International Journal of Mathematics Trends and Technology
Volume 9 | Number 2 | Year 2014 | Article Id. IJMTT-V9P519 | DOI : https://doi.org/10.14445/22315373/IJMTT-V9P519
In this paper, we propose a new method for solving Fully Fuzzy linear programming Problem (FFLP) using ranking method .In this proposed ranking method, the given FFLPP is converted into a crisp linear programming (CLP) Problem with bound variable constraints and solved by using Robust’s ranking technique and the optimal solution to the given FFLP problem is obtained and then compared between our proposed method and the existing method. Numerical examples are used to demonstrate the effectiveness and accuracy of this method.
1] T. Allahviranloo, K. H. Shamsolkotabi, N. A. Kiani and L. Alizadeh, Fuzzy Integer Linear Programming Problems, International Journal of Contemporary Mathematical Sciences, 2(2007), 167-181.
[2] T. Allahviranloo, F. H. Lotfi, M. K. Kiasary, N. A. Kiani and L. Alizadeh, Solving Fully Fuzzy Linear Programming Problem by the Ranking Function, Applied Matematical Sciences, 2(2008), 19-32.
[3] Amit Kumar, Jagdeep Kaur, Pushpinder Singh, Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints, International Journal of Mathematical and Computer Sciences, 6 (2010), 37-41.
[4] Amit Kumar, Jagdeep Kaur, Pushpinder Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modeling, 35(2011), 817-823.
[5] Bellman R. E and L. A. Zadeh, Decision Making in A Fuzzy Environment, Management Science, 17(1970), 141-164.
[6] . Buckley J and Feuring.T, Evolutionary Algorithm Solution to Fuzzy Problems: Fuzzy Linear Programming, Fuzzy Sets and Systems, 109(2000), 35-53.
[7] . M. Cadenas and J. L. Verdegay, Using Fuzzy Numbers in Linear Programming, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, 27(1997), 1016-1022
[8]Campos .Land ,. Verdegay J. L., Linear Programming Problems and Ranking of Fuzzy Numbers, Fuzzy Sets and Systems, 32( 1989), 1-11.
[9] Dehghan M, Hashemi B, Ghatee M, Computational methods for solving fully fuzzy linear systems, Appl. Math. Comput., 179 ( 2006 ), 328–343
[10] Ganesan Kand Veeramani P, Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers, Annals of Operations Research, 143 ( 2006 ), 305-315.
[11]Jayalakshmi.M, Pandian P A New Method for Finding an Optimal Fuzzy Solution For Fully Fuzzy Linear Programming Problems International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.247-254
[12] M. Jimenez, M. Arenas, A. Bilbao and M. V. Rodrguez, Linear Programming with Fuzzy Parameters: An Interactive Method Resolution, European Journal of Operational Research, 177 ( 2007 ), 1599-1609
[13] Maleki H.R. Tata .M and Mashinchi .M, Linear Programming with Fuzzy Variables, Fuzzy Sets and Systems, 109 ( 2000 ), 21-33.
[14] Maleki,H.R Ranking Functions and Their Applications to Fuzzy Linear Programming, Far East Journal of Mathematical Sciences, 4 ( 2002 ), 283-301.
[15] Rangarajan R, Solairaju,A “Computing improved fuzzy optimal Hungarian assignment problems with fuzzy costs under robust ranking techniques”. International Journal of Computer Applications, (2010) 6(4): 6-13.
[16]H. Tanaka, T, Okuda and K. Asai, On Fuzzy Mathematical Programming, Journal of Cybernetics and Systems, 3(1973), 37-46.
[17].Yager,R.R “ A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24,(1981), 143-161.
[18] Zimmermann,H.J “Fuzzy programming and linear programming with several objective functions”. Fuzzy Sets and Systems, (1978) 1: 45-55.
P. Rajarajeswari , A.Sahaya Sudha, "Solving a Fully Fuzzy Linear Programming Problem by Ranking," International Journal of Mathematics Trends and Technology (IJMTT), vol. 9, no. 2, pp. 159-164, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V9P519
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