基于主成分分析的模糊概念格
Fuzzy Concept Lattice Based on Principal Component Analysis
摘要: 形式背景中数据的增多，概念的数量就会随之增加。根据数据本身的特点，本文借助统计学方法提出基于主成分分析的模糊概念格以处理数据的多样性和复杂性。通过一般模糊形式背景的矩阵转化，分别定义了主成分属性和主成分模糊形式背景，并且给出了主成分属性算法，得到主成分属性模糊形式背景。利用该方法可以获得对原始形式背景的概念格属性约简，并且通过实例分析说明了该方法的可行性。
Abstract: The increase of data in formal context, the number of concepts will increase accordingly. Based on the characteristics of the data itself, this article proposes a fuzzy concept lattice based on principal component analysis using statistical methods to handle the diversity and complexity of data. Pass through matrix transformation through general fuzzy form background, defined principal compo-nent attributes and principal component fuzzy formal backgrounds respectively, and the principal component attribute algorithm is provided, obtain the fuzzy formal background of principal com-ponent attributes. By using this method, the concept lattice attribute reduction of the original for-mal background can be obtained, and the feasibility of this method was demonstrated through ex-ample analysis.
文章引用：张露迪. 基于主成分分析的模糊概念格[J]. 应用数学进展, 2023, 12(12): 4938-4945. https://doi.org/10.12677/AAM.2023.1212486

参考文献

[1] Wille, R. (1982) Restructuring Lattice Theory: Anapproach Based on Hierarchies of Concepts. In: Rival, I., ed., Ordered Sets, Springer, Berlin, Germany, 445-470. [Google Scholar] [CrossRef] 
[2] 赵晓倩, 武优西, 王月华, 李艳. 一种保序序列快速挖掘算法: RSMM [J]. 郑州大学学报(理学版), 2022, 54(4): 64-70.
[3] 张文修, 魏玲, 祁建军. 概念格的属性约简理论与方法[J]. 中国科学E辑: 信息科学, 2005, 35(6): 628-639.
[4] 李进金, 张燕兰, 吴伟志, 等. 形式背景与协调决策形式背景属性约简与概念格生成[J]. 计算机学报, 2014, 37(8): 1768-1772.
[5] 王霞, 彭致华, 李俊余, 吴伟志. 一种基于概念可辨识矩阵的概念约简方法[J]. 计算机科学, 2021, 48(1): 125-130.
[6] Burusco, R. and Fuentes-González, R. (2000) Concept Lattices Defined from Implication Operators. Fuzzy Sets and Systems, 114, 431-436. [Google Scholar] [CrossRef] 
[7] 张静, 马建敏. 基于依赖空间的F-C变精度概念格[J]. 山东大学学报(理学版), 2021, 56(1): 68-74.
[8] 张贤达. 矩阵分析与应用[M]. 北京: 清华大学出版社, 2013.
[9] 梁胜杰, 张志华, 崔立林, 钟强晖. 基于主成分分析与核独立成分分析的降维方法[J]. 系统工程与电子技术, 2011, 33(9): 2144-2148．
[10] Shao, M.W., Leung, Y., Wang, X.Z., et al. (2016) Granular Reducts of Formal Fuzzy Contexts. Knowledge-Based Systems, 114, 156-166. [Google Scholar] [CrossRef] 
[11] Ganter, B. and Wille, R. (1999) Formal Concept Analysis: Mathematical Foundations. Springer Berlin, Heidelberg. [Google Scholar] [CrossRef] 
[12] 袁志发, 宋世德. 多元统计分析[M]. 第二版. 北京: 科学出版社, 2009.

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