Relationships between three-way concepts and classical concepts

In this paper, we firstly present some properties of classical concepts (i.e., formal concepts induced by positive operators and negative operators) and three-way concepts, respectively. Based on this, we systematically study the relationships between two types of three-way concepts (i.e., object-induced three-way concepts and attribute-induced three-way concepts) and classical concepts. More specifically, we can obtain all object-induced (attribute-induced) three-way concepts based on four relationships between all classical concepts and object-induced (attribute-induced) three-way concepts, where the four relationships are characterized by four theorems. After that, two algorithms are proposed to build an object-induced concept lattice and an attribute-induced concept lattice, respectively, and examples are given to verify these algorithms.