区间集非交换剩余格〈∈,∈凵Q〉-广义Fuzzy蕴涵滤子的构造性刻画  

Constructive Characterization of Interval Sets Non-commutative Residual Lattice〈∈,∈凵Q〉-generalized Fuzzy Implication Filter

作　　者：乔希民 谢小军 罗俊丽 李粉红 吴洪博[3] QIAO Xi-min;XIE Xiao-jun;LUO Jun-li;LI Fen-hong;WU Hong-bo(Department of Basic Education,Guangzhou College of Technology and Business,Foshan 510850.China;School of Mathematics and Computer Application,Shangluo College,Shangluo 726000,China;College of Mathematics and Statistics.Shaanxi Normal University,Xi'an 710062.China)

机构地区：[1]广州工商学院通识教育学院,广东佛山510850 [2]商洛学院数学与计算机应用学院,陕西商洛726000 [3]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2022年第5期40-46,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61572016);陕西省自然科学基础研究计划项目(2013JM1023);广州工商学院科研课题(KAZX2021011)。

摘　　要：借鉴反映不确定性推理本质特征的滤子理论和用模糊粗糙集上、下近似集表述的区间集思想,引入了区间集非交换剩余格的概念,讨论构成区间集非交换剩余格的代数结构特征,构造性地给出了广义Fuzzy蕴涵滤子与其相应的〈∈,∈凵Q〉-广义Fuzzy蕴涵滤子间的等价性表示定理,体现了性质迥异的区间集非交换剩余格代数表示形式的内在相容性。The concept of non-commutative residual lattices of interval sets is introduced based on the filter theory which reflects the essential features of uncertainty reasoning and the idea of interval sets expressed by upper and lower approximate sets of fuzzy rough sets,this paper discusses the algebraic structural features of non-commutative residual lattices of interval sets,and gives the equivalent representation theorem between generalized Fuzzy implication filters and its corresponding〈∈,∈凵Q〉generalized Fuzzy implication filters,it shows the internal compatibility of the representations of interval sets non-commutative residual lattices algebras with different properties.

关 键 词：区间集非交换剩余格 广义Fuzzy滤子 〈∈ ∈凵Q〉-广义Fuzzy蕴涵滤子 构造性 

分 类 号：O159[理学—数学]