模糊同余与模糊群  

Fuzzy Congruences and Fuzzy Groups

作　　者：赵云平 ZHAO Yunping(School of Mathematics and Physics,West Yunnan University,Lincang,Yunnan Province,677000 China)

机构地区：[1]滇西科技师范学院数理学院,云南临沧677000

出　　处：《科技创新导报》2021年第9期223-225,232,共4页Science and Technology Innovation Herald

摘　　要：群上既是模糊左相容,又是模糊右相容的模糊等价关系称为群上的模糊同余关系。模糊同余关系属于模糊二元关系,是一种特殊形式的模糊集合,它具有模糊性,模糊性是客观事物中的不分明性和不确定性,其根源在于客观事物的差异之间存在着中介过渡。本文在模糊同余关系的基础上,给出了模糊同余关系下的相似关系、模糊相融、二元关系、模糊子群的概念,并讨论了模糊同余的一系列性质,得到了几个有意义的类似于群论基本定理的结论。The fuzzy congruence refers to the fuzzy equivalence relation on the group compatible with the left and the right.As a special form of fuzzy set with fuzziness,it belongs to fuzzy binary relation.Fuzziness is the ambiguity and uncertainty in objective things which originates from the existence of differences between objective things and intermediary transition.Based on fuzzy congruence relations,this paper gives the concepts of similar relations,fuzzy fusion,binary relations,and fuzzy subgroups under fuzzy congruence relations,discusses a series of properties of fuzzy congruence,and obtains several meaningful conclusions similar to the basic theorem of group theory.

关 键 词：模糊关系 代数 模糊同余 模糊群 

分 类 号：G64[文化科学—高等教育学]