模糊知识结构的一些性质  

Some properties of the fuzzy knowledge structures

作　　者：张纪平[1,4] 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)

机构地区：[1]泉州师范学院数学与计算机科学学院,福建泉州362000 [2]浙江海洋大学信息工程学院,浙江舟山316022 [3]闽南师范大学数学与统计学院,福建漳州363000 [4]福建省大数据管理新技术与知识工程重点实验室(泉州师范学院),福建泉州362000

出　　处：《山东大学学报(理学版)》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)。

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.

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 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]