摘要
基于模糊粗糙近似算子,提出上、下近似模糊知识状态的概念,讨论上、下近似模糊知识状态集族的表示法,获得上、下近似模糊知识状态集族形成模糊知识结构的充要条件。下近似模糊知识状态集族是模糊闭包空间的充要条件,上近似模糊知识状态集族是模糊知识空间的充要条件,证明同一对模糊粗糙近似算子诱导的模糊闭包空间与模糊知识空间是对偶的,探讨上、下近似模糊知识结构细关系。
Based on the fuzzy rough approximate operator,the concept of upper and lower approximate fuzzy knowledge states is proposed.A notation of upper and lower approximate fuzzy knowledge states is discussed.A necessary and sufficient conditions for upper and lower approximate fuzzy knowledge states family to form the fuzzy knowledge structure is obtained respectively.The lower approximate fuzzy knowledge state set family is a necessary and sufficient condition for the fuzzy closure space,and the upper approximate fuzzy knowledge state set family is a necessary and sufficient condition for the fuzzy knowledge space.It is also proven that the fuzzy closure space induced by the same pair of fuzzy rough approximation operators is dual to the fuzzy knowledge space,and the fine relationship of the upper and lower approximate fuzzy knowledge structures is explored.
作者
张纪平
吴伟志
周缪娟
李进金
ZHANG Jiping;WU Weizhi;ZHOU Miaojuan;LI Jinjin(School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou 362000,Fujian,China;School of Information Engineering,Zhejiang Ocean University,Zhoushan 316022,Zhejiang,China;School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,Fujian,China;Key Laboratory of New Technologies and Knowledge Engineering for Big Data Management in Fujian Province,Quanzhou Normal University,Quanzhou 362000,Fujian,China)
出处
《山东大学学报(理学版)》
北大核心
2025年第1期91-100,共10页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(12371466,12271191,11871259)
福建省自然科学基金资助项目(2023J01122,2023J01125,2023J05175,2022J01306,2022J05169)。
关键词
模糊粗糙近似算子
模糊知识结构
模糊闭包空间
模糊知识空间
细关系
fuzzy rough approximation operator
fuzzy knowledge structures
fuzzy closure space
fuzzy knowledge space
fine relation
作者简介
第一作者:张纪平(1971-),男,副教授,硕士,研究方向为基础数学、模糊集理论及其应用等.E-mail:zhangmat@qq.com;通信作者:吴伟志(1964-),教授,博士生导师,博士,研究方向为粗糙集与概念格、知识空间理论、近似推理等研究.E-mail:wuwz@zjou.edu.cn。
