Linear ranking functions are often used to transform fuzzy multiobjective linear programming (MOLP) problems into crisp ones. The crisp MOLP problems are then solved by using classical methods (eg, weighted sum, epsilon‐constraint, etc), or fuzzy ones based on Bellman and Zadeh's decision‐making model. In this paper, we show that this transformation does not guarantee Pareto optimal fuzzy solutions for the original fuzzy problems. By using lexicographic ranking criteria, we propose a fuzzy epsilon‐constraint method that yields Pareto optimal fuzzy solutions of fuzzy variable and fully fuzzy MOLP problems, in which all parameters and decision variables take on LR fuzzy numbers. The proposed method is illustrated by means of three numerical examples, including a fully fuzzy multiobjective project crashing problem.

中文翻译：

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一种完全模糊多目标线性规划的ε约束方法

线性排序函数通常用于将模糊多目标线性规划 (MOLP) 问题转换为清晰的问题。然后使用经典方法（例如，加权总和、epsilon 约束等）或基于 Bellman 和 Zadeh 决策模型的模糊方法来解决清晰的 MOLP 问题。在本文中，我们表明这种转换不能保证原始模糊问题的帕累托最优模糊解。通过使用词典排序标准，我们提出了一种模糊 epsilon 约束方法，该方法产生模糊变量和完全模糊 MOLP 问题的帕累托最优模糊解，其中所有参数和决策变量都采用 LR 模糊数。所提出的方法通过三个数值例子来说明，包括一个完全模糊的多目标项目崩溃问题。