n维凸模糊集与n维模糊数

n-Dimensional convex fuzzy sets and n-dimensional fuzzy numbers

在n维模糊集理论的基础上,给出了n维凸模糊集的定义,利用凸模糊集的有关性质研究了n维凸模糊集的有关性质.在此研究基础上,又给出了n维(闭)模糊数的概念,根据模糊数的有关性质得到了n维(闭)模糊数相应的运算性质和表示定理,为建立基于n维模糊集的凸分析理论奠定了基础.

Based on theory of n-dimensional fuzzy set,the definition of the n-dimensional convex fuzzy set is given.The properties of n-dimensional convex fuzzy sets are discussed by means of the properties of convex fuzzy sets.According to the above discussion and properties of fuzzy numbers,the notion of n-dimensional（closed） fuzzy numbers is introduced,and the corresponding operation properties and the representation theorem of n-dimensional（closed） fuzzy numbers are obtained.Furthermore,the above results are applied to establishing the foundation of the convex analysis of n-dimensional fuzzy set.