基于剩余格的模糊粗糙集的拓扑性质  

Topological Properties of Fuzzy Rough Sets Based on Residuated Lattices

作　　者：许思雨 秦克云[1] XU Si-yu;QIN Ke-yun(College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《计算机科学》2022年第S01期140-143,183,共5页Computer Science

基　　金：国家自然科学基金(61976130)。

摘　　要：研究了基于剩余格的L-模糊粗糙集模型的拓扑结构,给出了由模糊蕴涵确定的下近似算子诱导的L-模糊拓扑并讨论了它的基本性质。其中的知识为一般L-模糊关系,无需假设其自反性及强串行性。借助L-模糊关系的传递闭包构造了相应的L-模糊拓扑的内部算子及闭包算子。研究了不同的L-模糊关系确定的下近似算子诱导的L-模糊拓扑空间之间的关系,并借助相应的拓扑提出了一种L-模糊关系分类方法。This paper is devoted to the study of the topological structure of L-fuzzy rough sets based on residuated lattices.The L-fuzzy topologies induced by the lower approximation operators determined by fuzzy implication operators are presented and its basic properties being discussed.The knowledge of the L-fuzzy approximation space is a general L-fuzzy relation,and there is no need to assume its reflexivity and strong seriality.Based on the transitive closures of the L-fuzzy relations,the interior operators and closure operators of the corresponding L-fuzzy topologies are constructed.The relationships among L-fuzzy topologies induced by lower approximation operators corresponding to different L-fuzzy relations are investigated,and a classification method for L-fuzzy relations is presented by using related topologies.

关 键 词：剩余格 模糊粗糙集 模糊拓扑 模糊关系 近似算子 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]