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

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.