中文摘要：

在已有的n维模糊集和n维模糊集截集的概念基础上,发展出一种新的n维模糊集截集定义及其表示方法,并研究了n维模糊集截集的基本性质;同时结合模糊集的分解定理和表现定理,建立了n维模糊集的分解定理和表现定理。最后,应用该理论对n维模糊集的凸性问题进行了初步的研究和讨论。

英文摘要：

Based on the previous concepts and the cuts of n-dimensional fuzzy sets, a new one of the cut sets on n-dimensional fuzzy sets and their representations are introduced, corresponding properties are studied. Meanwhile, the decomposition theorems and the representation theorems of the n-dimensional fuzzy sets are established by use corresponding theorems of the fuzzy sets. Finally, we discuss the convexity of the n-dimensional fuzzy sets.