模糊完备格上的模糊同余关系  

Fuzzy congruence relations on fuzzy complete lattices

作　　者：刘敏[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2013年第1期5-9,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11171196;10871121)

摘　　要：在模糊完备格中引入模糊完备格同余关系的概念,讨论了模糊完备格同余与模糊闭包算子之间的关系.证明了一个模糊完备格上的模糊同余关系之集构成的模糊偏序集模糊序同构于其上的模糊闭包算子之集构成的模糊偏序集.给出了模糊完备格同余的商的概念,证明了任一模糊完备格满同态的像都模糊序同构于由该模糊完备格同态所诱导的同余关系的商.The concept of fuzzy complete lattice congruence relation on fuzzy complete lattice is defined, and the relation between fuzzy complete lattice congruence and fuzzy closure operator is discussed. It is proved that in a fuzzy complete lattice, the fuzzy poset of fuzzy complete lattice congruence relations is fuzzy order isomorphic to the fuzzy poset of fuzzy closure operators. The quotient of a fuzzy complete lattice congruence relation is defined. It is also proved that the image of a fuzzy complete lattice under a surjective fuzzy complete lattice morphism is fuzzy order isomorphic to the quotient of the fuzzy complete lattice congruence relation induced by the fuzzy complete lattice morphism.

关 键 词：模糊偏序集 模糊完备格 模糊完备格同余 模糊闭包算子 

分 类 号：O159[理学—数学]