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Solving Large-scale Three-level Linear Fractional Programming Problem with Rough Coefficient in Objective Function

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Mohamed Omran, O. E. Emam, Laila Abd-Elatif, M. Thabet

Mohamed Omran, O E Emam, Laila Abd-Elatif and M Thabet. Solving Large-scale Three-level Linear Fractional Programming Problem with Rough Coefficient in Objective Function. International Journal of Computer Applications 157(8):25-29, January 2017. BibTeX

	author = {Mohamed Omran and O. E. Emam and Laila Abd-Elatif and M. Thabet},
	title = {Solving Large-scale Three-level Linear Fractional Programming Problem with Rough Coefficient in Objective Function},
	journal = {International Journal of Computer Applications},
	issue_date = {January 2017},
	volume = {157},
	number = {8},
	month = {Jan},
	year = {2017},
	issn = {0975-8887},
	pages = {25-29},
	numpages = {5},
	url = {},
	doi = {10.5120/ijca2017912790},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


In this paper a Large-Scale three level fractional problem is considered with random rough coefficient in objective function, in order to solve this problem, The intervals technique used to convert rough nature in objective into equivalent crisp , Then Tailor Series transformation is used to convert the Large-Scale three level fractional to an equivalent three level linear programming problem , then a Traditional Method used to constructed solution of the three- level programming problem, then we will use Decomposition Technique to solve Large-ScaleProblem. Finally an auxiliary problem is discussed as well as an example is presented.


  1. Y. J. Lai, “Hierarchical optimization: a satisfactory solution,” Fuzzy Sets and Systems, Vol. 77 No. 3, (1996), pp. 321-335.
  2. M. Osman, M. Abo-Sinna, A. Amer , O. Emam, "A multi-level non-linear multi-objective decision-making under fuzziness", applied mathematics and computation. 153, ( 2004),pp.239-252.
  3. P. Kundu, S. Kar, M. Maiti, “Some Solid transportation Model with Crisp and Rough Costs”, World Academy of Science, Engineering and Technology, vol. 73, (2013),pp. 185-192.
  4. S. Pramanik, and T. K. Roy, “Fuzzy goal programming approach to multi-level programming problems,” European Journal of Operational Research, Vol. 176 (2), (2007), pp.1151-1166.
  5. N. Arbaiy, and J. Watada, “Fuzzy goal programming for multi-level multi-objective problem: an additive model,” Software Engineering and Computer Systems Communication in Computer and Information Sci-ence, Vol. 180, (2011), pp. 81-95.
  6. K. Lachhwani, and M. P. Poonia, Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach, Journal of Industrial Engineering International, Vol. 8, No. 16,(2012), pp. 1-11.
  7. M.A. Abo-sinna, and Abou - El- Enin, An interactive algorithm for large scale multiple objective programming problems with fuzzy parameters through TOPSIS approach , Yugoslav Journal of Operations Research, (21) (2011), 253 273.
  8. G. Dantzig, and P. Wolfe, The decomposition algorithm for linear programs Econometrica, Econometrics, 9 (4) (1961), 767– 778.
  9. A. A. El-Sawy, N. A. El-khouly, and T. H. M. Abou - El- Enin, An algorithm for decomposing the parametric space in large scale linear vector optimization problems : A fuzzy approach ,AMSE, Advances in Modeling &Analysis, 55 (2) (2000), 1-16 .
  10. T. I. Sultan, O. E. Emam and A. A. Abohany, A decomposition algorithm for solving a three–level large scale linear programming problem, Applied Mathematics and Information Science, 5 (Sep. 2014), 2217- 2223 .


Three-level problem; Fractional Problem; Rough interval Coefficient; Large-Scale; Tailor Series