Fuzzy Transportation Problem Using Improved Fuzzy Russells Method

 International Journal of Mathematical Trends and Technology (IJMTT) © 2014 by IJMTT Journal Volume-5 Year of Publication : 2014 Authors : R.Jahir Hussain , P.Jayaraman 10.14445/22315373/IJMTT-V5P522

R.Jahir Hussain , P.Jayaraman Article:Fuzzy Transportation Problem Using Improved Fuzzy Russells Method,International Journal of Mathematical Trends and Technology (IJMTT),V5:50-59: January 2014. Published by Seventh Sense Research Group.

Abstract
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.

References

[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.

Keywords
Ranking function, Triangular, Trapezoidal Number, Transportation problem, Fuzzy Dominant Method.