Document Type : Research Paper
Author
Department of Mathematics, College of Science and Arts, Ar Rass, Qassim University, Saudi Arabia.
Abstract
This paper deals with a multi-objective linear fractional programming problem in fuzzy environment. The problem is considered by introducing all the parameters as piecewise quadratic fuzzy numbers. Through the use of the associated real number of the close interval approximation and the order relation of the piecewise quadratic fuzzy numbers, the problem is transformed into the corresponding crisp problem. A proposed method introduces to generate ideals and the set of all fuzzy efficient solutions. The advantage of it helps the decision maker to handle the real life problem. A numerical example is given illustrate the method.
Keywords
- Linear fractional programming
- Multi-objective decision making
- Piecewise quadratic fuzzy number
- Close interval approximation
- Proposed method
- Hungarian method
- Fuzzy optimal solution
Main Subjects
- Arisawa, S., & Elmaghraby, S. E. (1972). Optimal time-cost trade-offs in GERT networks. Management science, 18(11), 589-599. https://doi.org/10.1287/mnsc.18.11.589
- Borza, M., & Rambely, A. S. (2021). A linearization to the sum of linear ratios programming problem. Mathematics, 9(9), 1004. https://doi.org/10.3390/math9091004
- Buckley, J. J., & Feuring, T. (2000). Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy sets and systems, 109(1), 35-53. https://doi.org/10.1016/S0165-0114(98)00022-0
- Jain, S. (2010). Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program. Iranian journal of operations research, 2(1), 77-88. https://www.sid.ir/en/Journal/ViewPaper.aspx?ID=172184
- Chakraborty, A. (2015). Duality in nonlinear fractional programming problem using fuzzy programming and genetic algorithm. International journal of soft computing, mathematics and control (IJSCMC), 4(1), 19-33.
- Dantzig, G. B., Blattner, W. O., & Rao, M. R. (1966). Finding a cycle in a graph with minimum cost to time ratio with application to a ship routing problem. Stanford Univ Ca Operations Research House. DOI: 21236/ad0646553
- Gupta, S., & Chakraborty, M. (1998). Linear fractional programming problem: a fuzzy programming approach. Journal of fuzzy mathematics, 6, 873-880.
- Isbell, J. R., & Marlow, W. H. (1956). Attrition games. Naval research logistic quarterly, 3(1-2), 71- 94. https://doi.org/10.1002/nav.3800030108
- Li, D., & Chen, S. (1996). A fuzzy programming approach to fuzzy linear fractional programming with fuzzy coefficients. Journal of fuzzy mathematics, 4, 829-834.
- Odior, A. O. (2012). An approach for solving linear fractional programming problems. International journal of engineering and technology, 1(4), 298- 304. https://www.sciencepubco.com/index.php/ijet/article/view/270
- Pandey, P., & Punnen, A. P. (2007). A simplex algorithm for piecewise-linear fractional programming problems. European journal of operational research, 178(2), 343-358. https://doi.org/10.1016/j.ejor.2006.02.021
- Pop, B., & Stancu-Minasian, I. M. (2008). A method of solving fully fuzzified linear fractional programming problems. Journal of applied mathematics and computing, 27(1), 227-242. https://doi.org/10.1007/s12190-008-0052-5
- Schaible, S. (1976). Fractional programming. i, duality. Management science, 22(8), 858-867. https://doi.org/10.1287/mnsc.22.8.858
- Schaible, S. (1982). Bibliography in fractional programming. Zeitschrift für operations research, 26(1), 211-241. https://doi.org/10.1007/BF01917115
- Simi, F. A., & Talukder, M. S. (2017). A new approach for solving linear fractional programming problems with duality concept. Open journal of optimization, 6(01), 1. 4236/ojop.2017.61001
- Stanojevic, B., & Stancu-Minasian, I. M. (2009). On solving fuzzified linear fractional programs. Advanced modeling and optimization, 11, 503-523.
- Tantawy, S. F. (2008). A new procedure for solving linear fractional programming problems. Mathematical and computer modelling, 48(5-6), 969-973. https://doi.org/10.1016/j.mcm.2007.12.007
- Xiao, Y., & Tian, X. (2021, April). Algorithm for solving linear fractional programming. Journal of physics: conference series(Vol. 1903, No. 1, p. 012044). IOP Publishing.
- Bajalinov, E., & Rácz, A. (2012). The ray-method: theoretical background and computational results. Croatian operational research review, 3(1), 137-149.
- Sakawa, M., Kato, K., & Mizouchi, R. (1998). An interactive fuzzy satisfying method for multiobjective block angular linear fractional programming problems with parameters. Electronics and communications in Japan (Part III: fundamental electronic science), 81(12), 45-54. https://doi.org/10.1002/(SICI)1520-6440(199812)81:12<45::AID-ECJC6>3.0.CO;2-Q
- Hassian, M. L., Khalifa, H. A., & Ammar, E. (2004). A parametric approach for solving the multicriteria linear fractional programming problem. Journal of fuzzy mathematics, 12(3), 527-536.