International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 5, No. 2, 8 Jan. 2013
Cover page and Table of Contents: PDF (size: 474KB)
A Method for Solving Fuzzy Transportation Problem (FTP) using Fuzzy Russell’s Method
Full Text (PDF, 474KB), PP.71-75
Views: 0 Downloads: 0
Author(s)
S. Narayanamoorthy
1,*
S.Saranya
1
S.Maheswari
1
Index Terms
Fuzzy Transportation Problem, Trapezoidal Number, Fuzzy Russell's Method
Abstract
The basic transportation problem was originally developed by Hitchcock. In the literature several methods are proposed for solving Fuzzy transportation problem. In this paper, we propose a new algorithm called Fuzzy Russell’s method for the initial basic feasible solution to a Fuzzy transportation problem. To examine the proposed method a numerical example is solved. Fuzzy numbers may be normal or abnormal, triangular or trapezoidal or any LR fuzzy number. We can use this proposed method for any kind of Fuzzy numbers.
Cite This Paper
S. Narayanamoorthy, S.Saranya, S.Maheswari, "A Method for Solving Fuzzy Transportation Problem (FTP) using Fuzzy Russell's Method", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.2, pp.71-75, 2013. DOI:10.5815/ijisa.2013.02.08
Reference
[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]Kim, K. and Park, K. S. ‘Ranking fuzzy number with index of optimism’, Fuzzy Sets and Systems, (1990), 35, pp: 143-150.
[10]Liou, T. S. and Wang, M. J. ‘Ranking fuzzy numbers with integral value’, Fuzzy Sets and Systems, (1992), 50, pp: 247-255.
[11]Nagoor Gani, A. and Abdul Razak, K. ‘Two Stage Fuzzy Transportation Problem’, Journal of Physical Sciences, (2006), Vol.10,pp:63-69.
[12]Narayanamoorthy, S., Anukokila P. ‘Robust fuzzy transportation problems based on extension principle under uncertain Demands’, IJMA, (2012), Vol.5.No.1. pp: 01-19.
[13]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.
[14]Shiang-Tai Liu, and Chiang Kao. ‘Solving fuzzy transportation problem based on extension principle’, Journal of Physical Science, (2006), 10, pp: 63-69.
[15]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.
[16]Tze-San lee. ‘A complete Russell’s method for the Transportation Problem’, (1986), Vol.28, No.4.
[17]Yager, R.R. ‘A procedure for ordering fuzzy subsets of the unit interval’, Information Sciences, (1981), 24, pp: 143-161.
[18]Zadeh, L. A. Fuzzy sets, Information and Control, (1965), 8, pp: 338-353.