模糊集层次结构的本质刻画

An Essential Description for Hierarchical Structure of Fuzzy Set

将Zadeh提出的模糊集的模糊结构提升到格值结构,引入赋予格值结构的集合概念,称之为格值集合,并给出了格值集合的表示定理。在此基础上,证明格值集合范畴可以嵌入到集合的层范畴,说明格值结构具有层结构这一特征,从而揭示格值集合具有层次结构,这一结果也刻画了Z adeh模糊集的层次结构的本质特征。

In this paper we introduce the concept of set equipped with lattice-valued structure callea lattice valued set arising from fuzzy structure of fuzzy set introduced by Zadeh. We give two important results： representation theorem of lattice-valued set, and embedding theorem, i.e. , category of lattice-valued sets can embedded into category of sets sheaves, which shows lattice-valued structure is sheaf structure and lattice-valued set is provided with hierarchical structure, these conclusions is an essential description for hierarchical structure of Zadeh＇s fuzzy set.