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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (1): 91-100.doi: 10.6040/j.issn.1671-9352.4.2024.013

• • 上一篇    

模糊知识结构的一些性质

张纪平1,4,吴伟志2*,周缪娟3,李进金1,3   

  1. 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
  • 发布日期:2025-01-10
  • 通讯作者: 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
  • 作者简介: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
  • 基金资助:
    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)

Some properties of the fuzzy knowledge structures

ZHANG Jiping1,4, WU Weizhi2*, ZHOU Miaojuan3, LI Jinjin1,3   

  1. 1. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, Fujian, China;
    2. School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China;
    3. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China;
    4. Key Laboratory of New Technologies and Knowledge Engineering for Big Data Management in Fujian Province, Quanzhou Normal University, Quanzhou 362000, Fujian, China
  • Published:2025-01-10

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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。

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

Abstract: 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.

Key words: fuzzy rough approximation operator, fuzzy knowledge structures, fuzzy closure space, fuzzy knowledge space, fine relation

中图分类号: 

  • TP182
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