非交换剩余格上的区间值模糊滤子  

Interval Valued Fuzzy Filter on Non-commutative Residual Lattice

作　　者：蔡德印 左卫兵 CAI De-yin;ZUO Wei-bing(College of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《兰州文理学院学报（自然科学版）》2024年第2期1-7,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：河南省自然科学基金(152300410112)。

摘　　要：在区间值模糊集理论的基础上,定义了非交换剩余格上的区间值模糊滤子,给出了区间值模糊滤子的刻画,研究了生成区间值模糊滤子的结构;证明了非交换剩余格上的区间值模糊滤子全体、区间值模糊正规滤子全体构成完备有界分配格;基于区间值模糊强同余关系,证明了非交换剩余格上的区间值模糊正规滤子集和区间值模糊强同余关系集同构.On the basis of interval value fuzzy set theory,the interval valued fuzzy filter on the non-commutative residual lattice is defined,the description of the interval value fuzzy filter is given,and the structure of the generating interval valued fuzzy filter is studied.It is proved that the set of intervals valued fuzzy filter and the set of interval valued fuzzy normal filter on the noncommutative residual lattice constitutes a complete bounded distribution lattice.Based on the interval valued fuzzy strong congruence relation,it is proved that the interval valued fuzzy normal filter all and the interval valued fuzzy strong congruence relations all are isomorphisms on the non-commutative residual lattice.

关 键 词：非交换剩余格 区间值模糊滤子 生成区间值模糊滤子 区间值模糊强同余关系 

分 类 号：O141.1[理学—数学] O159[理学—基础数学]