非交换剩余格上的广义区间值模糊滤子  

Generalized interval valued fuzzy filter on non-commutative residual lattice

作　　者：蔡德印 左卫兵 CAI Deyin;ZUO Weibing(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：《湖北大学学报(自然科学版)》2025年第2期180-191,共12页Journal of Hubei University:Natural Science

基　　金：河南省自然科学基金(152300410112)资助。

摘　　要：在区间值模糊集理论的基础上,结合属于和广义拟一致的概念定义非交换剩余格上的点态化的(∈,∈∨q(α,β])-区间值模糊滤子,研究其相关性质,由其引出非交换剩余格上的具有阈值的(α,β]-区间值模糊滤子的概念,得到(α,β]-区间值模糊滤子的一些性质和若干等价刻画。定义由区间值模糊集生成的(α,β]-区间值模糊滤子并建立其表示定理,证明全体(α,β]-区间值模糊滤子之集是一个完备格,在其上引入一个格同余,得到全体(α,β]-区间值模糊滤子之集的商代数的分配性。On the basis of interval value fuzzy set theory,combined with the concept of belonging and generalized quasi-coincidence,we defined the point-stateized(∈,∈∨q(α,β])-interval valued fuzzy filter on the non-commutative residual lattice,and investigated some of their related properties,and derived the concept of(α,β]-interval valued fuzzy filter with threshold on the non-commutative residual lattice,and obtained some properties and some equivalent descriptions of(α,β]-interval valued fuzzy filter.The(α,β]-interval valued fuzzy filter generated by the interval valued fuzzy set was defined and its representation theorem was established,which proved that the set of all(α,β]-interval valued fuzzy filters was a complete lattice,and a lattice congruence was introduced on it to obtain the distribution of the quotient algebra of the set of all(α,β]-interval valued fuzzy filters.

关 键 词：非交换剩余格 (∈ ∈∨q(α β])-区间值模糊滤子 (α β]-区间值模糊滤子 完备格 分配格 

分 类 号：O141.1[理学—数学] O159[理学—基础数学]