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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 435030, 4 pages
A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem
Department of Mathematics, Faculty of Art and Sciences, Yildiz Technical University, Davutpaşa, 34210 Istanbul, Turkey
Received 18 March 2013; Accepted 10 September 2013
Academic Editor: Mustafa Bayram
Copyright © 2013 Nuran Güzel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Y.-J. Lai and C. L. Hwang, Fuzzy Multiple Objective Decision Making, Springer, 1994.
- I. M. Stancu-Minasian and B. Pop, “On a fuzzy set approach to solving multiple objective linear fractional programming problem,” Fuzzy Sets and Systems, vol. 134, no. 3, pp. 397–405, 2003.
- D. S. Kim, C. L. Jo, and G. M. Lee, “Optimality and duality for multiobjective fractional programming involving -set functions,” Journal of Mathematical Analysis and Applications, vol. 224, no. 1, pp. 1–13, 1998.
- J.-C. Liu and K. Yokoyama, “-optimality and duality for multiobjective fractional programming,” Computers & Mathematics with Applications, vol. 37, no. 8, pp. 119–128, 1999.
- S. Tigan and I. M. Stancu-Minasian, “On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program,” Academy of Sciences of the Czech Republic. Mathematical Institute. Mathematica Bohemica, vol. 125, no. 2, pp. 227–234, 2000.
- R. Patel, “Mixed-type duality for multiobjective fractional variational control problems,” International Journal of Mathematics and Mathematical Sciences, no. 1, pp. 109–124, 2005.
- W. Dinkelbach, “On nonlinear fractional programming,” Management Science, vol. 13, pp. 492–498, 1967.
- M. T. Arévalo, A. M. Mármol, and A. Zapata, “The tolerance approach in multiobjective linear fractional programming,” Top, vol. 5, no. 2, pp. 241–252, 1997.
- H. I. Calvete and C. Gale, “The bilevel linear/linear fractional programming problem,” European Journal of Operational Research, vol. 114, pp. 188–197, 1999.
- S. R. Yadav and R. N. Mukherjee, “Duality for fractional minimax programming problems,” Australian Mathematical Society Journal B, vol. 31, no. 4, pp. 484–492, 1990.
- M. Sakawa, I. Nishizaki, and Y. Uemura, “Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters,” Fuzzy Sets and Systems, vol. 115, no. 1, pp. 93–103, 2000.
- M. Sakawa and I. Nishizaki, “Interactive fuzzy programming for two-level linear fractional programming problems,” Fuzzy Sets and Systems, vol. 119, no. 1, pp. 31–40, 2001.
- P. Gupta and D. Bhatia, “Sensitivity analysis in fuzzy multiobjective linear fractional programming problem,” Fuzzy Sets and Systems, vol. 122, no. 2, pp. 229–236, 2001.
- O. M. Saad, “An iterative goal programming approach for solving fuzzy multiobjective integer linear programming problems,” Applied Mathematics and Computation, vol. 170, no. 1, pp. 216–225, 2005.
- J. B. G. Frenk and S. Schaible, “Fractional Programming,” ERIM Report Series, Ref. No.ERS-2004-074-LIS., 2004.
- S. İ. Birbil, J. B. G. Frenk, and S. Zhang, “Generalized Fractional Programming with User Iteraction,” ERIM Report Series, Ref.No. ERS-2004-033-LIS., 2004.
- C. Mohan and H. T. Nguyen, “An interactive satisficing method for solving multiobjective mixed fuzzy-stochastic programming problems,” Fuzzy Sets and Systems, vol. 117, no. 1, pp. 61–79, 2001.
- N. Güzel and M. Sivri, “Proposal of a solution to multi objective linear fractional programming problem,” Sigma Journal of Engineering and Natural Sciences, vol. 2, pp. 43–50, 2005.
- M. Leber, L. Kaderali, A. Schönhuth, and R. Schrader, “A fractional programming approach to efficient DNA melting temperature calculation,” Bioinformatics, vol. 21, no. 10, pp. 2375–2382, 2005.
- R. Jagannathan, “On some properties of programming problems in parametric form pertaining to fractional programming,” Management Science, vol. 12, pp. 609–615, 1966.
- J. S. H. Kornbluth and R. E. Steuer, “Goal programming with linear fractional criteria,” European Journal of Operational Research, vol. 8, no. 1, pp. 58–65, 1981.
- M. Chakraborty and S. Gupta, “Fuzzy mathematical programming for multi objective linear fractional programming problem,” Fuzzy Sets and Systems, vol. 125, no. 3, pp. 335–342, 2002.
- M. K. Luhandjula, “Fuzzy approaches for multiple objective linear fractional optimization,” Fuzzy Sets and Systems, vol. 13, no. 1, pp. 11–23, 1984.
- D. Dutta, R. N. Tiwari, and J. R. Rao, “Multiple objective linear fractional programming—a fuzzy set-theoretic approach,” Fuzzy Sets and Systems, vol. 52, no. 1, pp. 39–45, 1992.
- B. I. Lee and D. W. Tcha, “An interactive procedure for fuzzy programming problems with linear fractional objectives,” Computers and Industrial Engineering, vol. 16, pp. 269–275, 1989.
- S. Schaible, Analyse und Anwendungen von Quotientenprogrammen, Anton Hain, Meisenheim am Glan, Germany, 1978.
- A. Charnes and W. W. Cooper, “Programming with linear fractional functionals,” Naval Research Logistics Quarterly, vol. 9, pp. 181–186, 1962.
- Y.-L. Chang and Q. S. B. Win, Version 1.0 for Windows, John Wiley & Sons, 2001.