In the present paper, we consider fuzzy optimization problems which involve fuzzy sets only in the objective mappings, and give two concepts of optimal solutions which are non-dominated solutions and weak non-dominated solutions based on orderings of fuzzy sets. First, by using level sets of fuzzy sets, the fuzzy optimization problems treated in this paper are reduced to set optimization problems, and relationships between (weak) non-dominated solutions of the fuzzy optimization problems and the reduced set optimization problems are derived. Next, the set optimization problems are reduced to scalar optimization problems which can be regarded as scalarization of the fuzzy optimization problems. Then, relationships between non-dominated solutions of the fuzzy optimization problems and optimal solutions of the reduced scalar optimization problems are derived.

中文翻译：

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模糊集优化问题的标量方法

在本文中，我们考虑了仅在目标映射中涉及模糊集的模糊优化问题，并基于模糊集的排序给出了最优解的两个概念，即非控制解和弱非控制解。首先，通过使用模糊集的水平集，将本文处理的模糊优化问题简化为集合优化问题，并推导了模糊优化问题的（弱）非支配解与约简集优化问题之间的关系。接下来，将集合优化问题简化为标量优化问题，可以将其视为模糊优化问题的标量化。然后，