This study first surveys fuzzy linearization approaches for solving multi-objective linear fractional programming (MOLFP) problems. In particular, we review different existing methods dealing with fuzzy objectives on a crisp constraint set. Those methods transform the given MOLFP problem into a linear or a multi-objective linear programming (LP or MOLP) problem and obtain one efficient or weakly efficient solution of the main MOLFP problem. We show that one of these popular existing methods has shortcomings, and we modify it to be able to find efficient solutions. The main idea of LP-based methods is optimizing a weighted sum of numerators and the negative form of denominators of the given fractional objective function over the feasible set. We prove there is no weight region to guarantee the efficiency of the optimal solutions of such LP-based methods whenever the interior of the feasible set is nonempty. Moreover, MOLP-based methods obtain an equivalent MOLP problem to the main MOLFP problem using fuzzy set techniques. We prove MOLFP problems with a non-closed efficient set are not equivalent to MOLP ones whenever the equivalency mapping is continuous.

本研究首先调查了用于解决多目标线性分数规划 (MOLFP) 问题的模糊线性化方法。特别是，我们回顾了在清晰约束集上处理模糊目标的不同现有方法。这些方法将给定的 MOLFP 问题转换为线性或多目标线性规划（LP 或 MOLP）问题，并获得主要 MOLFP 问题的一种有效或弱有效解决方案。我们表明这些流行的现有方法之一存在缺点，我们对其进行修改以能够找到有效的解决方案。基于 LP 的方法的主要思想是在可行集上优化给定分数目标函数的分子的加权和和分母的负形式。我们证明，只要可行集的内部非空，就没有权重区域来保证这种基于 LP 的方法的最优解的效率。此外，基于 MOLP 的方法使用模糊集技术获得与主要 MOLFP 问题等效的 MOLP 问题。我们证明当等价映射是连续的时，具有非封闭有效集的 MOLFP 问题不等同于 MOLP 问题。