Double threshold construction method for attribute-induced three-way concept lattice in incomplete fuzzy formal context

Concept lattice theory is the basis of formal concept analysis. It is an effective tool for knowledge representation and discovery. Three-way decision theory is a new decision theory based on rough sets and decision rough sets. In this study, a method is proposed for constructing attribute-induced three-way concept lattices in an incomplete fuzzy formal context. First, the authors introduce the related knowledge of the classical formal context, the fuzzy formal context and incomplete fuzzy formal context in detail. They put forward a method to fill the incomplete formal context. Secondly, they propose a double threshold operation, which divides the relationship between objects and attributes into three parts: belonging, not belonging and undetermined. Thirdly, they propose three methods to complement incomplete formal context and introduce their advantages and disadvantages. Fourthly, they deal with incomplete formal context by special symbol completion method and get related algorithms of attribute-induced three-way concept lattice. Finally, a case is given to verify the effectiveness of the algorithm for constructing attribute-induced three-way concept lattices.