基于模糊同余关系的模糊粗糙环及其应用  

Fuzzy Rough Ring Based on Fuzzy Congruence Relation and Its Application

作　　者：范爱琴 FAN Aiqin(School of Mathematics and Computer Science,Yuncheng Advanced Normal College,Yuncheng 044000,China)

机构地区：[1]运城师范高等专科学校数学与计算机系,山西运城044000

出　　处：《新乡学院学报》2020年第3期6-8,共3页Journal of Xinxiang University

摘　　要：基于环上的模糊理想给出模糊完备同余关系,以此为基础定义了模糊子集的粗糙上、下近似算子,给出了模糊粗糙近似算子的运算性质,研究了环的模糊粗糙子环与模糊粗糙理想。利用模糊理想在普通环上建立了模糊完备同余关系,得到了一个模糊粗糙集模型。利用由该模糊粗糙集的运算性质所得的结论导出了判断模糊粗糙子环的条件。The fuzzy complete congruence relations are given based on fuzzy ideals over rings.The rough upper and lower approximation operators of fuzzy subsets are defined on this basis.The operation properties of fuzzy rough approximation operators are given.The fuzzy rough subrings and fuzzy rough ideals of the ring are studied.The fuzzy complete congruence relation is established on ordinary rings by using fuzzy ideals,and a fuzzy rough set model is obtained.Based on the results obtained from the operation properties of the fuzzy rough set,the conditions for judging the fuzzy rough subring are derived.

关 键 词：模糊同余关系 上近似 下近似 模糊粗糙子环 模糊粗糙理想 

分 类 号：O159[理学—数学]