Granular matrix-based knowledge reductions of formal fuzzy contexts

Knowledge reduction is an important issue in formal fuzzy contexts, which can simplify the structure of concept lattices. In this paper, a novel granular matrix-based for knowledge reduction of crisp-fuzzy concept is investigated. Firstly, matrix representations of extents and intents of concepts are defined, respectively, which are used to characterize the join-irreducible elements and propose the corresponding algorithm. In this framework, granular consistent set and granular reduct are developed. Then the judgement theorem of reduction and its corresponding algorithm in formal fuzzy context are proposed. Furthermore, we generalize the matrix approach to formal fuzzy decision contexts. Finally, numerical experiments are conducted to evaluate the effectiveness of the proposed approaches. Our methods present a new framework for knowledge reduction in formal fuzzy contexts.