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

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. (C) 2013 Elsevier Inc. All rights reserved.