Attribute reduction in fuzzy decision formal contexts

The classical concept lattices express the precise relation between object sets and attribute sets, but fuzzy concept lattices express the uncertain relation between object sets and attribute sets. Therefore, it is important to study hierarchy fuzzy knowledge from a fuzzy formal context. In this paper, a kind of fuzzy decision formal context is proposed and (α, β) reduct based on this fuzzy decision formal context is defined. Furthermore, we propose a method to judge attribute consistent sets and reducts in fuzzy decision formal contexts. Finally, a Boolean method is also formulated to attribute reduction in fuzzy decision formal context from the view of the discernibility matrix.