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山东大学学报 (工学版) ›› 2026, Vol. 56 ›› Issue (5): 13-25.doi: 10.6040/j.issn.1672-3961.0.2025.126

• 机器学习与数据挖掘 • 上一篇    

三论域粗糙集模型

翁世洲1,2,吕跃进3,黄正伟1*   

  1. 1. 三峡大学经济与管理学院, 湖北 宜昌 443002;2. 广西民族师范学院管理学院, 广西 崇左 532200;3. 广西大学数学学院, 广西 南宁 530004
  • 发布日期:2026-10-19
  • 作者简介:翁世洲(1988— ),男,湖北宜昌人,副教授,硕士生导师,博士,主要研究方向为不确定决策集理论与方法. E-mail:wengshizhou1104@163.com. *通信作者简介:黄正伟(1972— ),男,湖北大冶人,教授,博士生导师,博士,主要研究方向为决策理论与方法、智能客服、物流与供应链管理. E-mail:Zhengweihuang@ctgu.edu.cn
  • 基金资助:
    广西高校中青年教师科研基础能力提升资助项目(2025KY0931)

Roughset models over three universes

Weng Shizhou1,2, Lü Yuejin3, Huang Zhengwei1*   

  1. Weng Shizhou1, 2, Lü Yuejin3, Huang Zhengwei1*(1. College of Economics and Management, China Three Gorges University, Yichang 443002, Hubei, China;
    2. College of Management, Guangxi Minzu Normal University, Chongzuo 532200, Guangxi, China;
    3. School of Mathematics, Guangxi University, Nanning 530004, Guangxi, China
  • Published:2026-10-19

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摘要： 经典粗糙集理论在处理日益复杂的不确定性决策问题时存在不足。为更好处理不确定性信息、服务知识获取与决策分析,基于单、双论域粗糙集理论,拓展至三论域,提出三论域粗糙集模型。定义元素的前继、后继邻域及集合的共有邻域和可能邻域等概念,并在此基础上定义下近似、上近似、近似精度和粗糙度等概念;归纳总结上述概念满足的相关性质定理并严格推导,辅以算例验证。为粗糙集理论完善提供新思路。

关键词: 三论域, 粗糙集, 邻域, 下近似, 上近似, 近似精度

Abstract: The classical rough set theory faces limitations when dealing with increasingly complex uncertainty decision-making problems. To better handle uncertain information, serve knowledge acquisition, and decision analysis, the rough set theory based on single and dual universes was extended to a triple universe, proposing a triple-universe rough set model. Concepts such as predecessor, successor neighborhood of elements were defined, as well as common neighborhood, and possible neighborhood of sets. Based on this, concepts such as lower approximation, upper approximation, approximation accuracy, and roughness were defined. The relevant properties and theorems satisfied by these concepts were summarized and rigorously derived, supplemented by numerical examples for verification. This provides new insights for the improvement of rough set theory.

Key words: three universes, rough set, neighborhood, lower approximation, upper approximation, approximate accuracy

中图分类号: 

  • TP301
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