Affiliations: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, P.R. China
Correspondence:
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Corresponding author. Hai-Long Yang, College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, P.R. China. E-mail: [email protected].
Abstract: Formal concept analysis (FCA) is a mathematical framework for data analysis and knowledge discovery. The main issue of knowledge discovery is knowledge reduction. In the process of constructing concept lattices, computational complexity is a key obstacle in obtaining all the concepts from a given formal context. It is necessary to handle the given formal context and decrease its size as far as possible. In this paper, we investigate object granular reduction of fuzzy formal contexts in the sense of reducing the non-essential objects without changing the structure of the initial concept lattice. Based on fuzzy formal contexts, the notions of fuzzy-crisp concepts, fuzzy-crisp concept lattices and derivation operators are introduced. The properties of meet-irreducible elements in a fuzzy formal context and its sub-context are systematically discussed. Furthermore, the notions of object granular consistent sets and object granular reduction are presented using granules, and a certain algorithm of object granular reduction by using discernibility object sets, object discernibility matrices and object discernibility functions is given. Finally, we introduce classification object reduction and discuss the relations between object granular reduction and classification object reduction.
