Abstract
Kaur and Kumar, 2013, use Mehar’s method to solve a kind of fully fuzzy linear programming (FFLP) problems withLRfuzzy parameters. In this paper, a new kind of FFLP problems is introduced with a solution method proposed. The FFLP is converted into a multiobjective linear programming (MOLP) according to the order relation for comparing theLRflat fuzzy numbers. Besides, the classical fuzzy programming method is modified and then used to solve the MOLP problem. Based on the compromised optimal solution to the MOLP problem, the compromised optimal solution to the FFLP problem is obtained. At last, a numerical example is given to illustrate the feasibility of the proposed method.
Highlights
The research on fuzzy linear programming (FLP) has risen highly since Bellman and Zadeh [1] proposed the concept of decision making in fuzzy environment
Steps of the proposed method are given to solve problem (20) as follows. This method is applicable to minimization of fully fuzzy linear programming (FFLP) problems, and the solution method of maximization problems is similar to that of minimization ones
We aim to find the compromised optimal solution and corresponding objective value of the following fully fuzzy linear programming problem: max z (x) = z (x1, x2)
Summary
The research on fuzzy linear programming (FLP) has risen highly since Bellman and Zadeh [1] proposed the concept of decision making in fuzzy environment. The FLP problem is said to be a fully fuzzy linear programming (FFLP) problem if all the parameters and variables are considered as fuzzy numbers. Some researchers such as Lofti and Kumar were interested in the FFLP problems, and some solution methods have been obtained to the fully fuzzy systems [2,3,4] and the FFLP problems [5,6,7,8,9,10,11,12,13]. The fuzzy programming method is modified and used to obtain a compromised optimal solution of the MOLP.
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