A new method for solving fuzzy linear fractional programming problem with new ranking function

Document Type: Research Paper


Department of Mathematics, National Institute of Technology, Jamshedpur, India.


Because of uncertainty in the real life applications, reaching to the optimal solution is always time consuming and even sometimes impossible. In order to overcome these limitations the fuzzy set theory is introduced to handle it but not only incomplete information but also indeterminate and inconsistent information which is common in real life conditions. In this paper, we have developed a new ranking function to solve a Fully Fuzzy Linear Fractional Programming (FFLFP). The ranking function is derived by replacing the non-parallel sides of the trapezoidal fuzzy number with non-linear functions. Various numerical examples are included and compared with the pre-existing methods.


Main Subjects

[1]      Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research logistics quarterly9(3‐4), 181-186.

[2]      Yager, R. R. (1981). A procedure for ordering fuzzy subsets of the unit interval. Information sciences24(2), 143-161.

[3]      Stanojević, B., & Stancu-Minasian, I. M. (2012). Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs. Yugoslav journal of operations research22(1), 41-50.

[4]      Stanojevic, B., & Stancu-Minasian, I. M. (2009). On solving fuzzified linear fractional programs. Advanced modeling and optimization11, 503-523.

[5]      Dutta, D., Tiwari, R. N., & Rao, J. R. (1992). Multiple objective linear fractional programming—a fuzzy set theoretic approach. Fuzzy sets and systems52(1), 39-45.

[6]      Stancu-Minasian, I. M., & Pop, B. (2003). On a fuzzy set approach to solving multiple objective linear fractional programming problem. Fuzzy sets and systems134(3), 397-405.

[7]      Buckley, J. J., & Feuring, T. (2000). Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy sets and systems109(1), 35-53.

[8]      Zadeh, L. A. (1965). Fuzzy sets. Information and control8(3), 338-353.

[9]      Chakraborty, M., & Gupta, S. (2002). Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy sets and systems125(3), 335-342.

[10]   Toksarı, M. D. (2008). Taylor series approach to fuzzy multi-objective linear fractional programming. Information sciences178(4), 1189-1204.

[11]   Sakawa, M., & Yano, H. (1988). An interactive fuzzy satisficing method for multio-bjective linear fractional programming problems. Fuzzy sets and systems28(2), 129-144.

[12]   Sakawa, M., Yano, H., & Takahashi, J. (1992). Pareto optimality for multiobjective linear fractional programming problems with fuzzy parameters. Information sciences63(1-2), 33-53.

[13]   Ezzati, R., Khorram, E., & Enayati, R. (2015). A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied mathematical modelling39(12), 3183-3193.

[14]   Ebrahimnejad, A. (2019). An effective computational attempt for solving fully fuzzy linear programming using MOLP problem. Journal of industrial and production engineering36(2), 59-69.

[15]   Das, S. K., Edalatpanah, S. A., & Mandal, T. (2018). A proposed model for solving fuzzy linear fractional programming problem: numerical point of view. Journal of computational science25, 367-375.

[16]   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 research51(1), 285-297.

[17]   Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Applied intelligence46(3), 509-519.

[18]   Das, S. K., & Mandal, T. (2017). A new model for solving fuzzy linear fractional programming problem with ranking function. Journal of applied research on industrial engineering4(2), 89-96.

[19]   Das, S. K., & Mandal, T. (2017). A MOLFP Method for Solving Linear Fractional Programming under Fuzzy Environment. International journal of research in industrial engineering6(3), 202-213.

[20]   Das, S. K. (2017). Modified method for solving fully fuzzy linear programming problem with triangular fuzzy numbers. International journal of research in industrial engineering6(4), 293-311.

[21]   Schaible, S. (1976). Fractional programming. i, duality. Management science22(8), 858-867.

[22]   Chinnadurai, V., & Muthukumar, S. (2016). Solving the linear fractional programming problem in a fuzzy environment: Numerical approach. Applied mathematical modelling40(11-12), 6148-6164.

[23]   Stanojević, B., & Stanojević, M. (2016). Parametric computation of a fuzzy set solution to a class of fuzzy linear fractional optimization problems. Fuzzy optimization and decision making15(4), 435-455.

[24]   Veeramani, C., & Sumathi, M. (2014). Fuzzy mathematical programming approach for solving fuzzy linear fractional programming problem. RAIRO-operations research48(1), 109-122.

[25]   Stanojević, B., & Stanojević, M. (2013). Solving method for linear fractional optimization problem with fuzzy coefficients in the objective function. International journal of computers communications & control8(1), 146-152.

[26]   Suneela, S., & Chakraverty, S. (2019). New ranking function for fuzzy linear programming problem and system of linear equations. Journal of information and optimization sciences40(1), 141-156.