, Solving the multi-objective possibilistic linear programming problem, European J. Oper. Res. 117 (1999), 175-182.
[16] P. Pandian and G. Natarajan, A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Appl. Math. Sci. 4 (2010), 79 90.
[17] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
[18] Ladji Kané, Hamala Sidibé, Souleymane Kané, Hawa Bado, Moussa Konaté, Daouda Diawara and Lassina Diabaté, A simplified new approach for solving fully fuzzy transportation problems with involving triangular fuzzy numbers, Journal of Fuzzy Extension and Applications (JFEA) 2(1) (2021), 89-105.
[19] F. L. Hitchcock, The distribution of a product from several sources to numerous localities, J. Math. Phys. 20 (1941), 224-330.
[20] R. Jain, Decision-making in the presence of fuzzy variables, IEEE Transactions on Systems, Man and Cybernetics 6 (1976), 698-703.
[21] Neetu M. Sharma and Ashok P. Bhadane, An alternative method to northwest corner method for solving transportation problem, International Journal of Research in Engineering Application and Management 1(12) (2016), 1-3.
[22] P. T. B. Ngastiti, B. Surarso and Sutimin, Zero point and zero suffix methods with robust ranking for solving fully fuzzy transportation problems, J. Phys.: Conf. Ser. 1022 (2018), 1-9.
[23] Omar M. Saad and Samir A. Abbas, A parametric study on transportation problems under fuzzy environment, J. Fuzzy Math. 11(1) (2003), 115 124.
[24] Y. J. Wang and H. S. Lee, The revised method of ranking fuzzy numbers with an area between the centroid and original points, Comput. Math. Appl. 55 (2008), 2033-2042.
[25] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1 (1978), 45-55.
[26] L. A. Zadeh, Fuzzy set as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978), 3-28.
[27] G. Ramesh and K. Ganesan, Duality theory for interval linear programming problems, IOSR Journal of Mathematics 4(4) (2012), 39-47.
[28] G. Sudha and K. Ganesan, A new algorithm for fully interval integer transportation problem, 1st International Conference on Mathematical Techniques and Applications AIP Conf. Proc. 2277, 2020, pp. 200010-1-200010-12.
https://doi.org/10.1063/5.0025569.
[29] G. Charles Rabinson and R. Chandrasekaran, A method for solving a pentagonal fuzzy transportation problem via ranking technique and ATM, International Journal of Research in Engineering, IT and Social Sciences 9(4) (2019), 71-75.
[30] S. Kalyani and S. Nagarani, A fully fuzzy transportation problem with hexagonal fuzzy number, Advances in Applicable Mathematics - ICAAM2020 AIP Conf. Proc. 2261, 2020, pp. 030078-1-030078-8. https://doi.org/10.1063/5.0016903.
[31] Avinash J. Kamble, Some notes on pentagonal fuzzy numbers, Int. J. Fuzzy Mathematical Archive 13(2) (2017), 113-121.
[32] Hamiden Abd El-Wahed Khalifa, Goal programming approach for solving heptagonal fuzzy transportation problem under budgetary constraint, operations research and decisions, Operations Research and Decisions 30(1) (2020), 85-96.
[33] A. Sahaya Sudha and S. Karunambigai, Solving a transportation problem using a heptagonal fuzzy number, International Journal of Advanced Research in Science, Engineering and Technology 4(1) (2017), 3118-3125.
[34] P. Rajarajeswari and G. Menaka, Octagonal fuzzy transportation problem using best candidates method, High Technology Letters 26(6) (2020), 856-864.
[35] P. Rajarajeswari and G. Menaka, New alpha cut arithmetic operations using octagonal fuzzy numbers, International Journal of Research and Analytical Reviews (IJRAR) 6(2) (2019), 336-349.
[36] A. Felix, S. Christopher and A. Victor Devadoss, A nonagonal fuzzy number and its arithmetic operation, International Journal of Mathematics and its Applications 3(2) (2015), 185-195.
[37] K. Deepika and S. Rekha, A new ranking function of nonagonal fuzzy numbers, International Journal for Modern Trends in Science and Technology 3(9) (2017), 149-151.
[38] Fahrudin Muhtarulloh and Atia Nuraini, Performance evaluation of new ranking function methods with current ranking functions using VAM and MM-VAM, advances in social science, education and humanities research, Proceedings of the 1st International Conference on Mathematics and Mathematics Education ICMMED 550, 2020, pp. 418-424.
[39] Kirtiwant P. Ghadle and Priyanka A. Pathade, Solving transportation problem with generalized hexagonal and generalized octagonal fuzzy numbers by ranking method, Glob. J. Pure Appl. Math. 13(9) (2017), 6367 6376.
[40] Dinesh C. S. Bisht and Pankaj Kumar Srivastava, One point conventional model to optimize trapezoidal fuzzy transportation problem, International Journal of Mathematical, Engineering and Management Sciences 4(5) (2019), 1251-1263.
[41] S. Nagadevi and G. M. Rosario, A study on fuzzy transportation problem using decagonal fuzzy number, Advances and Applications in Mathematical Sciences 18(10) (2019), 1209-1225.
[42] Ladji Kané, Moctar Diakité, Hawa Bado, Souleymane Kané, Moussa Konaté and Koura Traoré, The new algorithm for fully fuzzy transportation problem by trapezoidal fuzzy number (a generalization of triangular fuzzy number), Journal of Fuzzy Extension and Applications (JFEA) 2(3) (2021), 204-225.
[43] Ladji Kané, Moctar Diakité, Souleymane Kané, Hawa Bado and Daouda Diawara, Fully fuzzy transportation problems with pentagonal and hexagonal fuzzy numbers, Journal of Applied Research on Industrial Engineering 8(3) (2021), 251 269.
[44] Ladji Kané, Daouda Diawara, Lassina Diabaté, Moussa Konaté, Souleymane Kané and Hawa Bado, A mathematical model for solving the linear programming problems involving trapezoidal fuzzy numbers via interval linear programming problems, Journal of Mathematics Volume 2021, Article ID 5564598, 17 pages.