A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem

作者：Ezzati R^*; Khorram E; Enayati R

来源：Applied Mathematical Modelling, 2015, 39(12): 3183-3193.

DOI：10.1016/j.apm.2013.03.014

• Fully fuzzy linear programming problem
• Multi-objective linear programming problem
• Lexicographic ordering on triangular fuzzy numbers

Recently, two new algorithms have been proposed to solve a fully fuzzy linear programming (FFLP) problem by Lotfi et al. [F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Model. 33 (2009) 3151-31561 and Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 33 (2011) 817-824 In this paper, based on a new lexicographic ordering on triangular fuzzy numbers, a novel algorithm is proposed to solve the FFLP problem by converting it to its equivalent a multi-objective linear programming (MOLP) problem and then it is solved by the lexicographic method. By a theorem, it is shown that the lexicographic optimal solution of MOLP problem can be considered as an optimal solution of the FFLP problem. Then, a simple example and two real problems, as two case studies, will be used to illustrate our algorithm and compare it with the existing methods.

• 出版日期2015-6-15