Document Type : Research Paper
Authors
Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand 831014,India
Abstract
In this paper, a solution procedure is proposed to solve Fully Fuzzy Linear Fractional Programming (FFLFP) problem where all the variables and parameters are triangular fuzzy numbers. Here, FFLFP problem transformed into an equivalent Multi- Objective Linear Fractional Programming (MOLFP) problem. Then MOLFP converted into an equivalent multi objective linear programming problem by using mathematical programming approach. The proposed solution illustrated through numerical examples and compared with existing methods.
Keywords
Main Subjects
[1] Buckley, J. J., & Feuring, T. (2000). Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy sets and systems, 109(1), 35-53.
[2] Chakraborty, M., & Gupta, S. (2002). Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy sets and systems, 125(3), 335-342.
[3] Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval research logistics (NRL), 9(3‐4), 181-186.
[4] Dutta, D., Tiwari, R. N., & Rao, J. R. (1992). Multiple objective linear fractional programming—a fuzzy set theoretic approach. Fuzzy sets and systems, 52(1), 39-45.
[5] 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.
[6] Ezzati, R., Khorram, E., & Enayati, R. (2015). A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied mathematical modelling, 39(12), 3183-3193.
[7] Toksarı, M. D. (2008). Taylor series approach to fuzzy multiobjective linear fractional programming. Information sciences, 178(4), 1189-1204.
[8] Stancu-Minasian, I. M., & Pop, B. (2003). On a fuzzy set approach to solving multiple objective linear fractional programming problem. Fuzzy sets and systems, 134(3), 397-405.
[9] Stanojevic, B & Stancu-Minasian, I. M. (2009). On solving fuzzified linear fractional programs. Advanced modeling and optimization, 11, 503-523.
[10] Stanojević, B., & Stancu-Minasian, I. M. (2012). Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs. Yugoslav journal of operations research, 22(1), 41-50.
[11] Zadeh, L. A. (1996). Fuzzy sets. Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by lotfi a zadeh (pp. 394-432).
[12] Ebrahimnejad, A., & Tavana, M. (2014). A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers. Applied mathematical modelling, 38(17), 4388-4395.
[13] Kumar, A., Kaur, J., & Singh, P. (2011). A new method for solving fully fuzzy linear programming problems. Applied mathematical modelling, 35(2), 817-823.
[14] Lotfi, F. H., Allahviranloo, T., Jondabeh, M. A., & Alizadeh, L. (2009). Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied mathematical modelling, 33(7), 3151-3156.
[15] Maleki, H. R, Tata, M., Mashinchi, M., (1996). Fuzzy number linear programming. Proceeding of internat confference on intelligent and cognitive systems fss sponsored (pp. 145-148).Tehran, Iran: IEEE and ISRF.145-148.
[16] Veeramani, C., & Sumathi, M. (2014). Fuzzy mathematical programming approach for solving fuzzy linear fractional programming problem. RAIRO-Operations research, 48(1), 109-122.
[17] Lai, Y. J., & Hwang, C. L. (1992). Fuzzy mathematical programming. Fuzzy mathematical programming (pp. 74-186). Springer, Berlin, Heidelberg.
[18] Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55.
[19] Zimmermann, H. J. (1982). Trends and new approaches in European operational research. Journal of the operational research society, 597-603.
[20] Das, S., & Mandal, T. (2015). A single stage single constraints linear fractional programming problem. International journal of operational research, 2, 1-5.
[21] Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141.
[22] Ganesan, K., & Veeramani, P. (2006). Fuzzy linear programs with trapezoidal fuzzy numbers. Annals of operations research, 143(1), 305-315.
[23] Sapan, K. D., Mandal, T., & Edalatpanah, S. A. (2015). A note on “A new method for solving fully fuzzy linear fractional programming with a triangular fuzzy numbers”. Retrieved from http://dspace.unimap.edu.my/dspace/handle/123456789/41158.
[24] Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-Operations research, 51(1), 285-297.
[25] Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Applied intelligence, 46(3), 509-519.
[26] Das, S. K., & Edalatpanah, S. A. (2016c). A general form of fuzzy linear fractional programs with trapezoidal fuzzy numbers. International journal of data envelopment analysis and *operations research*, 2 (1), 16-19.
[27] Torabi, N., & Najafi, S. E. (2015). New model for ranking based on sum weights disparity index in data envelopment analysis in fuzzy condition. Journal of applied research on industrial engineering, 2(2), 111-119.
[28] Hatami, A., & Kazemipoor, H. (2013). Fuzzy big-M method for solving fuzzy linear programs with trapezoidal fuzzy numbers. International journal of research in industrial engineering, 2(3), 1-9.
[29] Sheikhi, H. (2012). A novel approach for solving fuzzy multi-objective zero-one linear programming problems. International journal of research in industrial engineering, 1(1).
[30] Najafi, H. S., & Edalatpanah, S. A. (2014). Homotopy perturbation method for linear programming problems. Applied mathematical modelling, 38(5), 1607-1611.
[31] Najafi, H. S., Edalatpanah, S. A., & Dutta, H. (2016). A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters. Alexandria engineering journal, 55(3), 2589-2595.
[32] Hosseinzadeh, A., & Edalatpanah, S. A. (2016). A new approach for solving fully fuzzy linear programming by using the lexicography method. Advances in fuzzy systems. doi: 10.1155/2016/1538496
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