Abstract: In this paper, a new kind of L-fuzzy set is introduced which is called Flou-valued fuzzy set to consider the deficiency of interval-valued fuzzy set and three-parameters interval-valued fuzzy set in expressing fuzzy information. It puts forward Flou nested set. Using Flou nested set and combined with cut sets as well as decomposition theorems of Flou-valued fuzzy set, the representation theorems are obtained and its effectiveness is vertified by a practical account case.

Key words: fuzzy set, Flou set, Flou-valued fuzzy set, representation theorem

摘要： 为了弥补区间值模糊集和三参数模糊集在模糊信息表达方面的不足，在Flou集的基础上，提出了一种新的L模糊集，Flou值模糊集，并用投票模型对其作出解释。引入Flou嵌套集的概念，结合Flou值模糊集截集的定义及分解定理，建立了Flou值模糊集的表现定理，并用一个实际算例验证了表现定理的有效性。它揭示了Flou集和Flou值模糊集的联系，提供了一种利用Flou嵌套集拼成Flou值模糊集的方法。为处理模糊信息提供了一种新的工具，并为Flou值模糊集的研究和应用奠定了初步的理论基础。

关键词: 模糊集, Flou集, Flou值模糊集, 表现定理