Fuzzy efficient and Pareto-optimal solution for multi-objective linear fractional programming problems

Many practical optimisation problems usually have several conflicting objectives. In these multi-objective optimisation problems, solution optimising all the objective functions simultaneously does not exist, in general. Instead, Pareto-optimal solutions, which are efficient in terms of all objective functions, are introduced. Nevertheless, many optimal solutions exist. A final solution among Pareto-optimal solutions is to be selected based on the balance among objective functions. In this paper, we find fuzzy efficient and Pareto-optimal solution to the multi-objective linear fractional programming problem (MOLFP). It has shown that when any fuzzy goal is fully achieved, the fuzzy efficient solution may or may not be Pareto-optimal. Therefore, a procedure is proposed to obtain fuzzy efficient solution which is also Pareto-optimal. The efficiency of proposed method is verified by numerical examples and a practical application in production planning.

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