Variable-precision three-way concepts in L-contexts

Abstract

The notion of fuzzy concept is proposed to deal with object-attribute data with L-values (where L is a truth-value structure). One disadvantage of fuzzy concept is that a fuzzy context contains a considerable number of fuzzy concepts. This makes it very time-consuming to generate a fuzzy concept lattice, and it is very difficult to find important concepts. In addition, the fuzzy concept shows great strictness when applying to crisp sets. To overcome these problems, we propose several new kinds of variable-precision concepts within L-contexts in this paper. First, we present two kinds of variable-precision two-way (VP2W) concepts: α-positive concept and β-negative concept. The family of each kind of VP2W concept forms a complete lattice. Next, considering both the positive and negative parts, we investigate two kinds of variable-precision three-way (VP3W) concepts: (α,β)-object-induced three-way concept and (α,β)-attribute-induced three-way concept. The family of each kind of VP3W concept forms a complete lattice. Then, we study the relationships between VP2W concepts and VP3W concepts. The results show that VP3W concept lattices can be directly generated by VP2W concept lattices. Finally, the experiments are preformed to verify the effectiveness of our model.