Attribute Reductions of Fuzzy-Crisp Concept Lattices Based on Matrix
LIN Yidong 1,2, LI Jinjin1, ZHANG Chengling1
1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000; 2. School of Mathematical Sciences, Xiamen University, Xiamen 361005
Abstract：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.
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2020, Vol. 33 
