模糊集层次结构的本质刻画  

An Essential Description for Hierarchical Structure of Fuzzy Set

作　　者：汤建钢[1] 汤娟[2] 

机构地区：[1]伊犁师范学院数学与统计学院,新缰伊宁835000 [2]四川大学电子信息学院,四川成都610064

出　　处：《模糊系统与数学》2013年第4期1-5,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11161050;31240020)

摘　　要：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.

关 键 词：格值集合 格值集轮 表示定理 层次结构 

分 类 号：O159[理学—数学]