A novel solution approach for solving intuitionistic fuzzy transportation problem of type-2

Document Type: Original Article

Author

Department of Mathematics, Kashan Branch, Islamic Azad University, Kashan, Iran

10.22121/aotp.2019.198947.1022

Abstract

In the cases that decision maker faces with uncertainty and hesitation together for determining a parameter of an optimization problem, considering intuitionistic fuzzy parameters is useful. A transportation problem with triangular intuitionistic fuzzy unit transportation costs is focused in this study. The fuzzy costs are crisped using the accuracy function of the literature. Then the algorithms e.g. the north west corner method, the least cost method, and the Vogel’s approximation method are applied to obtain an initial basic feasible solution for the crisp version of the problem. After that the modified distribution method is used to obtain the optimal solution of the problem. The performed computational experiments show the superiority of the proposed approach over those of the literature from the results’ quality and the computational difficulty point of views.

Keywords


Antony, R. J. P., Savarimuthu, S. J., Pathinathan, T. (2014). Method for solving the transportation problem using triangular intuitionistic fuzzy number. International Journal of Computing Algorithm, 03, 590–605.
Asunción, M. D. L., Castillo, L., Olivares, J. F., Pérez, O. G., González, A., Palao, F. (2007). Handling fuzzy temporal constraints in a planning environment. Annals of Operations Research, 155, 391–415.
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
Basirzadeh, H. (2011). An approach for solving fuzzy transportation problem. Applied Mathematical Science, 5(32), 1549–1566.
Bellman, R., Zadeh, L. A. (1970). Decision making in fuzzy environment. Management Science, 17(B), 141–164.
Cascetta, E., Gallo, M., Montella, B. (2006). Models and algorithms for the optimization of signal settings on urban networks with stochastic assignment models. Annals of Operations Research, 144, 301–328.
De, S. K., Sana, S. S. (2013). Backlogging EOQ model for promotional effort and selling price sensitive demand-an intuitionistic fuzzy approach. Annals of Operations Research, doi:10.1007/s10479-013-1476-3.
Dempe, S., Starostina, T. (2006). Optimal toll charges in a fuzzy flow problem. In: Proceedings of the international conference 9th fuzzy days in Dortmund, Germany, Sept 18–20.
Dinager, D. S., Palanivel, K. (2009). The transportation problem in fuzzy environment. International Journal of Algorithm, Computing and Mathematics, 12(3), 93–106.
Ganesan, K., Veeramani, P. (2006). Fuzzy linear programs with trapezoidal fuzzy numbers. Annals of Operations Research, 143, 305–315.
Kaur, A., Kumar, A. (2012). A new approach for solving fuzzy transportation problem using generalized trapezoidal fuzzy number. Applied Soft Computing, 12, 1201–1213.
Mahmoodirad, A., Hassasi, H., Tohidi, G., Sanei, M. (2014). On approximation of the fully fuzzy fixed charge transportation problem. International Journal of Industrial Mathematics, 6(4), 307–314.
Mahmoodirad, A., Allahviranloo, T., Niroomand, S. (2019). A new effective solution method for fully intuitionistic fuzzy transportation problem. Soft Computing, 23 (12), 4521-4530.
Mahmoodi-Rad, A., Molla-Alizadeh-Zavardehi, S., Dehghan, R., Sanei, M., Niroomand, S. (2014). Genetic and differential evolution algorithms for the allocation of customers to potential distribution centers in a fuzzy environment. The International Journal of Advanced Manufacturing Technology, 70(9), 1939–1954.
Mohideen, I. S., Kumar, P. S. (2010). A comparative study  on transportation problem in fuzzy environment. International Journal of Mathematics Research, 2(1), 151–158.
Nagoorgani, A., Razak,K. A. (2006). Two stage fuzzy transportation problem. Journal of Physical Sciences, 10, 63–69.
Niroomand, S., Hadi-Vencheh, A., Mirzaei, M., Molla-Alizadeh-Zavardehi, S. (2016). Hybrid greedy algorithms for fuzzy tardiness/earliness minimization in a special single machine scheduling problem: case study and generalization. International Journal of Computer Integrated Manufacturing, 29(8), 870-888.
Niroomand, S., Mahmoodirad, A., Heydari, A., Kardani, F., Hadi-Vencheh, A. (2016). An extension principle based solution approach for shortest path problem with fuzzy arc lengths. Operational Research an International Journal, doi: 10.1007/s12351-016-0230-4.
Pandian, P., Natarajan, G. (2010). A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problem. Applied Mathematical Sciences, 4(2), 79–90.
Singh, S. K., Yadav, S. P. (2014). Efficient approach for solving type-1 intuitionistic fuzzy transportation problem. International Journal of System Assurance Engineering and Management, doi:10.1007/s13198-014-0274-x.
Singh, S. K., Yadav, S. P. (2014). A new approach for solving intuitionistic fuzzy transportation problem of type-2. Annals of Operations Research, 243, 349–363.
Taassori, M., Niroomand, S., Uysal, S., Hadi-Vencheh, A., Vizvari, B. (2016). Fuzzy-based mapping algorithms to design networks-on-chip. Journal of Intelligent & Fuzzy Systems, 31, 27–43.
Xu, L. D. (1988). A fuzzy multi-objective programming algorithm in decision support systems. Annals of Operations Research, 12, 315–320.
Zadeh, L. A. (1965). Fuzzy sets. Information and Computation, 8, 338–353.