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.
作者
乔希民
谢小军
罗俊丽
李粉红
吴洪博
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)
出处
《模糊系统与数学》
北大核心
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)。
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
Interval Sets
Interval Sets non-commutative Residual Lattice
Generalized Fuzzy Filter
〈∈,∈凵Q〉-generalized Fuzzy Implication Filter
Constructiveness
作者简介
乔希民(1960-),男,陕西洛南人,教授,研究方向:非经典数理逻辑与格上拓扑学,模糊粗糙集代数分析;谢小军(1990-),男,湖南未阳人,讲师,研究方向:决策分析与预测,智能算法。
