直觉模糊格及其同态  

Intuitionistic Fuzzy lattices and Its Homomorphism

作　　者：刘春芝[1] 廖祖华[1] 曹姝[1] 张扬[1] 嵇敏[1] 李云[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《模糊系统与数学》2012年第3期51-57,共7页Fuzzy Systems and Mathematics

基　　金：江苏省教育科学"十一五"规划项目(D/2006/01/171);江苏省教育厅项目(2009-598);江南大学创新团队发展计划项目(200902)

摘　　要：在K.Atanassov引进直觉模糊集的基础上,定义了直觉模糊格,并讨论了它的简单性质,给出了直觉模糊集截集与直觉模糊格的关系,证明了A是格L的一个直觉模糊子格的充要条件是A的截集是L的一个子格,然后在格同态与同构意义下,研究了直觉模糊格的像与原像。最后给出了直觉模糊凸子格的概念,并得到了它的一些基本性质。On the basis of the Intuitionistic fuzzy sets being introduced by K. Atanassov, we define intuitionistic fuzzy lattice, then we discuss its simple properties, the relation between cut sets on intuitionistic fuzzy sets and an intuitionistic fuzzy subset of a lattice is given. It is proved that A is an intuitionistic fuzzy subset of a lattice L if and only if cut sets of A are sublattice of L. Next, in the sense of homomorphism and isomorphism of lattice, we investigate image and the inverse image of intuitionistic fuzzy lattice. Finally, the concept of intuitionistic fuzzy convex lattice is given, and we get its some basic properties.

关 键 词：直觉模糊集 截集 直觉模糊格 同态 同构 直觉模糊凸子格 

分 类 号：O159[理学—数学]