基于矩阵的模糊-经典概念格属性约简  

Attribute Reductions of Fuzzy-Crisp Concept Lattices Based on Matrix

作　　者：林艺东 李进金 张呈玲 LIN Yidong;LI Jinjin;ZHANG Chengling(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000;School of Mathematical Sciences,Xiamen University,Xiamen 361005)

机构地区：[1]闽南师范大学数学与统计学院,漳州363000 [2]厦门大学数学科学学院,厦门361005

出　　处：《模式识别与人工智能》2020年第1期21-31,共11页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.11871259,11701258,61379021,61603173);福建省自然科学基金项目(No.2019J01748)资助~~

摘　　要：基于模糊形式背景,文中研究模糊-经典概念的矩阵表示及属性约简的矩阵方法.首先,从矩阵视角提出模糊-经典概念的外延和内涵的矩阵表示,进一步给出属性粒矩阵的概念.为了得到模糊-经典概念格的最小生成组,研究交不可约元的矩阵判定定理.再在保持交不可约元外延不变的约简框架下,通过矩阵刻画属性子集之间的相似性,给出属性内外重要性的度量,提出模糊-经典概念格属性约简的矩阵方法.最后,通过数值实验验证文中方法的有效性.A matrix representation of fuzzy-crisp formal concepts based on fuzzy formal contexts and a matrix approach of attribute reduction are studied.Firstly,the matrix representations of the extension and intension of fuzzy-crisp concept are developed from the matrix perspective,respectively.The definition and the computing method of attribute granular matrix are formulated subsequently.To find the minimal generation group of fuzzy-crisp concept lattice,matrix judgment theorem of meet-irreducible elements is discussed,and it is utilized to construct the attribute reduction framework preserving the extents of meet-irreducible elements.The significance measure of attribute is proposed by introducing the similarity degree between attribute subsets with aforementioned matrices.And then a heuristic matrix-method of attribute reduction is developed.Finally,numerical experiments verify the effectiveness of the proposed approach.

关 键 词：属性约简 模糊-经典概念 矩阵表示 交不可约元 

分 类 号：O29[理学—应用数学] TP18[理学—数学]