Fuzzy efficient and pareto — Optimal solution for multiobjective linear plus linear fractional programming problem

Abstract

Many practical optimization problems usually have several conflicting objectives. In those multiobjective optimization, no solution optimizing all the objective functions simultaneously exists in general. Instead, pareto - optimal solutions, which are efficient in terms of all objective functions, are introduced. In general we have many optimal solutions. Therefore we need to decide a final solutions among pareto - optimal solutions taking in to account the balance among objective functions. In this paper we find fuzzy efficient and pareto - optimal solution to the multiobjective linear plus linear fractional programming problem and show that, in the case that, when any goal is fully achieved, then fuzzy efficient solution may or may not be pareto - optimal solution and therefore we propose a procedure to obtain fuzzy efficient solution which is pareto - optimal also and review some results. In the proposed approach each objective function is transformed into linear functions by using Taylor's theorem. Then the MOLLFP is changed into equivalent multiobjective linear programming problem (MOLP) and then find fuzzy efficient and pareto - optimal solution in finite number of steps. Efficiency of proposed method is verified by numerical examples. To explore the potential use of the proposed method, three numerical examples are solved.