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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报

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基于粗糙近似的经典–模糊概念格属性约简

李同军1,2,   吴明瑞1,   吴伟志1,2   

  1. 1. 浙江海洋大学信息工程学院，舟山 316022

    2. 浙江海洋大学浙江省海洋大数据挖掘与应用重点实验室，舟山 316022
  • 收稿日期:2022-11-24 接受日期:2023-03-20 出版日期:2025-10-15 发布日期:2025-10-15
  • 基金资助:
    国家自然科学基金 (61773349; 61976194).

Attribute Reduction of Crisp-fuzzy Concept Lattices Based on Rough Approximation Operations

LI Tongjun1,2,   WU Mingrui1,   WU Weizhi1,2   

  1. 1. School of Information and Engineering, Zhejiang Ocean University, Zhoushan 316022

    2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022
  • Received:2022-11-24 Accepted:2023-03-20 Online:2025-10-15 Published:2025-10-15
  • Supported by:
    The National Natural Science Foundation of China (61773349; 61976194).

摘要：

形式概念分析和粗糙集理论是两种有效的数据分析方法，两者相互融合。将模糊粗糙集引入模糊形式概念分析中，基于广义模糊粗糙近似提出模糊形式背景上的一种经典–模糊概念格模型，研究对应概念格的属性约简问题，主要包括：定义保持格结构不变的属性约简，给出协调集的判定定理、属性的特征刻画，以及基于辨识矩阵的约简计算方法。

关键词: 经典–模糊概念, 属性约简, 模糊形式背景, 辨识矩阵

Abstract:

Formal concept analysis and rough set theory are two effective data analysis methods, which merge with each other. Through introducing fuzzy rough sets into fuzzy formal concept analysis, based on generalized fuzzy rough approximations, a crisp-fuzzy concept lattice is proposed. Subsequently, the attribute reduction of the corresponding concept lattice is studied. The study involves the definition of attribute reduction to keep the lattice structure of the concept lattice unchanged, the judgement of consistent attribute sets, the feature characterization of different types of attributes, and a method of reduction computation based on discernibility matrix.

Key words: crisp-fuzzy concepts, attribute reduction, fuzzy formal contexts, discernibility matrix

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