Volume 5 | Number 1 | Year 2014 | Article Id. IJMTT-V5P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V5P522

In this paper, we investigate the new idea of optimal solution of squared triangular and trapezoidal fuzzy number via fuzzy russal’s method. This method is a modification of yager’s ranking method. A new algorithm is investigated and a suitable optimal solution is obtained. A numerical example is given based on the algorithms.

[1] Amarpreet kaur,Amit Kumar. ‘A new method for solving fuzzy transportation problem using ranking function’, Applied Mathematical Modeling, (2011), 35, pp: 5652-5661.

[2] Chanas, S and Kuchta, D.‘A concept of the optimal solution of the transportation problem with fuzzy cost coefficients’,Fuzzy sets and Systems,(1996),82, pp:299-305.

[3] Chanas.S, Kolodziejczyk.W and Machaj, A. ‘A fuzzy approach to the transportation problem’, Fuzzy Sets and Systems, (1984), 13, pp: 211–221.

[4] Campos, L. and Gonzalez Munoz, A. ‘A subjective approach for ranking fuzzy number’, Fuzzy Sets and Systems, (1989), 29, pp: 145-153.

[5] Campos, L. and Verdegay, J. L. ‘Linear programming problem and ranking of fuzzy numbers’, Fuzzy Sets and Systems, (1989),32,pp 1-11.

[6] F.L.Hitchcock. ‘The distribution of a product from several source to numerous localities’, J.Math.phys, (1941), 20,pp:224-230.

[7] Ismail Mohideen, S. and Senthil Kumar, P. ‘A Comparative Study on Transportation Problem in Fuzzy Environment’, International Journal of Mathematics Research, ISSN 0976-5840, (2010), Vol.2, Number 1, pp: 151-158.

[8] Jain, R. ‘Decision-making in the presence of fuzzy variables’, IEEE Transactions on Systems, Man and Cybernetics, (1976), 6, pp: 698-703.

[9]. R.Jahirhussain , P.Jayaraman fuzzy optimal transportation problem by improved zero suffix method via robust rank techniques International Journal of Fuzzy Mathematics and Systems (IJFMS). Volume 3 (2013) pp 303-311

[10] Kim, K. and Park, K. S. ‘Ranking fuzzy number with index of optimism’, Fuzzy Sets and Systems, (1990), 35, pp: 143-150.

[11] Liou, T. S. and Wang, M. J. ‘Ranking fuzzy numbers with integral value’, Fuzzy Sets and Systems, (1992), 50, pp: 247-255.

[12] S.Narayanamoorthy S.Saranya & S.Maheswari A Method for Solving Fuzzy Transportation Problem (FTP) using Fuzzy Russell’s Method I.J. Intelligent Systems and Applications, 2013, 02, 71-75

[13] Nagoor Gani, A. and Abdul Razak, K. ‘Two Stage Fuzzy Transportation Problem’, Journal of Physical Sciences, (2006), Vol.10,pp:63-69.

[14] Narayanamoorthy, S., Anukokila P. ‘Robust fuzzy transportation problems based on extension principle under uncertain Demands’, IJMA, (2012), Vol.5.No.1. pp: 01-19.

[15] Pandian, P and Natarajan, G. ‘A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problem’,Applied Mathematical Sciences,(2010),4, pp: 79-90.

[16] Shiang-Tai Liu, and Chiang Kao. ‘Solving fuzzy transportation problem based on extension principle’, Journal of Physical Science, (2006), 10, pp: 63-69.

[17] Stephen Dinagar, D and Palanivel, K., ‘The transportation problem in Fuzzy Environment’. International Journal of Algorithms, Computing and Mathematics, August 2009, Vol 2, Number 3.

[18] Tze-San lee. ‘A complete Russell’s method for the Transportation Problem’, (1986), Vol.28, No.4.

[19] Yager, R.R. ‘A procedure for ordering fuzzy subsets of the unit interval’, Information Sciences, (1981), 24, pp: 143-161.

[20] Zadeh, L. A. Fuzzy sets, Information and Control, (1965), 8, pp: 338-353.

R.Jahir Hussain , P.Jayaraman, "Fuzzy Transportation Problem Using Improved Fuzzy Russells Method," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 5, no. 1, pp. 50-59, 2014. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V5P522