On the use of cut set for attribute reduction in L-fuzzy concept lattice

Concept lattice is an effective tool for knowledge discovery and has been applied to many fields successfully. The objects and attributes have clear relations in the classical formal context, but there are a lot of fuzzy information in real-life applications. Therefore, it is important to study the fuzzy formal context. As we know, the fuzzy set and the classical set can be transformed into each other based on the cut set. Thus, it is believed that the cut set can be used in the research of fuzzy concept lattice. In this paper, a preliminary exploration to use the cut set is carried out. In particular, the cut set is employed to construct the discernibility matrix of L-fuzzy formal context and then all the reducts can be obtained via the use of discernibility function. After that, all the attributes are classified into three types by their significances in constructing the L-fuzzy concept lattice. The characteristics of these types of attributes are also analyzed. The obtained results in this paper are beneficial for the research of fuzzy formal context based on the cut set in further.